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Laboratory Manual

PY-120 Physics I

Wayne Warrick

Passaic County Community College

Laboratory Manual

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Introduction

As part of the Passaic County Community College physics course sequence, the laboratory is a required

and integral component to all offered physics courses within the Biological and Physical Sciences

Department. This manual will act as a comprehensive reference guide for students to follow during each

laboratory experiment. The following pages will detail the laboratory grading criteria, expected report

format, laboratory safety and etiquette protocol, and detailed instructions for each experiment. Each

laboratory section of this manual includes the necessary theoretical background, pertaining to physics,

in order for students to perform each experiment.

The laboratory aspect of physics, as with any physical or life science course, represents a

necessary part to gather not only an adequate understanding of physics but to obtain a solid foundation

which will benefit students of all STEM majors. This is why it is highly recommended to read through

this manual, ahead of time, so that you are prepared to not only follow along in the lab, but to actively

engage with each of your colleagues and understand each experiment. Additional references, links, and

helpful websites are listed within each experiment section.

Laboratory Manual Authored by: Wayne Warrick

May 22nd, 2019

Rev: August 27th, 2019, January 7th, 2020, June 2020, August 2020

Table of Contents

Laboratory Requirements___________________________________________________________ 1

Lab Report Grading Criteria________________________________________________________ 2

Sample Laboratory Report__________________________________________________________ 3

Laboratory 1: Data Acquisition and Data Analysis________________________________________ 4

Laboratory 1: Prelab________________________________________________________________ 9

Laboratory 2: Free-Fall_____________________________________________________________12

Laboratory 2: Prelab_______________________________________________________________ 13

Laboratory 3: Projectile Motion______________________________________________________15

Laboratory 3: Prelab_______________________________________________________________17

Laboratory 4: NewtonÃ¢â‚¬â„¢s Second Law of Motion_________________________________________ 20

Laboratory 4: Prelab_______________________________________________________________21

Laboratory 5: Friction Analysis ______________________________________________________24

Laboratory 5: Prelab_______________________________________________________________ 27

Laboratory 6: The Conservation of Mechanical Energy____________________________________ 29

Laboratory 6: Prelab_______________________________________________________________ 30

Laboratory 7: The Conservation of Linear Momentum____________________________________ 32

Laboratory 7: Prelab_______________________________________________________________ 33

Laboratory 8: The Ballistic Pendulum_________________________________________________ 36

Laboratory 8: Prelab_______________________________________________________________ 37

Laboratory 9: Uniform Circular Motion________________________________________________ 39

Laboratory 9: Prelab_______________________________________________________________ 40

Laboratory 10: Rotational Dynamics__________________________________________________ 43

Laboratory 10: Prelab______________________________________________________________45

Laboratory 11: Conservation of Angular Momentum _____________________________________47

Laboratory 12: Fluid Dynamics and Heat Exchange_______________________________________49

References ______________________________________________________________________ 50

Laboratory Requirements

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

The laboratory portion of the course counts towards 25% of the final course grade. In total, throughout

the semester, there will be twelve (12) laboratory experiments. Each lab report will be graded out of a

total of 10 (ten) points. Unless otherwise stated, each experiment will require a written report. The

required format of this report is detailed in the Sample Lab Report section of this manual. The laboratory

assessment for each report is divided into the following categories: Prelab, Participation, Experimental

Data Collection, and the submitted Lab Report. Each of these categories and grading criteria is explained

below.

1) Prelab

The prelab is intended to prepare students for the laboratory experiment. Before handling sensitive

apparatus, complicated equipment, computer-controlled data collection, or virtual lab simulations, etc.,

it is necessary to have an adequate understanding of the experimental requirements prior to beginning

the lab. The prelab will test your knowledge and comprehension of the necessary theory of physics

required to perform the experiment as well as a training preview to demonstrate each studentÃ¢â‚¬â„¢s level of

preparedness for the experiment. The prelab questions do not have to be submitted, rather these questions

will be asked by the instructor at the beginning of each lab session. Students who do not successfully

answer the prelab questions are not permitted to perform the experiment for that week. The prelab for

each experiment can be found in the lab manual.

Read Ahead! It is imperative to read the lab manual prior to performing each experiment.

2) Participation

Laboratory attendance is mandatory. For the beginning of each lab session students are required to

participate, e.g. answer questions posed by the instructor. The experiments are to be performed

individually by each student on their own time. Additional details regarding the attendance portion of

the lab can be found on the course syllabus.

Lab Safety

The instructor will discuss the safety aspects of each experiment at the beginning of the laboratory as if

the experiments were conducted in a non-virtual environment.

3) Experimental Data

During each lab experiment, students will collect data, often a lot of data. Sometimes this is manual data,

read from protractors, meter sticks, and scales, other times it is data from electronic instrumentation,

micro-controlled devices, or as in the case of this semester, virtual simulation data. Each student will be

graded on the quality and completeness of their collected data. It is recommended that each student

record their data from each experiment in a lab notebook.

4) Report

Each student will submit one lab report corresponding to each lab. The format for the report can be found

in the Sample Lab Report section of this lab manual.

1

Lab Report Grading Criteria

Each lab report is graded out of ten (10) points. The grading is based on the following criteria:

Ã¢â‚¬Â¢

Ã¢â‚¬Â¢

Ã¢â‚¬Â¢

Ã¢â‚¬Â¢

Ã¢â‚¬Â¢

Ã¢â‚¬Â¢

Ã¢â‚¬Â¢

Did the student include the abstract?

Does the abstract include a brief summary of the critical results, values and findings from the

experiment?

Does the lab report contain and present all of the required experimental data?

Does the lab report contain data analysis, calculations, tables, graphs with each axis labeled? Are

the correct units included? etc.

Does the lab report contain plagiarized content?

Were all of the questions answered correctly?

Was the lab report submitted by the due date? Refer to the syllabus.

Careful! If a lab report contains data, pictures, answers, etc. obtained from external sources, for

example, internet, other lab groups, etc., this will count as plagiarism, and the student

will receive a zero for that report.

Lab Report Submission

The lab reports must be typed up. This includes data, tables, answers to questions, etc. The graphs and

plots must be electronically created. The calculations may either be typed up or hand-written. The

completed lab reports must be submitted electronically as one file. The completed lab report is to be

submitted to Blackboard. Each report is due one week after the lab session experiment.

Lab Final Exam

There will be a lab final exam at the end of the semester, usually the last lab session. This exam will be

based on the laboratory experiments from the semester. The lab exam will be a cumulative assessment

based on prelab questions, virtual experiments, and the introductions as found in the lab manual. The lab

final exam will count towards 10% of the lab portion of the course. If a student fails the lab portion of

the course, the student will receive a failing grade for the course.

Please review the course syllabus for additional details regarding the lab portion of the course.

2

Sample Lab Report-Fall 2020 Only

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Lab #

Lab Title

Student First and Last name

Date of Experiment: mm/dd/year

InstructorÃ¢â‚¬â„¢s Name:

Abstract

An abstract is a brief overall summary of the experiment. The abstract should be written as though you

were explaining this to a colleague as a summary of the experiment. A reader should be able to grasp a

basic understanding of what happened during the experiment simply by reading the abstract. It is

preferred to use the active voice. This means that you write as though the event was recently performed

in the lab, not in the past. For example: instead of writing Ã¢â‚¬Å“we studied,Ã¢â‚¬Â you should write Ã¢â‚¬Å“in this

experiment we study the effects of…Ã¢â‚¬Â Here, you will also summarize the conclusions from the

experiment. The abstract only needs to be one paragraph. Include a brief summary of the critical

results, values and findings in the abstract.

Results and Analysis

In this section, you will present your experimental results. This is where you report your data, equations,

calculations, tables, graphs, etc. Be sure to show all pertinent calculations. Number the tables, graphs,

pictures, etc. Label each axis of a graph and include units. Do not copy material from the instructorÃ¢â‚¬â„¢s lab

manual.

Questions

In the lab report, include the complete answers to all questions in the lab manual pertaining to the specific

experiment.

Lab Report Submission

The lab reports must be typed up. This includes data, tables, answers to questions, etc. The graphs and

plots must be electronically created. The calculations may either be typed up or hand-written. The

completed lab reports must be submitted electronically as one file. The completed lab report is to be

submitted to Blackboard. Each report is due one week after the lab session experiment.

3

Laboratory 1

Data Acquisition and Data Analysis

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Introduction

The objective of this laboratory is to introduce students to data acquisition and data analysis techniques

used in physics. Students will collect and analyze data by performing a simple kinematic experiment.

By the end of the lab, students should be able to collect and analyze data, perform calculations involving

experimental error, uncertainty, standard deviation, and perform graphical analysis.

All measurements have some type of error. Measurement error is the difference between the

measured or observed value (quantity) and its Ã¢â‚¬Å“trueÃ¢â‚¬Â value. By Ã¢â‚¬Å“trueÃ¢â‚¬Â value, we mean a recognized

standard or agreed upon value. An error is not a Ã¢â‚¬Å“mistake,Ã¢â‚¬Â rather, it is an inherent part of a measurement

process. Accuracy of a measurement is how close the measured value is to the Ã¢â‚¬Å“trueÃ¢â‚¬Â value of the quantity

being measured. Therefore, errors reduce the accuracy of a measurement.

Let us imagine you are asked to measure the length of a small steel cylinder approximately 1 in

long. At first, you might decide to use a ruler. But, the ruler is not capable of very accurate or precise

measurements. Measurement errors may arise from imperfections in the Ã¢â‚¬Å“tickÃ¢â‚¬Â marks, human

observation, and instrumental errors, i.e. they depend on or are limited to the design of the instrument.

Random error is caused by unknown or unpredictable occurrences in an experiment, e.g.

electrical noise, vibrations, etc. When a measurement is repeated, the next value is unpredictable due to

fluctuations in readings of the apparatus or in your interpretation of the instrument. We cannot usually

control random errors.

The precision of a measurement is a measure of how reproducible experimental values are, i.e.

how close a number of measurements of the same quantity agrees with each other. The deviation of data

is called the range. The smaller the range, the more precise the result. The precision is also limited by

random errors and instrument limitations. This can usually be reduced by repeating the measurements.

From Figure 1, try to determine which target (bullÃ¢â‚¬â„¢s-eye) represents accuracy and precision.

Figure 1. BullÃ¢â‚¬â„¢s-eye target with black dots representing trials. Images: [1].

Regardless of the type of instrument you use to make a measurement, you need to either calibrate,

or verify the instrument is calibrated. If the instrument is not calibrated correctly, this could lead to

systematic error which results when the measured values are consistently inconsistent with the standard

values. They are usually predicable and constant. If you can identify the error, it might be possible to

eliminate it.

4

Zero error is when the instrument does not read zero when it should. Think of a bathroom scale

that is not correctly calibrated and reads 5 lb at the zero mark. Each measurement will be consistently

offset by +5 lb., For example, if your Ã¢â‚¬Å“trueÃ¢â‚¬Â weight is 135 lb., the offset scale will read 140 lb.

Compounded with this is the fact that while looking at the scale, your eyes will distort the reading,

due to what is called parallax error. This occurs when reading an analog scale viewed from the wrong

angle. For example, when you look down at your gas gauge in your car, the pointer looks like it is on the

E, but when you place your head back a little, and observe the gauge straight on, the pointer is slightly

above the E mark.

All measurements have some type of uncertainty. Experimental uncertainty is an estimate

(range) of how close the measured value is to the Ã¢â‚¬Å“trueÃ¢â‚¬Â value. There are different types of measurement

uncertainties. Precision limit uncertainty is introduced by an inaccuracy inherent in the system, either

by the observation or the measurement process. In the case of a ruler, it may be 0.5 mm, for example. If

you require high precision a Vernier caliper or micrometer should be used instead.

Random uncertainties, as the name suggests, are unpredictable during your experimental

situation. For example, there could be temperature variations, mechanical vibrations, or fluctuations in

the readings caused by the person making the readings.

Naturally, we want to take these experimental uncertainties and error(s) into account when we

calculate our final values. Reporting the measured value is not complete unless it is accompanied by an

associated uncertainty. It is necessary to represent the error(s) and uncertainties when reporting our data.

2. How to Report Experimental Uncertainty

Absolute Uncertainty is the probable difference between the experimental value (what

you measured) and other measurements.

Percent Uncertainty % unc. =

!”#$%&'( &*+(,’-.*’/

012(,.3(*’-% 4-%&(

Ãƒâ€” 100 %

3. How to Report Experimental Error

Absolute Error is the absolute difference between the measured (experimental) value

and the Ã¢â‚¬Å“trueÃ¢â‚¬Â value. The smaller the absolute error the greater the accuracy.

Percent Error is stated as, % Ã°ÂÂÂ¸Ã°Ââ€˜Å¸Ã°Ââ€˜Å¸Ã°Ââ€˜Å“Ã°Ââ€˜Å¸ =

Percent Difference =

!”#$%&'( (,,$,

=,&( 4-%&(

Ãƒâ€” 100 %

!”#$%&'( (,,$,

!4(,->( $? (12(,.3(*’-% -*@ ‘,&( 4-%&(#

Ãƒâ€” 100 %

4. Error Propagation

If there are many measurements, each with some uncertainty, the uncertainties from each measurement

propagate throughout the calculations. We need to consider the uncertainty of each measurement in order

to calculate the uncertainty of the final result.

5. Rules for Propagation of Uncertainties through Calculations

If we Add or Subtract measured values, we add the absolute uncertainties.

Example: 2.5 Ã‚Â± 0.05 cm and 5 Ã‚Â± 0.05 cm = 7.5 Ã‚Â± 0.1 cm.

5

Even when subtracting measured values, we still add the uncertainties. Even though we are subtracting,

the overall uncertainty increases (it is compounded).

Example: During a filtration experiment 4.22 Ã‚Â± 0.005g remains on the filter paper. The initial amount

was 5.23 Ã‚Â± 0.005g. How much quantity was sifted from the paper?

5.23 g Ã¢â‚¬â€œ 4.22 g = 1.01 Ã‚Â± 0.01 g

If we Multiply or Divide, the percent uncertainty for the final result is equal to the sum of the percent

uncertainties of the multiplied or divided value.

Example:

mass = 25.00 Ã‚Â± 0.5 g, volume = 10.0 Ã‚Â± 0.1cm3

Calculate the density and the percent uncertainty of the density.

Density = mass/volume = 25.00 g/10.0 cm3 = 2.50 g/cm3.

% unc. = (0.5/25.00) x 100 + (0.1/10.0) x 100 = 3.0%

The correct way to report the density is: 2.50 g/cm3 Ã‚Â± 3.0%

An alternative way to express this is: 2.50 Ã‚Â± 0.07 g/cm3

Example

You measure the following linear dimensions: L = 2.0 Ã‚Â±0.2 m, W = 3.5 Ã‚Â± 0.3 m, H = 4.0 Ã‚Â± 0.2 m

The volume is X Ãƒâ€” Y Ãƒâ€” Z = 2.0 Ãƒâ€” 3.5 Ãƒâ€” 4.0 = 28 m3.

The total percent uncertainty for volume is 23.6 % which can be rounded to 24%.

We can report the volume as:

28.0 m3 Ã‚Â± 24 %.

We can also report the volume as: 28.0 Ã‚Â± 6.7 m3.

6. How to Present Data in a Report

All measured values must be reported with their corresponding uncertainty. For example, you measured

the mass of an object to be 10.923 g, but you were only confident of this value to within a measurement

uncertainty of 0.2 g. In other words, the mass could be as high as 10.923 + 0.2 g or as low as 10.923 Ã¢â‚¬â€œ

0.2 g. Notice how the 9 is the Ã¢â‚¬Å“doubtfulÃ¢â‚¬Â figure. So, if the 9 is doubtful, then for certain, the numbers

that come after are even more uncertain, and can be ignored. The proper way to report this measurement

is to write: Mass = 10.9 Ã‚Â± 0.2 g. This means that with high probability, the mass is within the range 10.7

g to 11.1 g. As a rule, the least significant digit of a value should be of the same power of 10 as that of

the least significant digit of the uncertainty for that value.

Uncertainty and Significant Figures

Reported uncertainty should only have one or two significant figures. For the purposes of this course,

reporting one significant figure is adequate. The number of significant figures after the decimal of the

uncertainty must be equal to the number of significant figures after the decimal of the measured value.

Example

The speed of an object is measured to be: 0.33 m/s with an uncertainty of 0.05 m/s. Both the measured

value and the uncertainty have two significant figures after the decimal place. This should be reported

as: 0.33 Ã‚Â± 0.05 m/s.

If the uncertainty has fewer decimal places than our calculations, we round off the measured value to

match the number of decimal places as our uncertainty.

6

Example 4.45 Ã‚Â± 0.1 g should be stated as 4.5 Ã‚Â± 0.1 g.

Where to place units when reporting?

This is really a preference of the person collecting the data. A common format is:

2.50 g/cm3 Ã‚Â± 3.0% (the unit is placed after the measured value)

2.50 Ã‚Â± 0.07 g/cm3 (the unit is placed after the percent absolute uncertainty)

7. Standard Deviation

Standard deviation (SD) is a measure to quantify how much the data is spread out. Specifically, it tells

us how much the data varies from the mean. The figure below illustrates a histogram plot. A Ã¢â‚¬Å“best-fitÃ¢â‚¬Â

bell curve, which illustrates the range (spread) of the measurements, has been placed over the histogram.

The average value of the measured quantity is on the x-axis located at the center of the bell curve.

Consider studentÃ¢â‚¬â„¢s exam scores ranging from 0 to 100. Let the x-axis be segments of the score range

100-91, 90-81, etc. Let the y-axis be the frequency (height) of those scores. The number of students

receiving a grade between 91-100 would be the frequency for that grade range. The histogram would

have a bin width of 10 (i.e. all possible scores between 91 and 100). The greater the number of students

receiving a particular score, the taller the bar and closer to the center.

The width of the histogram is characterized by the SD which has the symbol s. 1Ã°ÂÅ“Å½ tells us that

68% of the data is centered around the mean. 2s indicates that 95% of the data is centered around the

mean. 3s indicates that 99.7% of the data is centered around the mean. A low SD tells us that the data is

close (clustered) around the mean. A high SD tells us that the data is spread out far from the mean.

Best-fit curve

Figure 2. Histogram plot of the data with a best-fit curve.

How to Calculate the Standard Deviation:

1) Calculate the mean of the data, which is called Ã°Ââ€˜â€¹D.

F

D E

2) The variance can be expressed as, Ã°ÂÅ“Å½ E = G Ã¢Ë†â€˜G

.LF(Ã°Ââ€˜â€¹ Ã¢Ë†â€™ Ã°Ââ€˜â€¹) . N is the number of measurements or

trials. X is an individual value.

F

D E

3) The SD is the square root of the variance and can be written as, Ã°ÂÅ“Å½ = MG Ã¢Ë†â€˜G

.LF(Ã°Ââ€˜â€¹ Ã¢Ë†â€™ Ã°Ââ€˜â€¹) .

7

Example

Five students in class have the following test scores: 70, 75, 80, 85, 90. The mean of the scores is 80.

Calculate the deviations of each data point (score) from the mean and square the result.

(70-80)2 = 100

(75-80)2 = 25

(80-80)2 = 0

(85-80)2 = 25

(90-80)2 = 100

We find the variance of the mean by adding these values and dividing by the number of scores. Ã°ÂÅ“Å½ E = 50.

The SD is the square root of the variance, s = Ã¢Ë†Å¡50 ~ 7. What this means is that the average test score of

80 Ã‚Â± 7 has a 68% chance of being found. 80 Ã‚Â± 2s (i.e. 80 Ã‚Â± 14) has a 95% of being found, etc.

8. Rules for Determining the Uncertainty of an Experimental Measurement

1) If only one measurement is made from a single instrument, then the uncertainty to report for that

measurement is the uncertainty for that particular instrument.

2) The uncertainty from a linear regression least squares fit is the standard deviation of the graph.

3) If multiple measurements are made from a single instrument, the uncertainty is the average of

individual measurements (the uncertainty of the average) which is found by using the equation,

Ã°ÂÅ“Å½/Ã¢Ë†Å¡Ã°Ââ€˜Â. N is the number of recordings.

8

Laboratory 1-Prelab

Data Acquisition and Data Analysis

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Question 1

Can a measurement be made without any error?

Question 2

What is measurement error?

Question 3

Explain the difference between accuracy and precision.

Question 4

Name two types of measurement uncertainties.

Question 5

Explain the difference between percent error and percent difference.

Question 6

The mass of a certain sample of material is 25.00 Ã‚Â± 0.5 g. Its volume is 10.0 Ã‚Â± 0.1cm3.

Calculate the density and the percent uncertainty of the density.

Question 7

Calculate the standard deviation and the uncertainty of the average of the following test scores: 70, 75,

80, 85, 90

9

Lab Procedure

Each student will collect and analyze data by performing a series of virtual kinematic experiments. By

the end of the lab, students should be able to collect and analyze data, perform calculations involving

experimental error, uncertainty, standard deviation, and perform graphical analysis.

Part 1

A lab experiment was performed in which a student pushed a wheeled-cart along a track on a work

bench. The distance the cart traveled and the time intervals were measured and recorded in Table 1.

Ã¢â‚¬Â¢

Ã¢â‚¬Â¢

A stop watch, with an uncertainty of 10.0 ms, was used to measure the time intervals.

A meter-stick, with an uncertainty of 0.5 mm, was used to measure the distance the car traveled.

Step 1) Using graphical analysis software, plot the distance the cart traveled as a function of time.

Step 2) Use a linear regression tool to plot the best-fit regression line from the data points.

Ã¢â‚¬Â¢

If you do not have access to Excel, Vernier Graph Analysis can be downloaded online for free.

Table 1

Time (s)

0

0.52

1.10

1.54

2.05

2.50

Distance (m)

0

0.25

0.44

0.67

0.83

0.98

Slope ___________

Standard Deviation of the Slope_____________

Part 2

Step 1) The bumper of the same cart is placed at the zero mark of the track.

Step 2) The cart is gently pushed forward and the total distance the cart travels and the total time is

recorded. The same meter-stick and stop watch from Part 1 are used.

Step 3) These steps were repeated four times for a total of five trials and recorded in Table 2.

Trial #

1

2

3

4

5

Table 2

Distance (m) Time (s) Speed (m/s)

1.22

1.01

1.20

0.97

1.19

0.95

1.25

1.04

1.17

0.94

Average of the Speed _______________

Variance of the Speed ________________

Standard Deviation of the Speed_____________

Uncertainty of the Average Speed ____________

10

Part 3

Step 1) Visit the website: https://ophysics.com/k6.html

Step 2) Set the initial position of the car to x = 0 for all steps in Part 3.

Step 3) Set the acceleration of the car to 0.

Step 4) Give the car some initial velocity and click Run.

Step 5) Calculate the displacement of the car after 5.0 s has elapsed.

Step 6) Give the car some positive acceleration and use the same value for initial velocity as Step 4.

Step 7) Calculate the displacement of the car after 5.0 s has elapsed.

Part 4

The displacement of a car as a function of time graph is shown below. The initial velocity is zero.

Step 1) By analyzing the plot, determine the acceleration of the car.

Step 2) Kinematics tells us that the displacement of an object as a function of time is given by,

1

Ã°Ââ€˜Â¥? = Ã°Ââ€˜Â¥. + Ã°Ââ€˜Â£. Ã°Ââ€˜Â¡ + Ã°Ââ€˜Å½Ã°Ââ€˜Â¡ E

2

The starting point of the car is the zero-reference point. The derivative of the expression as a function

of time is the velocity of the car. It is not possible to differentiate directly.

Step 3) Create a table in which one column is ÃŽâ€Ã°Ââ€˜Â¥ and another column is ÃŽâ€Ã°Ââ€˜Â¡.

Step 4) Moving left to right, choose points from this graph and fill in this table.

Step 5) Plot the data points from the table. This plot represents velocity as a function of time.

Displacement vs. Time

300

Displacement (m)

250

200

150

100

50

0

1

2

3

4

5

6

7

8

9

Time (s)

10

11

12

13

14

15

16

Questions

1) What is the difference between percent error and percent difference? Explain.

2) If your work bench was sloped, what type of error would this produce?

3) If a cluster of data has a low standard deviation, what does that tell us about the spread?

4) What does the slope of the distance vs. time plot represent?

5) What is the difference between RMSE, linear regression, and Ã¢â‚¬Å“best-fitÃ¢â‚¬Â?

6) In Part 3, if the velocity of the car is constant, what is its acceleration?

7) In Part 3, once the car accelerates, is the displacement as a function of time still linear? Explain.

Include all data, graphs, tables, calculations, and answers to these questions in the lab report.

11

Laboratory 2

Free-Fall

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Introduction

The standard value for the acceleration due to gravity (g) is 9.80 m/s2 and is assumed constant. In this

laboratory, the rate of acceleration due to gravity of a falling object in free-fall will be experimentally

determined. By utilizing the equations of kinematics and graphical analysis tools, the standard value of

9.80 m/s2 will be compared to the experimentally determined value.

The force due to gravity pulls objects towards the earth. For the purposes of this course, the rate

of acceleration due to gravity is assumed constant with a standard value of 9.80 m/s2. This is an average

value and varies depending on the location and topography of where measurements are performed.

Although this value may vary, it is very reasonable to consider it a constant for the purposes of this lab.

As an object falls, its velocity is continually increasing. However, the acceleration of the object

remains constant regardless of its mass. In this laboratory a simple free-fall experiment will be conducted

to determine the acceleration due to gravity of an object in free-fall. This value will then be compared to

the standard value of g.

There are many ways to determine the value of g. The method used in this lab utilizes a simple

apparatus: two combined meter sticks attached to a steel post. The purpose of this is to allow a longer

fall time for the ball. The ball will be released from rest and allowed to hit the ground. Simultaneously,

the elapsed time of free-fall will be recorded using a stop watch. From this data, the acceleration due to

gravity can be determined.

The value for (g) obtained will likely not be equal to the standard value. This is due to 1) the

experiment has inherent errors in it. 2) The ball will experience air resistance, which is not taken into

account. 3) Human observational error may occur.

Beyond measuring the value of g, this lab will allow you to gain experience collecting data, in

particular, how to eliminate anomalous data points. Further insight will be gained by plotting the data as

well as working with non-linear functions. From the graph of distance over time, the slope will yield

critical information pertaining to the experiment.

From kinematics, the equation of motion for vertical displacement can be expressed as,

F

Ã°Ââ€˜Â¦ = Ã°Ââ€˜Â¦$ + Ã°Ââ€˜Â£$ Ã°Ââ€˜Â¡ Ã¢Ë†â€™ E Ã°Ââ€˜â€Ã°Ââ€˜Â¡ E

(1)

The initial displacement can be chosen as Ã°Ââ€˜Â¦$ = 0. As long as the object is allowed to freely fall, there is

no initial velocity and Ã°Ââ€˜Â£$ = 0. Eq. (1) can be rearranged to solve for the acceleration due to gravity. This

is left as an exercise necessary for this lab. Notice the negative sign in Eq. (1). This indicates that the

object is falling and the downward direction is taken to be negative.

12

Laboratory 2-Prelab

Free-Fall

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Question 1

What is the standard value for the acceleration due to gravity?

Question 2

What is the purpose of todayÃ¢â‚¬â„¢s laboratory experiment?

Question 3

Which equations will be used for this experiment? Demonstrate this to the instructor.

Question 4

How does the mass of an object affect its rate of vertical fall?

Question 5

Plot the following function: y(t) = 4.9t2 and determine the slope and y-intercept.

From this function determine the velocity and acceleration as a function of time and plot both of these

functions.

13

Lab Procedure

Step 1) Watch this video: https://www.youtube.com/watch?v=aRhkQTQxm4w

Step 2) Watch this video: https://www.youtube.com/watch?v=J6lqgJsA6Xk

The experiment from Step 2 was performed in the lab. One student initially positioned the ball close to

the ground and aligned it parallel to a vertical meter stick (unc. = 0.5 mm). Another student recorded the

elapsed time of fall using the stopwatch.

A mechanical release mechanism was used so that no initial velocity is imparted to the ball.

Step 3) At the instant the ball is released, the stop watch (unc. = 10.0 ms) was activated.

Step 4) For each trial, the ball was incrementally raised to a new height, released and the elapsed

time of fall was recorded for a total of ten (10) trials. Be sure to include the uncertainty in your

final answer for the average acceleration due to gravity.

Step 5) Using graphical analysis software, plot the vertical position as a function of the square of elapsed

time for the ball. The y-axis scale should have units of cm for higher resolution.

Step 6) Plot the velocity and acceleration of the falling ball as a function of time.

Explain in your lab report why your average value of (g) is different than the standard value.

Discuss observed discrepancies from the video and what may have contributed to this.

Step 7) Plot the vertical displacement of the ball as it fell using the increments of time from Table 1.

Trial

1

2

3

4

5

6

7

8

9

10

Distance (cm)

20.00

40.00

60.00

80.00

100.00

120.00

140.00

160.00

180.00

200.00

t (s)

0.21

0.29

0.35

0.41

0.47

0.49

0.52

0.56

0.59

0.65

Table 1

t2 (s2)

g (m/s2)

v (m/s)

a (m/s2)

Average Value of g _____________m/s2

Standard Deviation of g __________

Uncertainty of the Average ________

Questions

1) What does the slope of the plot y vs. t2 represent?

2) What does human reaction time indicate? Where could this have occurred in this experiment?

3) If the mass of the ball was doubled, how would this affect the acceleration due to gravity?

4) During a free-fall experiment, a solid metal ball and a hollow metal ball are positioned at the same

height and released at the same instant. The metal of each ball has the same density. Which ball has a

greater inertia? Should the ball with greater inertia fall more slowly than the lighter ball?

Include all data, graphs, calculations, and answers to these questions in the lab report.

14

Laboratory 3

Projectile Motion

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Introduction

The purpose of this lab is to experimentally verify the equations of kinematics for projectile motion as

well as to show the relationship between projectile launch angle, initial velocity and horizontal range.

This lab will also verify that the horizontal range of a projectile is a function of both its initial velocity

initial launch angle. The lab is divided into two parts. For the first part, the initial angle of the launcher

will remain constant, while the initial velocity will be varied. From this data, the range of the projected

object can be determined as well as other parameters of the trajectory. For the second part, the initial

velocity will be constant while the initial angle of launcher will be varied. For each part the measured

horizontal range will be compared to the theoretical value.

The first necessary step, before the experiments begin, is to determine the initial velocity of the

object as it is projected out of the launcher. The initial velocity cannot easily be measured directly.

However, by setting the angle of the launcher to zero degrees and measuring the horizontal range of the

projectile and the time of flight, the initial velocity can be determined using Eq. 1. The projectile launcher

has three initial velocity settings, each of which yields a different initial velocity.

For the first part, the initial velocity will be varied and the angle of the launcher will remain

constant. The values of the initial velocity correspond to the three settings on the projectile launcher.

Due to the non-zero initial angle, the initial velocity will have both a horizontal and vertical component.

The horizontal component remains constant. In order to determine the vertical component of the initial

velocity, trigonometry needs to be utilized. If the experiment is carefully performed, it should be

observed that the greater the initial velocity, the greater the horizontal range as indicated from Fig. 1 a).

The maximum vertical height of the ball can also be determined using Eq. 3 and Eq. 4. The velocity and

angle the instant prior to impact can also be determined using Eq. 3. and Eq. 6.

For part two, the initial velocity is held constant while the initial launch angle is varied. Notice

from Fig. 1 b), how the range varies as a function of initial angle. Using the medium range of the

projectile launcher, the angle will be varied and the time of flight measured. Eq. 1 can then be used to

determine the horizontal range. If the experiment is carefully performed, it should be observed that the

greater the initial launch velocity, the greater the horizontal range up until 45o. Angles greater than this

reduce the horizontal range.

Ã°Ââ€˜â€¦ = Ã°Ââ€˜Â£.1 Ã°Ââ€˜Â¡

Ã°Ââ€˜â€¦=

(1)

4]^ _`a (Eb] )

(2)

c

Ã°Ââ€˜Â£/ = Ã°Ââ€˜Â£./ Ã¢Ë†â€™ Ã°Ââ€˜â€Ã°Ââ€˜Â¡

Ã°Ââ€˜Â¦ = Ã°Ââ€˜Â¦. + Ã°Ââ€˜Â£./ Ã°Ââ€˜Â¡ Ã¢Ë†â€™

Ã°Ââ€˜Â£ E = Ã°Ââ€˜Â£1E + Ã°Ââ€˜Â£/E

4

h

Ã°ÂÅ“Æ’ = Ã°Ââ€˜Â¡Ã°Ââ€˜Å½Ã°Ââ€˜â€ºfF g 4 j

i

15

(3)

F

E

Ã°Ââ€˜â€Ã°Ââ€˜Â¡ E

(4)

(5)

(6)

Figure 1. Projectile trajectory range as a function of initial velocity and angle. a) Initial velocity is varied and the initial

angle is constant. b) The initial velocity is constant and the initial angle is varied. [1].

Figure 2. Projectile launcher with labels indicating critical features.

16

Laboratory 3-Prelab

Projectile Motion

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Question 1

What is the purpose of this experiment?

Question 2

How many range settings does the projectile launcher have?

Question 3

How can the angle of the projectile launcher be measured?

Question 4

If the initial velocity of a projectile is known, how can we determine its horizontal and vertical

components?

Familiarize yourself with the projectile launcher and be aware of the safety precautions using this device.

Refer to Fig. 2.

17

Lab Procedure

Step 1) Visit the website: https://phet.colorado.edu/en/simulation/projectile-motion

Step 2) Select the Lab icon.

Step 3) When this experiment is performed in the lab, it is an arduous process to determine the initial

velocity of the projectile. Here, all you have to do is set the initial velocity using the slide scale.

The choice of value for the initial velocity is up to you.

Part 1-Varying Ã°Ââ€™â€”Ã°Ââ€™Å Constant Ã°ÂÅ“Â½Ã°Ââ€™Å

Step 1) Reduce the height of the launcher until it indicates 0 m.

Step 2) Angle the launcher to 45o.

Step 3) Choose incrementally increasing values of the initial velocity. For example, 10.0 m/s, 15.0 m/s,

20.0 m/s and record these as the short range, medium range, and long range respectively. Make

sure that the values chosen allow the landing point of the projectile to still be visible on screen.

Step 4) Choose a projectile object from the menu on the right side of the screen.

Step 5) Make sure the gravity is set to 9.81 m/s2 and the air resistance box is not selected.

Step 6) Click the red launch button and wait until the projectile lands.

Step 7) Click and drag the Time, Range, Height meter and position it at the points of interest and

record this data in Table 1. Fill in Table 1. There is also a tape measure available for manual

measurements.

Step 8) Using the same projectile and parameters, repeats Steps 5 through 7 by now varying the initial

velocity.

Average Values

Ã°Ââ€˜Â£.1 (m/s)

Ã°Ââ€˜Â£./ (m/s)

Time of Fight(s)

Maximum Height (m)

Range (m)

Ã°Ââ€˜Â£?1 (m/s)

Ã°Ââ€˜Â£?/ (m/s)

Ã°Ââ€˜Â£? (m/s)

Ã°ÂÅ“Æ’? (Degrees)

Table 1 Constant Ã°ÂÅ“Â½Ã°Ââ€™Å = 45o

Short Range Ã°Ââ€˜Â£.!4>

Medium Range Ã°Ââ€˜Â£.!4>

Long Range Ã°Ââ€˜Â£.!4>

Part 2-Varying Ã°ÂÅ“Â½Ã°Ââ€™Å Constant Ã°Ââ€™â€”Ã°Ââ€™Å

Step 1) Set the initial velocity of the projectile launcher to the same value used for the medium range in

Part 1.

Step 2) Angle the launcher to 25o.

Step 3) Click the red launch button and wait until the projectile lands.

Step 4) Click and drag the Time, Range, Height meter and position it at the points of interest and

record this data in Table 2.

Step 5) Repeat Steps 2) through 4) with varying angles as indicated in Table 2. Fill in Table 2.

18

Average Values

Ã°Ââ€˜Â£.1 (m/s)

Ã°Ââ€˜Â£./ (m/s)

Time of Fight(s)

Maximum Height (m)

Range (m)

Ã°Ââ€˜Â£?1 (m/s)

Ã°Ââ€˜Â£?/ (m/s)

Ã°Ââ€˜Â£? (m/s)

Ã°ÂÅ“Æ’? (Degrees)

Table 2 Constant Velocity (Medium Range)

Ã°ÂÅ“Æ’. = 25$

Ã°ÂÅ“Æ’. = 45$

Ã°ÂÅ“Æ’. = 75$

Part 1-Questions

1) Does the mass of the ball have any effect on the range? Explain.

2) Does the horizontal range of the ball increase with increasing initial velocity? Explain.

3) Does the height of the ball increase with increasing initial velocity? Explain.

4) If the height of the launcher is increased, what effect would this have on the final velocity of the

projectile? Explain.

Part 2-Questions

1) Why does the range increase with increasing initial angle? Explain.

2) What is the optimal initial angle in order to obtain maximum horizontal range? Explain.

3) Why does the range decrease for angles greater than the optimal initial angle? Explain.

Include all data, calculations, and answers to these questions in the lab report.

19

Laboratory 4

NewtonÃ¢â‚¬â„¢s Second Law of Motion

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Introduction

The objective of this lab is to verify NewtonÃ¢â‚¬â„¢s Second Law of motion and determine the acceleration of

a moving object. For Part 1, a wheeled-cart is placed on a horizontal, frictionless track. The cart is

tethered to a string which is wrapped around a pulley with a hanging mass on the other end of the string,

as shown in Fig. 1 a). By application of NewtonÃ¢â‚¬â„¢s second law, the acceleration of the cart can be

determined while neglecting friction. For Part 2, the same cart will be placed on an inclined, frictionless

track. By application of NewtonÃ¢â‚¬â„¢s second law, the acceleration of the cart can be determined.

Figure 1. Part 1: Cart on a horizontal, frictionless track with a weight hung across a frictionless pulley.

Figure 2. Part 2: Cart on an inclined, frictionless track.

When the cart is on the horizontal track a force is needed in order to impart it with acceleration. Ideally,

this force should be constant and controllable. This is the purpose of the vertical masses. The force due

to gravity on the hanging vertical masses will impart a force on the cord and this tension will pull the

cart along the track. The acceleration of the cart can be determined using NewtonÃ¢â‚¬â„¢s second law of motion.

20

Laboratory 4-Prelab

NewtonÃ¢â‚¬â„¢s Second Law of Motion

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Question 1

Sketch the free-body diagram for a block resting on a friction-less horizontal surface.

Question 2

Sketch the free-body diagram for a cable wrapped around the pulley.

Question 3

A force is now applied to the block, what does NewtonÃ¢â‚¬â„¢s second law of motion tell us?

21

Lab Procedure

Part 1

Refer to Fig. 1. This is what your experimental setup should look like.

Here is a video of a very similar setup: https://www.youtube.com/watch?v=wTN16q8mcto

Step 1) Visit the website: https://www.walter-fendt.de/html5/phen/newtonlaw2_en.htm

Step 2) Set the coefficient of friction to 0. This neglects the friction between the cart and track.

Step 3) Set the mass of the cart (wagon) to a 500.0 g and initially set the hanging mass to 20.0 g

Step 4) Click the Start button.

Step 5) Repeat Steps 4 and 5 by incrementally increasing the hanging mass and record this data in

Table 1.

Step 6) Calculate the velocity and acceleration of the block for each increment of the hanging mass.

Step 7) Plot the calculated acceleration of the block as a function of applied force acting on the cart.

Hanging

Mass

(kg)

Force

(N)

Table 1

ÃŽâ€x (m) Time

(s)

Velocity

(m/s)

acceleration

(m/s2)

Part 2

Refer to Fig. 2. This is what your experimental setup should look like.

Step 1) A 1-m track is placed onto the workbench and inclined to 5o using a track support.

Step 2) The angle of incline is measured using a protractor.

Step 3) Photogate 1 is placed at the top of the track. Photogate 2 is placed near the bottom of the track.

Step 4) The cart is initially placed at the top of the track and held. The cart is released and allowed

to pass through both photogates. The times from each photogate are recorded in Table 2.

ÃŽâ€tF and ÃŽâ€t E represent the amount of time it took the cart to pass though photogate 1 and photogate 2

respectively.

Step 5) The length of the cart is measured to be 15.0 cm and remains constant.

Step 6) ÃŽâ€x is the displacement between the photogates. This is measured to be 0.50 m. This also remains

constant.

Step 7) Calculate the velocity of the cart as it passes through each photogate and the acceleration of the

cart as it moves down the incline. Show all steps and fill in Table 2.

Step 8) Make a plot of the acceleration of the block as a function of the angle of incline.

22

Ã°ÂÅ“Æ’ (degrees)

Photogate 1

ÃŽâ€tF (s)

Photogate 2

ÃŽâ€t E (s)

5

10

15

20

25

1.02

0.81

0.72

0.55

0.29

0.16

0.11

0.09

0.08

0.07

Table 2

Ã°Ââ€˜Å¡

Ã°Ââ€˜Å¡

Ã°Ââ€˜Â£F g j Ã°Ââ€˜Â£E g j

Ã°Ââ€˜Â

Ã°Ââ€˜Â

Acceleration

(m/s2)

Acceleration

Motion Sensor

(m/s2)

0.85

1.70

2.54

3.35

4.14

Questions

1) How does the mass of the cart affect its acceleration when placed on the horizontal track?

2) Is the tension in the pulley cord the same on both sides?

3) Is the acceleration of the cart the same as the hanging mass?

4) What are the percent differences between the calculated values of the acceleration of the cart and that

measured with the motion sensor?

Include all data, graphs, calculations, and answers to these questions in the lab report.

23

Laboratory 5

Friction Analysis

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Introduction

The purpose of this lab is to analyze friction and quantify the effect it has on the acceleration of an object.

For Part 1, a microanalysis of friction will be conducted using an optical microscope. Since the track

used in this lab is made of aluminum and a wood block is to be placed on top of it, the samples used

under the microscope are wood and Al as shown in Fig. 1(a). These samples will be placed under an

optical microscope, Fig 1(b). The Al surface appears smooth and polished to the eye. However, when

zoomed in, the surface is actually rough and jagged as shown in Fig. 1 (c).

Figure 1. (a) Optical microscope used for Part 1 [1]. (b) Zoomed in image of two surfaces [2]. (c) Image of Al surface

under the microscope [3].

For Part 2 of this lab, a wood block will slide down an incline while considering the effects of friction.

Using NewtonÃ¢â‚¬â„¢s second law of motion, the acceleration of the block can be calculated and compared to

the value of acceleration from a motion sensor. The acceleration of the block with and without friction

will be compared. It will also be verified that the acceleration of any object moving down an incline is

independent of its mass.

Consider an object sliding on an inclined plane as shown in Fig. 2 (a). The object has some mass

m. The weight of the object is indicated as W. The normal force of the object is N. The kinetic frictional

force is fk. The frictional force is always opposite to the direction of motion. N is the normal force of the

track acting on the block. W is the vertical hanging weight. For the block, the acceleration in the y

direction is zero since the block does not move up or down.

Figure 2. Experimental setup for part 2 of the laboratory. A block slides down an inclined plane.

24

If an external force is applied to an object which results in no motion of the object, the coefficient of

static friction is given the inequality,

Ã°Ââ€˜â€œ# Ã¢â€°Â¤ Ã°ÂÅ“â€¡# Ã°Ââ€˜Â

(1)

For small angles of incline, the block will not move due to the static frictional forces between the block

and surface. At the microscopic level, these are atomic welds between the two surfaces. At a certain

critical angle, Ã°ÂÅ“Æ’+ , the block will have impending motion, in which the block starts to slip, Eq. 2.

Ã°Ââ€˜â€œ# = Ã°ÂÅ“â€¡# Ã°Ââ€˜Â

(2)

If a greater external force (gravity in the case of the inclined surface) is applied to the block and the

block starts to move, the frictional forces are kinetic as shown in equation 3. As the block moves down

the incline, the atomic welds between the two surface break apart as shown in Fig. 1 b.

fk = Ã°ÂÅ“â€¡{ N

(3)

From Fig. 2 (a), the greater the applied force, or weight or angle of the object in this case, the greater the

frictional force. This is the linear portion of the plot. When the applied force (or weight or angle of

incline) reaches a certain threshold the frictional forces become independent of the applied force.

Interestingly, the coefficient of static friction is only a function of the critical angle.

Ã°ÂÅ“â€¡# = Ã°Ââ€˜Â¡Ã°Ââ€˜Å½Ã°Ââ€˜â€º(Ã°ÂÅ“Æ’+ )

(4)

Angles of incline greater than this will lead to the block sliding down the inclined surface with some

acceleration. The greater the angle of incline, the greater the

acceleration of the block. If the expression for the coefficient of

kinetic friction has the same form as Eq. (3), then as the angle

of incline increases, the coefficient increases. This does not

make any sense because the coefficient of kinetic friction

remains constant. Instead, consider a critical angle Ã°ÂÅ“Æ’+| which is

less than the critical angle, as shown in Eq. (4). In order to obtain

motion for angles less than the critical angle, the bonds between

the two surfaces need to be broken and the velocity of the block

needs to be constant so that it has no acceleration.

Figure 3. Plot of the frictional force as a function of the applied force acting on an object [4].

Ã°ÂÅ“Æ’+| < Ã°ÂÅ“Æ’+
(5)
The coefficient of kinetic friction can then be expressed as,
Ã°ÂÅ“â€¡? = Ã°Ââ€˜Â¡Ã°Ââ€˜Å½Ã°Ââ€˜â€º(Ã°ÂÅ“Æ’Ã¢â‚¬Â²+ )
25
(6)
For Part 3 of this lab, the effects of motion will be studied when the resistance of the medium in which
the object is moving is not neglected. For example, when and object such as a ball falls through a gas,
such as air, there exists a force which resists this flow of motion, as shown in Fig 3 (a). This force is
called air drag or simply the resistive force. If the object is not moving too fast, then the resistive force
in which the air exerts on it is given by,
Ã°Ââ€˜â€¦ = Ã¢Ë†â€™Ã°Ââ€˜ÂÃ°Ââ€˜Â£
(a)
(7)
(b)
Figure 4. (a) An object falling through medium with resistive forces. (b) Plot of the velocity of the object as a function of
time. Image (a): and (b) [5].
Where b is a constant based on the properties of the medium and the geometry of the object. It is called
the drag coefficient. Ã°Ââ€˜Â£ is the velocity of the object relative to the air. Just as with frictional forces, this
resistive force is in the opposite direction of the motion of the object. The longer the object is falling in
the medium, the greater the magnitude of the resistive force. When the magnitude of this resistive force
is equal to the weight of the object, the total (net) force acting on the object is zero. The velocity of the
object has reached its terminal velocity. The relationship between this terminal velocity, b, and time is
given by Eq. 8. Ã°Ââ€˜Â£ = is the terminal velocity.
Ã°Ââ€˜Â£=
3>

”

Ã¢â€šÂ¬1 Ã¢Ë†â€™ Ã°Ââ€˜â€™ f”‘/3 Ã¢â‚¬Å¡ = Ã°Ââ€˜Â£ = Ã¢â€šÂ¬1 Ã¢Ë†â€™ Ã°Ââ€˜â€™ f”‘/3 Ã¢â‚¬Å¡

26

(8)

Laboratory 5-Prelab

Friction Analysis

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Question 1

Sketch the free-body diagram for a block on an inclined plane with friction.

Question 2

Use NewtonÃ¢â‚¬â„¢s second law of motion to determine an expression for the acceleration of the block as it

slides down the incline. Be sure to include friction.

Question 3

Can the coefficient of static or kinetic friction normally be greater than one?

Question 4

What does the expression Ã°Ââ€˜â€œ# Ã¢â€°Â¤ Ã°ÂÅ“â€¡# Ã°Ââ€˜Â represent?

Question 5

What does the expression Ã°Ââ€˜â€œ# = Ã°ÂÅ“â€¡# Ã°Ââ€˜Â represent?

27

Lab Procedure

Part 1

This part of the lab is a demonstration by the instructor. Two known samples will be placed on a

microscope slide. Using an optical microscope, the surfaces of each sample will be analyzed. What

should become clear is that no matter how smooth or flat a surface may appear, at the microscopic level

all surfaces are rough and jagged.

Part 2

Step 1) Watch this video: https://www.youtube.com/watch?v=eUpZ0yyFNyc

Step 2) Visit the website: https://ophysics.com/f2.html

Step 3) Look up the value for the coefficient of static friction and kinetic friction between the aluminum

track and the aluminum block and set these values into the simulation

Step 4) Set the initial angle of incline to 10 degrees. Set the initial velocity to 0.

Step 5) Click Run.

Step 6) Repeat Steps 4 and 5 with increasing incline angles and calculate the acceleration of the

block with and without friction. Fill in Table 1.

Step 7) Determine the percent difference between the acceleration of the block with and without friction.

Ã°ÂÅ“Æ’ (degrees)

Table 1

Acceleration (m/s2)

Without Friction

Acceleration (m/s2)

With Friction

10

15

20

25

30

Part 3

The mass of the coffee filter is 10.0 g. It is positioned 2.0 m from the ground and is released with no

initial velocity. Using the data in Table 3, determine the terminal velocity of the filter and the velocity

of the filter relative to the air.

Table 3

Trial

1

2

3

Ã°Ââ€˜Â£ = (m/s)

t (s)

2.94

2.81

3.05

Ã°Ââ€˜Â£ (m/s)

Questions

1) Use NewtonÃ¢â‚¬â„¢s Second Law of motion to show that the acceleration of the block sliding down an

inclined plane is independent of its mass.

2) Once the track is inclined to the critical angle, the block begins to slide. As the block slides down the

track, the angle of incline is decreased. Will the block continue to slide?

3) Can the coffee filter be considered a particle under a net force? Explain.

4) What is the average time it took the filter to fall?

5) If air resistance was neglected how long would it take the filter to fall? Compare these values of time.

Include all data, calculations, and answers to these questions in the lab report.

28

Laboratory 6

The Conservation of Mechanical Energy

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Introduction

The purpose of this lab is to verify the conservation of mechanical

energy. We will be using a double-sloped track and a steel ball.

Initially positioning the ball to a height h2 transfers gravitational

potential energy to the ball. The ball will roll down the track, pass

through the bottom (dotted line) and roll back up to the other side

of the track to some height h3. Due to friction between the track

and the ball, the height h3 will not be the same as h2. The

conservation of mechanical energy will be used to determine the

velocity of the ball when it is at the bottom of the track.

Figure 1. Double track indicating three critical positions of the ball.

The conservation of mechanical energy can be expressed as,

ÃŽâ€Ã°ÂÂÂ¾Ã°ÂÂÂ¸ + ÃŽâ€Ã°Ââ€˜Æ’Ã°ÂÂÂ¸> + Ã°Ââ€˜Å *+ = Ã°Ââ€˜Å (1′

(1)

KE is the kinetic (motional) energy an object has as it moves with some velocity. PEg is the gravitational

potential energy due to an objectÃ¢â‚¬â„¢s position relative to some reference point. Wnc is the work done against

non-conservative forces, friction for example. Friction between the two surfaces increases the total

amount of work needed to change the kinetic energy of the system. Wext is external work done on the

system due to an external force. Substituting the appropriate equations into each term gives us,

F

E

F

Ã°Ââ€˜Å¡Ã°Ââ€˜Â£?E Ã¢Ë†â€™ E Ã°Ââ€˜Å¡Ã°Ââ€˜Â£.E + Ã°Ââ€˜Å¡Ã°Ââ€˜â€Ã¢â€žÅ½? Ã¢Ë†â€™ Ã°Ââ€˜Å¡Ã°Ââ€˜â€Ã¢â€žÅ½. + Ã°Ââ€˜Å *+ = Ã°Ââ€˜Å (1′

(2)

For this lab, external forces, though necessary to supply the system with initial energy, will not be taken

into account in the calculations, so the last term in Eq. 2 can be neglected. Work is the product between

force and distance; therefore, the non-conservative work can be expressed as,

Ã°Ââ€˜Å *+ = Ã°Ââ€˜â€œ{ Ã°Ââ€˜â€˜ = Ã°ÂÅ“â€¡{ Ã°Ââ€˜ÂÃ°Ââ€˜â€˜

(3)

N is the normal force opposing the weight of the object. The expression for this can be determined

using NewtonÃ¢â‚¬â„¢s second law.

When the ball is placed on the bottom of the track, it quickly reaches an equilibrium state and

has no motion. This also means that there is no energy in the ball-track system. An external force is

required to give the ball some initial energy. In order to visualize the motion of the ball as it rolls along

the track, the initial energy supplied to the ball will be gravitational potential energy.

29

Laboratory 6-Prelab

The Conservation of Mechanical Energy

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Question 1

What is the purpose of todayÃ¢â‚¬â„¢s lab?

Question 2

Write down the conservation of mechanical energy and briefly explain each term.

Question 3

What is the difference between kinetic energy and gravitational potential energy?

Question 4

Can energy be lost or created? Explain.

30

Lab Procedure

Steps

Step 1) Look up the value for the coefficient of kinetic friction between the steel ball and steel track.

Step 2) The ball is raised up to a height near the top of the right side of the track. Record this as h2.

Step 3) The ball is released with no initial velocity and allowed to roll down the track.

Step 4) Determine the velocity of the ball when it reaches the bottom of the track.

Step 5) Compare the calculated velocity of the ball at the bottom of the track with the value measured

by the motion sensor.

Step 6) The height the ball reaches on the opposite side of the track is recorded as h3.

Step 7) Complete Tables 1 and 2.

mBall (kg)

0.05

PE1 (J)

PE2 (J)

PE3 (J)

Ã°ÂÅ“Æ’ (degrees)

30

Table 1

Ã°ÂÅ“â€¡{

Table 2

Ã°Ââ€˜Â£Ã‹â€ F (m/s) Ã°Ââ€˜Â£Ã‹â€ E (m/s)

h2 (m)

0.85

Ã°Ââ€˜Â£Ã‹â€ Ã¢â‚¬Â° (m/s)

h3 (m)

0.75

N (N)

d (m)

Wnc (J)

Ã°Ââ€˜Â£Ã‹â€ F (Ã°Ââ€˜Å¡Ã°Ââ€˜â€™Ã°Ââ€˜Â¡Ã°Ââ€˜â€™Ã°Ââ€˜Å¸) = 3.5 m/s

Loss of Energy = ________________ J

Questions

1) Does the conservation of mechanical energy hold? If it does not, discuss any discrepancies.

2) Is the height the ball reaches on the opposite side of the track the same as its initial starting position?

3) If the answer to question 2) is no, then explain why.

4) After the ball has been raised up, it is released and passes through the bottom of the track. Can the

velocity of the ball at the bottom of the track be determined using NewtonÃ¢â‚¬â„¢s Laws of motion? Explain.

5) What is the percent difference between the calculated and measured values of Ã°Ââ€˜Â£Ã‹â€ F ?

6) Was there a loss of energy of the ball? If so, what was this energy transformed into?

Include all data, calculations, and answers to these questions in the lab report.

31

Laboratory 7

The Conservation of Linear Momentum

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Introduction

This laboratory experiment will demonstrate and verify the conservation of linear momentum. This

fundamental principle states that the total momentum of a system remains constant. In this lab, a series

of collision experiments will be performed to demonstrate this principle. The mass of each object is

known and the velocities can be measured before and after the collision. According to the conservation

of linear momentum, the total momentum of the system prior to the collision is equal to the total

momentum of the system after the collision if no other external forces are present.

The objects in question are two collision carts. These are specially designed wheeled carts with

spring-loaded bumpers to absorb the impact of the collision. These springs also ensure us that the

collision remains elastic. The masses of these carts are known. For all parts of this lab, the unknown

variable can be solved using the conservation of linear momentum which can be expressed as,

Ã°Ââ€™â€˜F,. + Ã°Ââ€™â€˜E,. = Ã°Ââ€™â€˜F,? + Ã°Ââ€™â€˜E,?

(1)

The subscripts indicate the specific cart and the initial and final state. This expression can be written in

terms of mass and velocity. Note that the initial and final subscripts only apply to the velocities since the

mass of each cart remains constant. Also notice that friction is being neglected.

Ã°Ââ€˜Å¡F Ã°Ââ€™â€”F,. + Ã°Ââ€˜Å¡E Ã°Ââ€™â€”E,. = Ã°Ââ€˜Å¡F Ã°Ââ€™â€”F,? + Ã°Ââ€˜Å¡E Ã°Ââ€™â€”E,?

(2)

An elastic collision is one in both the linear momentum and the kinetic energy is conserved. The

conservation of energy for our two cart system can be written as,

F

E

F

F

F

E

E

Ã°Ââ€˜Å¡F Ã°Ââ€™â€”F,.

+ E Ã°Ââ€˜Å¡E Ã°Ââ€™â€”EE,. = E Ã°Ââ€˜Å¡F Ã°Ââ€™â€”F,?

+ E Ã°Ââ€˜Å¡E Ã°Ââ€™â€”EE,?

(3)

Eq. 3 can be used to calculate the energy lost in the two-cart system. For example, even though friction

is being neglected in the calculations, there is still a loss of energy outside of the system due to friction

between the wheels of the carts and the track.

During an inelastic collision, the linear momentum is conserved but the kinetic energy is not. For

a perfectly inelastic collision, the total linear momentum is still conserved as shown in Eq. 4. After a

perfectly inelastic collision the carts will remain stuck together and move with some final velocity. In

order to determine the final velocity of this new combined cart system, the masses of each cart can be

added together and the final velocity can be determined using Eq. 5.

dÃ°Ââ€™â€˜ = 0 Ã¢â€ â€™ Ã°Ââ€™â€˜. = Ã°Ââ€™â€˜?

(4)

Ã°Ââ€˜Å¡F Ã°Ââ€™â€”F. + Ã°Ââ€˜Å¡E Ã°Ââ€˜Â£E. = (Ã°Ââ€˜Å¡F + Ã°Ââ€˜Å¡E )Ã°Ââ€™â€”?

(5)

32

Laboratory 7-Prelab

The Conservation of Linear Momentum

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Question 1

What is the purpose of todayÃ¢â‚¬â„¢s lab?

Question 2

Does the total momentum of a closed system remain constant?

Question 3

What is the difference between an elastic and inelastic collision?

Question 4

Sketch a simple one-dimensional elastic collision and show the direction of the momentum for each

object before and after the collision.

33

Lab Procedure

Figure 1. Part 1 experimental setup of the dynamic carts, photogates, and track.

Part 1: Cart 1 Moving, Cart 2 at Rest

For Part 1, prior to the elastic collision, Cart 1 will be pushed along the track and move with some initial

velocity. Cart 2 will initially be as rest. After the collision, Cart 1 will be moving with a new velocity

and Cart 2 will now have a non-zero velocity. Each cart has the same mass.

Step 1) Visit the website: https://www.walter-fendt.de/html5/phen/collision_en.htm

This simulation will be used for all parts of this lab.

Step 2) Set the mass of each cart to 0.50 kg.

Step 3) Set the initial velocity of Cart 1 and Cart 2. These values are your choice.

Step 4) Click the Start button. Make sure that Cart 1 collides into Cart 2.

Step 5) Determine if linear momentum was conserved.

Step 6) Fill in Table 1.

Cart 1

mass (kg)

0.50

Cart 2

mass (kg)

0.50

v1, i

(m/s)

Table 1

v2, i

v1, f

(m/s) (m/s)

v2, f

(m/s)

pi

(kgÃ¢Ë†â„¢m/s)

pf

(kgÃ¢Ë†â„¢m/s)

For all parts, calculate the initial and final momentum and explain whether or not the

conservation of momentum is validated.

Part 2: Cart 1 Moving, Cart 2 Moving

For Part 2, prior to the elastic collision, Cart 1 will move with some initial velocity. Cart 2 will also move

with some initial velocity. After the collision, Cart 1 and Cart 2 will be moving with some velocity

slower than the initial velocity. Each cart has the same mass.

Step 1) Using the simulation, set the velocities of Cart 1 and Cart 2 so they collide into each other.

Step 2) Determine if linear momentum was conserved.

Step 3) Fill in Table 2.

34

Cart 1

mass (kg)

0.50

Cart 2

mass (kg)

0.50

v1, i

(m/s)

Table 2

v2, i

v1, f

(m/s) (m/s)

v2, f

(m/s)

pi

(kgÃ¢Ë†â„¢m/s)

pf

(kgÃ¢Ë†â„¢m/s)

Part 3: Cart 1 Moving with Added Mass, Cart 2 at Rest

Step 1) Using the simulation, increase the mass of Cart 1 and assure that Cart 2 is initially at rest.

Step 2) Determine if linear momentum was conserved.

Step 3) Fill in Table 3.

Cart 1

mass (kg)

Cart 2

mass (kg)

0.50

v1, i

(m/s)

Table 3

v2, i

v1, f

(m/s) (m/s)

v2, f

(m/s)

pi

(kgÃ¢Ë†â„¢m/s)

pf

(kgÃ¢Ë†â„¢m/s)

Part 4: Cart 1 and Cart 2 Moving with the Same Velocities

Step 1) Using the simulation, the collision is now inelastic.

Step 2) Set the initial velocities of each cart so that their velocities are equal in magnitude.

Step 3) Determine if linear momentum was conserved.

Step 4) Fill in Table 4.

Cart 1

mass (kg)

Cart 2

mass (kg)

0.50

v1, i

(m/s)

Table 4

v2, i

v1, f

(m/s) (m/s)

v2, f

(m/s)

pi

(kgÃ¢Ë†â„¢m/s)

pf

(kgÃ¢Ë†â„¢m/s)

For all parts, calculate the initial and final momentum and explain whether or not the

conservation of momentum is validated.

Questions

1) Is momentum conserved during an elastic collision?

2) Is kinetic energy conserved during an elastic collision?

3) Is momentum conserved during an inelastic collision?

4) Is kinetic energy conserved during an inelastic collision?

5) When this experiment is performed in the lab the initial and final kinetic energies during an elastic

collision are not equal. Does this violate the conservation of mechanical energy?

6) If Part 1 was repeated with the track inclined to some angle, would the conservation of linear

momentum still hold? Explain

Include all data, calculations, and answers to these questions in the lab report.

35

Laboratory 8

The Ballistic Pendulum

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Introduction

The ballistic pendulum is a commonly used laboratory apparatus to demonstrate the conservation of

linear momentum. An object, in this case a plastic ball, is horizontally fired with some initial velocity

into a pendulum. At impact, the pendulum swings upward as shown in Fig. 1. The pendulum reaches

some height (h) depending on the momentum of the ball. The maximum height (h) in which the

pendulum rises depends on the initial kinetic energy of the ball. The usefulness of this is that we can

determine the initial velocity of the ball without directly measuring it.

Refer to Fig. 1 below. The mass (m) is the mass of the ball. After impact, the mass is combined

with the block as labeled (M + m). The pendulum bob swings upward to a height (h). It is easiest to think

of this experiment in two parts: 1) The ball and pendulum are combined into one system during an

inelastic collision and moves with some initial kinetic energy (KE). 2) This kinetic energy is transformed

into gravitational potential energy (PEg) as the pendulum swings upward to a height (h).

(a)

(b)

Figure 1. a) Image: PASCO 6831 Ballistic pendulum and launcher [6]. b) Schematic of the ball being fired into the ballistic

pendulum.

Once the ball impacts the pendulum, the ball-box system move as one mass with the same velocity.

Ã°Ââ€˜Å¡Ã°Ââ€˜Â£$ = (Ã°Ââ€˜Å¡ + Ã°Ââ€˜â‚¬)Ã°Ââ€˜Â£?

(1)

After the collision, the ball-box system moves upward to a height (h). From the conservation of

mechanical energy, the initial KE is transformed into PEg.

F

E

(Ã°Ââ€˜Å¡ + Ã°Ââ€˜â‚¬)Ã°Ââ€˜Â£?E = (Ã°Ââ€˜Å¡ + Ã°Ââ€˜â‚¬)Ã°Ââ€˜â€Ã¢â€žÅ½

We can solve for Ã°Ââ€˜Â£$ simply by measuring the height (h) of the pendulum.

36

(2)

Laboratory 8-Prelab

The Ballistic Pendulum

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Question 1

What is the purpose of a ballistic pendulum?

Question 2

Why not just measure the velocity of the projectile directly?

Question 3

When the projectile embeds itself into the block and the block swings upward, what transformation of

energy has taken place?

Question 4

In order to solve for the initial speed of the projectile it is necessary to divide the problem up into two

parts, explain this.

37

Lab Procedure

Steps

Step 1) The projectile (ball) is carefully loaded into the launcher using the ram-rod.

Step 2) The launcher is set to its medium setting.

Step 3) Visit the website: https://ophysics.com/e3.html

Step 4) The pendulum angle gauge is set to the 0o mark.

Step 5) Set the mass of the projectile to 50.0 g.

Step 6) Slide the initial velocity scale to the middle.

Step 7) Set the mass of the wood block to 3.5 kg.

Step 8) A motion sensor is setup to record the velocity of the ball. Click the box at the bottom of the

page to see the initial velocity.

Step 9) The projectile is loaded and settles into the chamber before launching.

Step 10) Slide the height scale to align parallel to the projectile.

Step 11) Click the Fire button. When the system reaches its maximum height, click the Pause button.

Step 12) While paused, slide the height scale so that it aligns parallel to the projectile and record this

value.

Step 13) Determine the initial velocity of the projectile (ball) and the final velocity of the system. Show

all steps in your calculations.

Initial Velocity of Ball (vo) _________________ m/s

Final Velocity of System (vf) _______________ m/s

Questions

1) What type of collision was this?

2) Was linear momentum of the system conserved?

3) Was kinetic energy of the system conserved?

4) In the actual lab experiment, there is always a discrepancy between the calculated initial velocity of

the projectile and that of the motion sensor. What is the cause for this discrepancy?

Include all data, calculations, and answers to these questions in the lab report.

38

Laboratory 9

Uniform Circular Motion

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Introduction

In this laboratory uniform circular motion (UCM) will be studied and NewtonÃ¢â‚¬â„¢s Second Law for

centripetal acceleration and centripetal force will be verified. A plastic ball will be attached to a spring

and a cord and rotated in UCM. Since the spring constant and displacement of the spring can easily be

determined, the centripetal force can be calculated. From this, the tension in the cord can be determined.

When an object rotates in a circle with constant velocity, this type of motion is called uniform

circular motion. Consider a ball, which can be approximated as a particle, on a string rotating in a circle.

NewtonÃ¢â‚¬â„¢s Second Law of motion still holds; however, the acceleration of the ball is given by the

expression as shown in Eq. 1. Where v, is the tangential velocity of the ball and r is the radius of the

circle. Substituting this back into NewtonÃ¢â‚¬â„¢s Second Law gives us Eq. 2. Since direct measurements of

the tension of the string would be difficult a spring can be used to determine the centripetal force acting

on the string. HookeÃ¢â‚¬â„¢s law is given by Eq. 3.

From Eq. 3, Ã°Ââ€˜Ëœ is the spring constant and x is the displacement of the spring. This is the amount

the spring has stretched from its equilibrium position. The negative sign is the restoring force of the

spring. Note that if the spring is displaced in the y-direction, just replace x with y.

Ã°Ââ€˜Å½+ =

4^

(1)

,

ÃŽÂ£Ã°ÂÂÂ¹+ = Ã°Ââ€˜Å¡Ã°Ââ€˜Å½+ =

34 ^

,

Ã°ÂÂÂ¹Ã¢Æ’â€” = Ã¢Ë†â€™Ã°Ââ€˜ËœÃ°Ââ€˜Â¥Ã¢Æ’â€”

(2)

(3)

A plastic ball will be attached to a spring and a cord and rotated in UCM, as shown in Fig. 1. The

spring constant of the spring is not known, but can be determined by measuring the displacement of the

spring and applying HookeÃ¢â‚¬â„¢s law.

Figure 1. Diagram for the ball-spring system indicating the displacement of the spring.

39

Laboratory 9-Prelab

Uniform Circular Motion

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Question 1

What is the purpose of todayÃ¢â‚¬â„¢s experiment?

Question 2

During uniform circular motion, which quantity remains constant?

Question 3

Sketch the free-body diagram of a ball attached to a string and rotating in uniform circular motion.

Question 4

In what direction would the ball fly off at if the string were cut?

Question 5

Write and label each part of HookeÃ¢â‚¬â„¢s law.

40

Procedure

Steps-Part a

Step 1) In order to calculate the spring constant, the spring is positioned vertically and a small mass is

attached to its lower hook.

Step 2) Visit the site:

https://phet.colorado.edu/sims/html/masses-and-springs-basics/latest/masses-and-springsbasics_en.html

Step 3) Select the Lab icon.

Step 4) Make sure the damping is set to none. Using the ruler, measure the displacement of the spring

and calculate the spring constant.

Step 5) The mass is removed and securely attached to an inelastic cord. On other end of the cord is

attached to the spring. Another segment of cord is attached to the other side of the spring. The

opposite end of this cord is left free. This is the end in which the system will be rotated. The setup

is shown in Fig. 1. The ball is rotated in a horizontal circle.

Step 6) The radius of the system is measured before the spring is displaced.

Step 7) The system is now spun around until uniform circular motion is achieved and the spring

displacement is measured.

Spring Constant Data

Suspended Mass: 0.100 kg

Spring Displacement___________m

Spring constant ______________ N/m

Uniform Circular Motion Data

Mass of Ball: 10.0 g

Unstretched Spring Length: 10.0 cm

Total Cord Length: 0.5 m

Stretched Spring Length: 30.0 cm

Radius of Circle Before Displacement _____________ m

Radius of Circle After Displacement _____________ m

Centripetal Acceleration _______________ m/s2

Tangential Velocity ___________________ m/s

Centripetal Force _____________________ N

Tension in the Cord ___________________ N

41

When the velocity of the ball is no longer constant, the circular motion is no longer uniform. The total

acceleration on the ball is now the sum of the tangential component and the radial component,

Ã¢â‚¬Â¢Ã¢Æ’â€” = Ã°Ââ€™â€š

Ã¢â‚¬Â¢Ã¢Æ’â€”, + Ã°Ââ€™â€š

Ã¢â‚¬Â¢Ã¢Æ’â€”’

Ã°Ââ€™â€š

(4)

The total centripetal force acting on the ball is,

Ã¢â‚¬Â¢Ã¢â‚¬Â¢Ã¢Æ’â€” = Ã¢â‚¬Â¢Ã°Ââ€˜ÂÃ¢Æ’â€”, + Ã¢â‚¬Â¢Ã°Ââ€˜ÂÃ¢Æ’â€”’

ÃŽÂ£Ã°Ââ€˜Â

(5)

Steps-Part b

Step 1) On a circle, sketch the components of the total acceleration from Eq. (4)

Step 2) Sketch the components of the total centripetal force acting on the ball from Eq. (5).

Questions

Part a

1) What keeps the ball in uniform circular motion?

2) In what direction would the ball fly off at if the cord broke?

3) Determine the centripetal force in the cord as the ball moves in UCM.

4) Sketch a circle with radius, r, and indicate the directions of centripetal acceleration, tangential

velocity, centripetal force and tension of the ball as it rotates with UCM.

5) What is the magnitude of the tangential component of the acceleration?

6) What does the tangential component of the force represent?

Part b

1) What could have caused this additional tangential component of acceleration to act on the ball?

2) Will this component have any effect on the radial component of acceleration? Explain.

Be sure to include all diagrams, data, calculations and answers to these questions in your lab report.

42

Laboratory 10

Rotational Dynamics

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Introduction

In this lab we will explore rotational dynamics for two systems. In Part 1, an Atwood machine will be

constructed with two unequal masses wrapped over a pulley. The translational velocity of the system

can be determined by applying the conservation of mechanical energy. For Part 2, two objects of equal

mass will be rolled down an incline. One object is solid and the other hollow. It is not intuitive as to

which one wins the race to the finish line. Using the conservation of mechanical energy and rotational

dynamics, the angular and translational velocities can be determined for each object.

Part 1: The Atwood machine

Fig. 1. is an illustration of an Atwood machine. Two unequal masses are wrapped

over a pulley. The friction between the axis and the pulley is neglected. Assume

there is no slippage between the cord and the pulley. When this is the case, the

two connected masses move with the same acceleration. If no external forces act

on the system, the system is isolated. With no external forces and friction

neglected, the conservation of mechanical energy is,

ÃŽâ€Ã°ÂÂÂ¾Ã°ÂÂÂ¸ + Ã°Ââ€˜Æ’Ã°ÂÂÂ¸> = 0

(1)

The initial and final kinetic and potential energies of each object must be taken

into account. This also includes the pulley.

Figure 1. Atwood Machine [5].

Part 2: Rolling Down a Hill

From Fig. 2 we see a sphere at the top of an inclined plane. In this

lab, two spheres will be used, one solid, the other hollow. Both start

at the same location at the top of the incline. Which sphere will win

the race and reach the bottom of the incline first? It is easiest to solve

this problem using energy considerations. When the spheres are

placed at the top of the inclined plane, they each have gravitational

potential energy. When they are released and roll down the plane,

this energy is transformed into kinetic energy. Since the sphere is

rotating there is also rotational kinetic energy present.

Figure 2. Sphere rolling down and inclined plane. [5].

Depending on how much friction there is between the surface of the plane and spheres determines

whether they roll, slip, or both. We will assume there is some friction present. This implies that they will

roll and most likely slip a little as well. Both translational and rotational kinetic energy are present.

43

To best understand the three possibilities of rotation of an object, refer to Fig. 3. When there is

no translational motion, the object moves with pure rotation, as shown in Fig. 3a. The only velocity

present is angular velocity. If one were to observe the center of mass of the object, they would notice no

translational motion. If there is slippage between the ball and the surface, e.g. car tires on ice, as shown

in Fig. 3b. If there is both rotational motion and a bit of slippage, then the translational motion of the

object is a combination of these two types of motion.

Figure 3. An object moving with a) pure rotation, b) pure translation, c) both rotational and translational motion. [5].

When each sphere is at the top of the incline it has some initial gravitational potential energy. As each

sphere rolls down the incline, its initial gravitational potential energy is transformed into both rotational

kinetic energy and translational kinetic energy. The parallel axis theorem can be used to determine the

moment of inertia of the point P some distance R from the center of mass of the sphere.

Ã°ÂÂÂ¼Ã‹Å“ = Ã°ÂÂÂ¼+3 + Ã°Ââ€˜â‚¬Ã°Ââ€˜â€¦E

(2)

Ã°ÂÂÂ¼+3 is the moment of inertia of the center of mass of the sphere. Ã°Ââ€˜â‚¬Ã°Ââ€˜â€¦E is the moment of inertia at a point

some distance R from the center of the sphere. The total kinetic energy of the sphere is the sum of the

kinetic energy of the translational motion and the kinetic energy of the rotational motion.

F

F

Ã°ÂÂÂ¾Ã°ÂÂÂ¸ = E Ã°ÂÂÂ¼+3 Ã°ÂÅ“â€E + E Ã°Ââ€˜â‚¬Ã°Ââ€˜â€¦E Ã°ÂÅ“â€E

(3)

It is much easier to measure the translational velocity than the angular velocity. Substitute Ã°ÂÅ“â€ = Ã°Ââ€˜Â£+3 /Ã°Ââ€˜â€¦

into Eq. 3. Where Ã°Ââ€˜Â£+3 is the velocity of the center of mass of the sphere.

F

Ã°ÂÂÂ¾Ã°ÂÂÂ¸, = E Ã°ÂÂÂ¼+3 g

4Ã…Â¡Ã¢â‚¬Âº E

Ã…â€œ

F

j + E Ã°Ââ€˜â‚¬(Ã°Ââ€˜Â£+3 )E

(4)

The conservation of energy can now be applied to the sphere. Once the terms are placed into this

expression, the translational velocity can be determined. This value can then be compared to the

measured value. Once the translational velocity is determined, the translational acceleration of each

sphere can also be determined. Hint: use an expression from kinematics.

44

Laboratory 10-Prelab

Rotational Dynamics

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Question 1

What is the purpose of todayÃ¢â‚¬â„¢s experiment?

Question 2

How does rotational dynamics differ from uniform circular motion?

Question 3

What is the difference between translational and rotational motion?

Question 4

Does the moment of inertia depend on the distribution of the mass of an object, e.g. a ball?

Question 5

Write down the expression for rotational motion, using the conservation of energy, when a solid sphere

rolls down a hill.

45

Lab Procedure

Part 1: The Atwood Machine

Step 1) A pulley is secured to the end of a track using a clamp.

Step 2) An inelastic cord is wrapped around the pulley and two unequal masses are secured.

Step 3) Visit the website: https://ophysics.com/r5.html

Step 4) Set the radius of the pulley to be 0.5 m and its mass to be 2.0 kg.

Step 5) Select the Solid Cylinder box.

Step 6) Select the Two Masses box.

Step 7) Name the mass on the left-side Mass 1 and the mass on the right-side Mass 2. M1 Ã¢â€°Â M2.

Step 8) Release the system from rest by clicking the Start button.

Step 9) Record the translational and angular acceleration of the system.

Step 10) Determine the displacement of each mass from their initial to final position using this data.

You will need to choose a time interval in order to complete Step 10.

Step 11) Determine the angular velocity of the pulley while it is rotating.

Step 12) Determine how many revolutions the pulley made from its initial to its final position.

Step 13) Calculate the net torque acting on the pulley.

Step 14) Create a table with all of this data and results. Show all calculations.

Part 2: Rolling Down an Incline

Step 1) Visit the website: https://ophysics.com/r3.html

Step 2) Incline the track to 25 degrees.

Step 3) Select two objects and make sure that each is positioned at the top of the incline.

Step 4) A photogate is positioned at the bottom of the incline.

Step 5) Click the Run button.

Step 6) Record which object wins the race.

Step 7) Attribute each of these objects with physical dimensions and mass.

Step 8) Show through calculations why one object moves faster than the other.

Step 9) Present these results in a table.

Questions

Part 2

1) What happens if we neglect friction as the objects move down the inclined plane? Explain.

2) During another experiment, a solid sphere is placed on top of the incline next to a hollow

sphere with the same outer radius. Using the concepts of moment of inertia, determine which

one wins the race.

Be sure to include all data, calculations and answers to these questions in your lab report.

46

Laboratory 11

Conservation of Angular Momentum

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Introduction

If a disk is rotated as shown in Fig. 1 (a), it develops some angular velocity and angular momentum. If

you let your right hand represent the spinning disk, the direction of your thumb points in the same

direction as the angular velocity and angular momentum shown in Fig. 1 (b). By using the right-handrule we can determine the direction of these quantities for any type of rotating object. The expression for

torque is given by Eq. 1. and also points in the same direction as angular momentum.

Figure 1. (a) Rotating disk. (b) Right-hand-rule representing the spinning disk. Images: [1].

ÃŽÂ£Ã°ÂÂâ€° =

@Ã°Ââ€˜Â³

@’

Ã°Ââ€˜Â³=Ã°Ââ€™â€œ Ãƒâ€”Ã°Ââ€™â€˜

(1)

(2)

If a wheel is spun CCW as shown in Fig 1 (a), then by using the right-hand-rule we can determine that

the direction of angular velocity and angular momentum points towards her left. If she applies a force

downward with her left hand and a force upward with her right hand in an attempt to rotate the wheel,

the resulting motion of it is not intuitive. Using the right-hand-rule, the wheel will have a component of

angular momentum towards her, as shown in Fig. 2 b. Since torque also points in the same direction,

there will be an additional torque directed towards here as well. This is called gyroscopic precession.

Figure 2. (a) Forces applied to spinning wheel. (b) Vector representation of angular momentum. Images [4].

47

The purpose of this experiement is to determine the angular precessional velocity of a rotating wheel as

a torque is applied. The equation for precessional angular velocity is given by Eq. 3.

Ã°ÂÅ“â€2 =

,3>

Ã‚Â¡Ã‚Â¢

(3)

r: is the distance from the pivot point to the center of mass.

m: is the mass of the wheel.

g: is the acceleration due to gravity.

I: is the moment of inertia of the wheel.

Ã°ÂÅ“â€: is the angular velocity of the wheel.

The relationship between the precessional angular velocity and the angular momentum using vector

notation is given in Eq. 4.

Ã¢â‚¬Â¢Ã¢â‚¬Â¢Ã¢Æ’â€” Ãƒâ€” Ã°ÂÂÂ¿Ã¢â‚¬Â¢Ã¢Æ’â€”

Ã°ÂÅ“ÂÃ¢Æ’â€” = ÃŽÂ©

(4)

Ã¢â‚¬Â¢Ã¢Æ’â€” is the precessional angular velocity. Ã°ÂÂÂ¿Ã¢â‚¬Â¢Ã¢Æ’â€” is the angular

Ã°ÂÅ“ÂÃ¢Æ’â€” is the torque acting on the spinning wheel. Ã¢â‚¬Â¢ÃŽÂ©

momentum of the spinning wheel.

The period of rotation of the wheel is,

Ã°Ââ€˜â€¡2 =

EÃ‚Â¨

Ã‚Â¢Ã‚Â©

(5)

Lab Procedure

Step 1) Watch the following videos to gain a better understanding of the conservation of angular

momentum and precession:

Step 2) The purpose of Lab 11 is to design an experiment based on gyroscopic precession and determine

the precessional angular velocity and period of rotation of an object. Each student needs to

choose an object, for example a wheel, disk, sphere, etc. The dimensions and mass of this object

is also to be chosen by the student.

Step 3) The object now moves with gyroscopic precession.

Step 4) Indicate on a sketch the direction of angular velocity, precessional angular velocity, angular

momentum and torque.

Step 5) Explain how the object is able to maintain its motion without falling over.

Step 6) Calculate the precessional angular velocity and period of rotation of the object.

Be sure to include all data, calculations and answers to these questions in your lab report.

48

Laboratory 12

Fluid Dynamics and Heat Exchange

PY-120 Physics I Laboratory

Passaic County Community College

Professor: Wayne Warrick

Introduction

In Part 1 of this lab a fluid-flow experiment will be performed to verify BernoulliÃ¢â‚¬â„¢s equation. Since the

fluid needs to be incompressible with a well-known density, water will be used. The water will flow

through a hose and into a nozzle all while maintaining steady flow. This lab will allow students to

visualize the relationship between the velocity of a fluid and pressure. In Part 2 of this lab, the water

flowing out of the nozzle will be directed over a vessel containing ice. By knowing the flow rate of the

fluid emitted from the nozzle, the duration of time necessary to melt the ice can be determined.

Lab Procedure

Part 1

Step 1) Visit the website: https://ophysics.com/fl2.html

Step 2) Slide the scale for h1 to 0 and slide the scale for h2 to 0.

Step 3) Set the radius of r1 to 1.0 m.

Step 4) Set the radius of r2 to 0.5 m. This now represents a hose with a nozzle attached.

Step 5) Select the velocity of the water flowing through the hose to 2.0 m/s.

Step 6) Record the velocity in the nozzle, and the pressures in both the hose and nozzle.

Step 7) Calculate the flow rate of the water in the hose and nozzle.

Step 8) Use BernoulliÃ¢â‚¬â„¢s equation to determine the pressure in the hose and nozzle.

Part 2

Step 1) The flow rate of water out of the nozzle remains constant.

Step 2) The measured temperature of the water is 20o C

Step 3) The nozzle is directed over a vessel containing a block of ice at a temperature of 0o C.

Step 4) The initial volume of the ice block is 100.0 cm3

Step 5) Determine the volume of water required to completely melt the ice block.

Step 6) Determine how long the water must continue to flow in order to completely melt the ice.

Questions

Part 1

1) Is the velocity greater in the hose or the nozzle?

2) Is the pressure greater in the hose or the nozzle?

3) Is the energy the same at all points along each streamline of the water as it flows? Explain.

4) Does the potential energy of the water change as it flows? Explain.

5) Does the internal energy of the water vary while it flows? Explain.

Part 2

1) How much heat was transferred from the water to the ice.

2) Once thermal equilibrium is established, what is the temperature of the system?

Be sure to include all data, calculations and answers to these questions in your lab report.

49

References

[1]

Paul Peter Urone, Roger Hinrichs, OpenStax, College Physics, Jun 21, 2012, Houston, Texas,

Book URL: https://openstax.org/books/college-physics/pages/1-introduction-to-science-andthe-realm-of-physics-physical-quantities-and-units.

[2]

https://www.zeiss.com/microscopy/int/products/stereo-zoom-microscopes/stemi-305.html

[3]

https://en.wikipedia.org/wiki/Galling

[4]

William Moebs, Samual J. Ling, Jeff Sanny, OpenStax, University Physics Vol. 1, Sep. 19, 2016,

Houston, Texas, Book URL: https://openstax.org/books/university-physics-volume-1/pages/1introduction.

[5]

Serway and Jewett, Physics for Scientists and Engineers with Modern Physics, 10th Ed. Cengage

Learning.

[6]

PASCO 6831 Ballistic Pendulum Launcher

50

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