Part A: A 21.0-kg child is sliding down a 10.0 m long slide that is angled 25.0° above the horizontal. What is the gravitational potential energy of the child-Earth system when the child is at the top of the slide (10.0 m from the bottom) ?

Part B: When the child reaches the bottom of the slide, they have a speed of 3.70 m/s. Assuming the child starts from rest, what is the change in the kinetic energy of the child?

Part C: What is the change in thermal energy of the slide-child-Earth system?

vertical height of child

= 10 sin25

= 4. 22 m

gravitational potential energy of the child-Earth system

mgh

21 x 9.8 x 4.22

= 868.47 J

B)

Change in kinetic energy

1/2 mv² - 0

=.5 x 21 x 3.7²

= 143.74 J

C)

The potential energy of the child sitting at height is converted into kinetic energy. But we see that the kinetic energy at the bottom is less than potential energy. The difference in this energy must have been converted into heat energy due to friction.

So

the change in thermal energy of the slide-child-Earth system

= 868.47 J - 143.74 J

= 724.73 J