Problem 57P

A 23-kg child swings back and forth on a swing suspended by 2.5-m-long ropes. Plot the gravitational potential energy of this system as a function of the angle the ropes make with the vertical, assuming the potential energy is zero when the ropes are vertical. Consider angles up to 90° on either side of the vertical.

Solution 57P

Step 1 of 2

We have to plot the gravitational potential energy of the system as a function of the angle the ropes make with the vertical, assuming the potential energy is zero when the ropes are vertical.

A 23-kg child swings back and forth on a swing suspended by 2.5-m-long ropes as shown in the figure below.

The height of the swing from the ground can be generalized as

=

Where,

is the angle made by the rope with the vertical

Hence, the potential energy at the height is

=

Where,

mass of the child in kg

acceleration due to gravity in m/s2

length of the rope in m

Now at o ,

Substituting 23 kg for , for and m for

= 560 J

and at

= 560 J