(1) How does the work required to stretch a spring 2 cm compare with the work re

Question

(1) How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm?

(2) A cart starting from rest rolls down a hill and at the bottom has a speed of 4 m/s. If the cart were given an initial push,so its initial speed at the top of the hill was 3 m/s, what would be its speed at the bottom?

(3) Is it possible to do work on an object that remains at rest?

(4) A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension?

(5) By what factor does the kinetic energy of a car change when its speed is tripled?

Explanation / Answer

here,
Work required on spring to stretch or compress can be found out by using :

Ws = 1/2 * K * X^2
Where,
K = spring constant
x = Strech(+) or compress distance(-)

1.)
case 1, X = 2 cm = .02m
Ws1 = 1/2 * K * .02^2

case 2, X = 1 cm = .01m
Ws2 = 1/2 * K * .01^2

Ws1/Ws2 = .02^2 / .01^2

Ws1 = 4 Ws2

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