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?

Answer 1

1)

as potential energy = 0.5 * k * x^2

work done to stretch the spring = 0.5 * k * x^2

work required to stretch 2 cm /work required to stretch 1 cm = 0.5 * k * 0.02^2/(0.5 * k * 0.01^2)

work required to stretch 2 cm /work required to stretch 1 cm = 4

the ratio work required to stretch 2 cm to work required to stretch 1 cm is 4 J

2)

let the speed of velocity is v

0.5 * m * v^2 = 0.5 * m * 4^2 + 0.5 * m * 3^2

v = 5 m/s

the speed at the bottom is 5 m/s

3)

as the displacement = 0 m

work done = 0 * force

work done = 0 J

4)

as the tension in perpendicular to the direction of motion

work done = F * d * cos(90)

work done = 0 J