Starting from rest, Jack and Jill skateboard down a hill as shown in the sketch.

Question

Starting from rest, Jack and Jill skateboard down a hill as shown in the sketch.
Assume that friction and air resistance are negligible.
Jack has more mass than Jill and rides steeper side but their height of descent is same.

Jack Jill Starting from rest, Jack and Jill skateboard down a hill as shown in the sketch. Assume that friction and air resistance are negligible. Jack has more mass than Jill and rides steeper side but their height of descent is same. (a) Is the speed at the bottom of the hill greater for Jack, greater for Jill, or the same for both? Support your answer with laws of physics and good explanation. (b) Is the time it takes to get to the bottom of the hill greater for Jack, greater for Jill, or same for both? Explain (c) Is the kinetic energy at the bottom of the hill greater for Jack, greater for Jill, or the same for both? Explin (d) Is the work done by the gravitational force greater for Jack, greater for Jill, or the same for both? Explain. e) Is the work done by the gravitational force greater for Jack, greater for Jill, or the same for both? Explain.

Explanation / Answer

Solution:

According to conservation of energy , total energy at the highest point = total energy at the lowest point of travel.

Speed at the bottom of the hill is same for both.From the law of conservation of energy

the potential energy at the highest point is equal to the kinetic energy on reaching the bottom.

mgh= 1/2mv^2. For a given mass or object, the velocity is therefore independent of the mass of the body. It depends only on gravity and height of fall.

b) Time taken to reach the bottom of the hill t =final velocity/ gravity from v f=vi +at

So it is same (equal) for both.

c) Jack has more mass than Jill. SO the heavier one has MORE kinetic energy.

Jack has more kinetic energy =1/2 Mv^2

d) gravitational force = Mg for Jack , if his mass is M

gravity force for Jill is mg , if Jill's mass is m

Work done depends on the mass . So more work is done on Jack since his mass is greater.

Work done by GPE = mgh

e) Same as part d.

it is the gravitational potential energy which does work and is Mgh &mgh respectively, for both Jack & Jill.

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