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A 23-kg child swings back and forth on a swing suspended

Physics with MasteringPhysics | 4th Edition | ISBN: 9780321541635 | Authors: James S. Walker ISBN: 9780321541635 54

Solution for problem 57P Chapter 8

Physics with MasteringPhysics | 4th Edition

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Physics with MasteringPhysics | 4th Edition | ISBN: 9780321541635 | Authors: James S. Walker

Physics with MasteringPhysics | 4th Edition

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Problem 57P

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.

Step-by-Step Solution:

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

Step 2 of 2

Chapter 8, Problem 57P is Solved
Textbook: Physics with MasteringPhysics
Edition: 4
Author: James S. Walker
ISBN: 9780321541635

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A 23-kg child swings back and forth on a swing suspended