Question

If a child swinging to and fro on a playground swing stands up, her time for a to-and-fro swing is:

a) Decreased
b) Increased
c) Remains the same
d) Cannot be determined from the information provided

Answer 1

The time for a to-and-fro swing on a playground swing remains unchanged when a child stands up, as the swing's period is determined by the length of the swing and gravity, not the child's position.

Step-by-step explanation:

If a child swinging to and fro on a playground swing stands up, her time for a to-and-fro swing is unchanged. This can be explained by the physics of a simple pendulum, which dictates that the period of a swing is determined primarily by the length of the pendulum and the acceleration due to gravity, not by the mass or position of the swinging object. Therefore, standing up does not change the length of the swing or the force of gravity acting on the child, so the time for a to-and-fro swing remains the same.

When considering the energies involved, the kinetic energy increases when the child swings downward and the potential energy increases when the child swings upward. These energy changes are related to the speed and height of the child on the swing, but not the sitting or standing position.