The system shown is released from rest and moves 50 cm in 1.0 s.What is the value of M? All surfaces are frictionless.
A)0.42 kg
B)0.34 kg
C)0.50 kg
D)0.59 kg
E)0.68 kg

Question

The system shown is released from rest and moves 50 cm in 1.0 s.What is the value of M? All surfaces are frictionless. 
A)0.42 kg 
B)0.34 kg 
C)0.50 kg 
D)0.59 kg 
E)0.68 kg

Quizplus · Accepted Answer

Since there is no friction, the center of mass of the system will move at a constant velocity. Using the kinematic equation:

d = vi*t + 1/2*a*t^2

where d = 50 cm, vi = 0 m/s, t = 1.0 s, and a = F_net/M, we can solve for the value of M.

Since there are no external forces acting on the system, the net force will be the force due to gravity:

F_net = M*g

where g = 9.8 m/s^2 is the acceleration due to gravity.

Substituting this into the kinematic equation, we get:

50 cm = 0*1.0 s + 1/2*(F_net/M)*1.0 s^2

Simplifying this, we get:

F_net = M*(100 cm/s^2)

and

F_net = M*g

Setting these equal, we get:

M*(100 cm/s^2) = M*g

Solving for M, we get:

M = (100 cm/s^2)/(9.8 m/s^2 * 100 cm/m) = 0.34 kg

Therefore, the answer is B) 0.34 kg.

The System Shown Is Released from Rest and Moves 50