Block B in (Figure 1) is free to slide on the horizontal surface. With block C p
ID: 1517232 • Letter: B
Question
Block B in (Figure 1) is free to slide on the horizontal surface. With block C placed on top of B. the system undergoes simple harmonic motion with an amplitude of 0.12 m. Block B has a speed of 0.22 m/s at a displacement of 0.075 m from its equilibrium position. Determine the period of the motion. Express your answer with the appropriate units. What minimum value for the coefficient of static friction mu_s between B and C is needed if C is never to slip? Ignore any friction between B and the horizontal surface.Explanation / Answer
(A)
time period of the motion, T = (2*)/
A = 0.12 m
We know at x = 0.0075 , v = 0.22 m/s
x = A*sin(t)
v = A*cos(t)
0.075 = 0.12 * sin(t)
t = sin^-1(0.075/0.12)
t = 38.7o
0.22 = 0.12 * * cos(t)
0.22 = 0.12 * * cos(38.7)
= 2.35 rad/s
T = (2*)/2.35 s
T = 2.67 s
(B)
The force of static friction: Fs = N = ma.
Where, N = mg
*m*g = ma.
*g = a
So Max Acceleration in S.H.M is given by, A*^2
*g = A*^2
*9.8 = 0.12*2.35^2
= 0.067