Question

A stone disk is sliding on frictionless ice to the west with speed v, as shown in the figure above. As the disk slides by, a child uses a rubber mallet to hit the disk it point X, exerting a force directly toward the center of the disk. The child hits point X every half second for about 10 s, changing the trajectory of the disk but not causing it to rotate. Which of the following most closely approximates the path of the disk while the child is hitting it?

Answer 1

The path of the stone disk sliding on frictionless ice after being struck repeatedly by a child with a mallet toward the center will most closely approximate a curved trajectory. This is due to repeated impulses changing the disk's momentum and direction of motion, leading to a series of connected tangential arcs.

Step-by-step explanation:

The question pertains to the path taken by a sliding stone disk on frictionless ice after being struck by a force directed towards the center of the disk. If a force is applied towards the center of a disk moving in a straight line on a frictionless surface, there will be a change in direction of the disk's velocity without causing rotation, assuming the force is applied in line with the center of mass. Every time the child hits the disk, it imparts an impulse that changes the disk's momentum and thus its direction. The path the disk will follow would most closely approximate a curved trajectory, essentially the result of superimposing the force's direction on the initial westward velocity.

Given that the question states the disk does not rotate and the force is directed towards the center, the scenario is similar to the physics concept of central force which results in circular or elliptical motion. Since the force is exerted repeatedly at fixed intervals, the actual path might resemble a series of connected tangential arcs, creating a smooth curve rather than a perfect circle or ellipse as friction is not present to reduce the lateral velocity.