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?

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

ConcepcionPetillo ConcepcionPetillo · Answer 2 · 2022-03-10T13:37:43+01:00

(A) The gravitational potential energy of the child-Earth system is 868.47 J

(B) The change in the kinetic energy of the child is 143.74 J

(C) The change in thermal energy is 724.73 J

Conversion of potential energy to thermal energy:

(A) The gravitational potential energy of the child-Earth system is:

PE = mgh

now, according to the question the vertical position of the child is:

h = 10 sin25 = 4. 22 m

So,

PE = 21 x 9.8 x 4.22

PE = 868.47 J

(B) The change in kinetic energy of the child is:

KE = ¹/₂ mv²

KE = 0.5 x 21 x 3.7²

KE = 143.74 J

(C) According to the conservation of energy, the potential energy at the top must have been converted into kinetic energy at the bottom totally, but we see that the kinetic energy is less. So the remaining potential energy must have been converted into thermal energy.