Question

A child rocks back and forth on a porch swing with an amplitude of 0.260 m and a period of 2.60 s.

A. Find the frequency of the swing.

B. Calculate the maximum speed of the child.

C. Determine the potential energy of the child at the highest point.

D. All of the above.

Answer 1

The frequency of the swing is 0.385 Hz, the maximum speed of the child is 0.628 m/s, and the potential energy of the child at the highest point cannot be determined without the mass.

Step-by-step explanation:

To find the frequency of the swing, we can use the formula:

frequency = 1 / period

Substituting the values, we have:

frequency = 1 / 2.60 s = 0.385 Hz

To calculate the maximum speed of the child, we can use the formula:

maximum speed = 2 * pi * amplitude / period

Substituting the values, we have:

maximum speed = 2 * 3.14 * 0.260 m / 2.60 s = 0.628 m/s

To determine the potential energy of the child at the highest point, we can use the formula:

potential energy = mass * gravity * height

Since the height at the highest point is equal to the amplitude, we have:

potential energy = mass * gravity * amplitude

However, we do not have the mass of the child, so we cannot determine the potential energy without that information.