8-16 A littel person is going down a slide at the playground. She discovers that

Question

8-16 A littel person is going down a slide at the playground. She discovers that she has some control over her velocity by pressing her feet outward against the side rails of the slide so as to change the rate at which her engergy is converted into heat by friction.

Given: The little person has a mass of 20.kg and starts at the top of a 15m long slide, which is inclined at an angle of 50. degrees to the ground. Only 25% of her potential energy is coverted into kinetic energy.

a) What is the little person's potential energy when she is at the top of the slide?

b) How much Kinetic energy does she have at the bottom of the slide?

c) What is her speed at the bottom of the slide?  

Explanation / Answer

Here,

m = 20 Kg

L = 15 m

theta = 50 degree

a) little person's potential energy = mgh

little person's potential energy = 20 * 9.8 * 15 * sin(50 degree)

little person's potential energy = 2252 J

b)

for the kinetic energy at the bottom

kinetic energy at the bottom of the slide = 0.25 * potential energy at the top

kinetic energy at the bottom of the slide = 0.25 * 2252

kinetic energy at the bottom of the slide = 563 J

c)

let the speed is v

0.50 * 20 * v^2 = 563

v = 7.50 m/s

the speed at the bottom is 7.50 m/s

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