Some easy physic questions

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Homework #13

1) In the figure a uniform beam of weight 500 N and length 3.00 m is suspended horizontally. On

the left it is hinged to a wall; on the right it is supported by a cable bolted to the wall at distance

D above the beam. The least tension that will snap the cable is 1200 N. (a) What value of D

corresponds to that tension? (b) To prevent the cable from snapping, should D be increased or

decreased from that value?

2) The system shown below is in equilibrium. A concrete block of mass 225 kg hangs from the

end of the uniform strut of mass 45.0 kg. A cable runs from the ground, over the top of the strut,

and down to the block, holding the block in place. For angles Ãâ€¢ = 30.0Ã‚Â° and ÃŽÂ¸ = 45.0Ã‚Â°, find (a)

the tension T in the cable and the (b) horizontal and (c) vertical components of the force on the

strut from the hinge.

3) In the figure a lead brick rests horizontally on cylinders A and B. The areas of the top faces of

the cylinders are related by AA = 2AB; the YoungÃ¢â‚¬â„¢s moduli of the cylinders are related by EA =

2EB. The cylinders had identical lengths before the brick was placed on them. What fraction of

the brickÃ¢â‚¬â„¢s mass is supported (a) by cylinder A and (b) by cylinder B? The horizontal distances

between the center of mass of the brick and the centerlines of the cylinders are dA for cylinder A

and dB for cylinder B. (c) What is the ratio dA/dB?

4) An oscillator consists of a block attached to a spring (k = 400 N/m). At some time t, the

position (measured from the systemÃ¢â‚¬â„¢s equilibrium location), velocity, and acceleration of the

block are x = 0.100 m, v = Ã¢Ë†â€™ 13.6 m/s, and a = Ã¢Ë†â€™ 123 m/s2. Calculate (a) the frequency of

oscillation, (b) the mass of the block, and (c) the amplitude of the motion.

Homework #13

5) The graph below shows the stressÃ¢â‚¬â€œstrain curve for a material. The scale of the stress axis is set

by s = 300, in units of 106 N/m2. What are (a) the YoungÃ¢â‚¬â„¢s modulus and (b) the approximate

yield strength for this material?

6) The graph below on the left shows a partial graph of the position function x(t) for a simple

harmonic oscillator with an angular frequency of 1.20 rad/s; The graph on the right is a partial

graph of the corresponding velocity function v(t). The vertical axis scales are set by xs = 5.0 cm

and vs = 5.0 cm/s. What is the phase constant of the SHM if the position function x(t) is in the

general form x = xm cos(Ãâ€°t + Ãâ€¢)?

7) If the phase angle for a blockÃ¢â‚¬â€œspring system in SHM is Ãâ‚¬/6 rad and the blockÃ¢â‚¬â„¢s position is

given by x = xm cos(Ãâ€°t + Ãâ€¢), what is the ratio of the kinetic energy to the potential energy at time

t = 0?

8) What is the phase constant for the harmonic oscillator with the velocity function v(t) given in

the graph below if the position function x(t) has the form x = xm cos(Ãâ€°t + Ãâ€¢)? The vertical axis

scale is set by vs = 4.0 cm/s.

9) A 5.00 kg object on a horizontal frictionless surface is attached to a spring with k = 1000 N/m.

The object is displaced from equilibrium 50.0 cm horizontally and given an initial velocity of

10.0 m/s back toward the equilibrium position. What are (a) the motionÃ¢â‚¬â„¢s frequency, (b) the

initial potential energy of the blockÃ¢â‚¬â€œspring system, (c) the initial kinetic energy, and (d) the

motionÃ¢â‚¬â„¢s amplitude?

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