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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 ϕ = 30.0° and θ = 45.0°, 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 Young’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 brick’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 system’s equilibrium location), velocity, and acceleration of the
block are x = 0.100 m, v = − 13.6 m/s, and a = − 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 stress–strain 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 Young’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(ωt + ϕ)?
7) If the phase angle for a block–spring system in SHM is π/6 rad and the block’s position is
given by x = xm cos(ωt + ϕ), 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(ωt + ϕ)? 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 motion’s frequency, (b) the
initial potential energy of the block–spring system, (c) the initial kinetic energy, and (d) the
motion’s amplitude?

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