(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)VELOCITY OF MASS AFTER COLLISION

V= (m2v0)/(m1+m2)= 6.538 m/s

ampltude A= vsqrt(m/k)= 2.81 m

now

w= sqrt(k/m1+m2)= 2.32 rad/s

x= Asin wt

at x=A

sinwt=1

wt= pi/2

t= pi/2w= 0.67 s

3) keq= k1*k2/(k1+k2)= 4.44

w= sqrt(k/m)= 1.49 rad/s

f= w/2pi= 0.23 Hz

4)

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