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A 23-kg child swings back and forth on a swing suspended
Chapter 8, Problem 57P(choose chapter or problem)
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.
Questions & Answers
QUESTION:
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.
ANSWER:
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