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 of 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 of 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 there is no friction between the wedge and the horizontal surface, there is no net force acting on the wedge in the horizontal direction. Therefore, the horizontal component of the velocity of the wedge remains constant at 6.0 m/s.

To find the direction of the velocity, we need to consider the direction of the frictional force acting on the block, which is opposite to the direction of motion of the block. Since the block is moving towards the right, the frictional force acts towards the left. This frictional force is also acting on the wedge in the opposite direction, which means that the wedge moves towards the right. Therefore, the velocity of the wedge is 6.0 m/s to the right.

A Large Wedge with a Mass of 10 Kg Rests