Question

A ball moves in the direction of the arrow labeledin Figure. The ball is struck by a stick that briefly exerts a force on the ball in the direction of the arrow labeled. Which arrow best describes the direction of, the change in the ball's momentum?

Short answer

The correct direction of the ball's momentum change is .

Step-by-step solution

Understanding the action of force applied perpendicularly to a moving object

When a body moves in a specific direction at a specific velocity and an external force acts on it in a perpendicular direction to its motion, the body's speed remains constant, but its direction of motion changes.

Representation of the situation diagrammatically

• The body's motion is circular, and the velocity vector is always tangential to the circular path on which it moves.
• In this example, a force acted on the body in an inward direction, which is responsible for the body's circular trajectory.
• The direction of velocity change is the same as the direction of momentum change.
• The force applied by the stick and the ball's initial velocity is depicted in the diagram below as,

Representation of an arrow describing the change in the ball’s momentum

• The ball moves in the direction of, whereas the force moves in the direction of e.
• As a result, the direction of acceleration is along, and the change in velocity direction is also along e .
• The direction of change in velocity is the same as the change in momentum, as it is well known. As a result, momentum will flow in the direction of e .
• As a result, the right direction of the ball's momentum changes is,e.