(1) A mass m 1 = 8 kg is at rest on a frictionless horizontal surface and connec

Question

(1) A mass m1 = 8 kg is at rest on a frictionless horizontal surface and connected to a wall by a spring with spring constant k = 70 N/m as shown in the figure. A second mass m2 = 5 kg is moving to the right at vo = 17 m/s. The two masses collide and stick together. How long (in s) will it take after the collision to reach the maximum compression of the spring?

(2) A 2 kg mass is riding on top of a 4 kg mass as it oscillates on a frictionless surface. The spring constant is k = 150 N/m and the coefficient of static friction between the two blocks is ms = 0.2. What is the maximum oscillation amplitude (in cm) for which the upper block does not slip?

(3) A simple harmonic oscillator is created by attaching two springs with spring constants k1 = 8 N/m and k2 = 10 N/m to a 2 kg mass as shown in the figure below. What is the frequency (in Hz) of the oscillations of this system?

(4) A torsion pendulum is created by attached a uniformly dense rigid rod of mass 0.4 kg and length 0.5 m to a massless string. The rod is suspended from its midpoint as shown in the figure below. Rotating the rod through an angle q results in elastic potential energy being stored in the string; the equation for this energy is U = (1/2)*k*q^2. The effective

Explanation / Answer

(1)

V2 = velocity jsut after collision   = m2*17/(m1+m2) = 6.53 m/s

F = force on block   = -kx

a = acceleration   = -kx/(m1+m2)

A =maximum compression   of spring   = [(m1+m2)*v2^2/(k)]^0.5

A   = 2.81 m

a   =   -70*x/13

t = time reqiured for maximum compression = =(pi/2)*[k/(m1+m2)]^0.65

t = 3.64 s

2) x = maximum oscilation amplitude

    kx = 2*mu*g

    x =2*0.2*9.8/150 =2.6 cm

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