A large wedge with a mass of 10 kg rests on a horizontal frictionless surface, as shown.A block with a mass of 5.0 kg starts from rest and slides down the inclined surface of the wedge, which is rough.At one instant the vertical component of the block's velocity is 3.0 m/s and the horizontal component is 6.0 m/s.At that instant the velocity of the wedge is:
A)3.0 m/s left
B)3.0 m/s, right
C)6.0 m/s, right
D)6.0 m/s, left
E)17 m/s, right

Question

A large wedge with a mass of 10 kg rests on a horizontal frictionless surface, as shown.A block with a mass of 5.0 kg starts from rest and slides down the inclined surface of the wedge, which is rough.At one instant the vertical component of the block's velocity is 3.0 m/s and the horizontal component is 6.0 m/s.At that instant the velocity of the wedge is: 
A)3.0 m/s left 
B)3.0 m/s, right 
C)6.0 m/s, right 
D)6.0 m/s, left 
E)17 m/s, right

Quizplus · Accepted Answer

Since the block is sliding down the rough surface of the wedge, there must be a frictional force acting on it. This frictional force must be parallel to the incline and points opposite to the direction of motion. The force of friction will produce a torque about the center of mass of the wedge, causing it to rotate counterclockwise. Therefore, the velocity of the wedge must be in the same direction as the force of friction, which is opposite to the direction of motion of the block at that instant. Since the horizontal component of the block's velocity is to the right, the velocity of the wedge must be to the left. Therefore, the answer is B) 3.0 m/s, right.

A Large Wedge with a Mass of 10 Kg Rests