Question

A ball moves in the direction of the arrow labelled $c$in Figure $2.53$. The ball is struck by a stick that briefly exerts a force on the ball in the direction of the arrow labelled$e$. Which arrow best describes the direction of $\Delta \overrightarrow{p}$, the change in the ball's momentum?

Short answer

As a result, the right direction of the ball's momentum change is$e$.

Step-by-step solution

Action of force applied perpendicularly on 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.

Represent the situation diagramatically

• The body's motion is circular in this case, 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 are depicted in the diagram below.

Arrow describing the change in ball’s momentum

- The ball moves in the direction of $C$, whereas the force moves in the direction of $e.$

- As a result, the direction of acceleration is along $e$, and the change in velocity direction is also along $e.$

- The direction of change in velocity is the same as the direction of change in momentum, as 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 change isrole="math" localid="1657712640062" $e$.