# Calculations for Work, Potential Energy, and Power

An iron ball having a mass of 5 kg is lifted from the floor to a height of 2.5 meters above the floor.

a) How much work was done to lift the ball?

b) How much potential energy did the ball gain?

c) If the motor lifting the ball raises it 2.5 meters in ten seconds, what is its power?

If a 600 kg car is moving with a speed of 25 m/s, that what is its kinetic energy? State your answer in Joules. What is its momentum? What are the correct units of measurement for momentum?

A 200 g ball is thrown upwards with an initial kinetic energy of 10 Joules. What maximum height will the ball reach? (neglect air resistance)

If a 200 g ball is dropped from 100 meters what is its velocity just before it hits the ground? What is its velocity after it has fallen halfway to the ground (50 m)? (neglect air resistance)

Two bumper cars collide head-on. Before the collision, car 1 is coming from the right at 3 m/s and has a total mass of 200 kg. Car 2 is coming from the left at 5 m/s and has a total mass of 250 kg (the driver of car 2 is a lot fatter than the driver of car 1) At the time of the collision, the bumpers lock and the cars remain stuck together after the (inelastic) collision. Calculate the velocity (direction and speed) of the linked cars following the collision.

#### Solution Preview

a) When the ball is raised, work is done against gravity. The amount of work done is equal to the energy gained by the ball. Let us use the value of the acceleration due to gravity g as 10m/s^2 throughout this problem.

m = 5kg, h = 2.5m, g = 10m/s^2

W = m x g x h = 5kg x 2.5m x 10m/s^2 = 125J

b) Potential energy gained = work done on the ball = 125J

Remember that work is done each time energy is converted from one form to another and that work and energy have the same units.

c) Power is the rate at which work is done, that is, power = work/ time

= 125J/10s = 12.5J/s (or Watts)

Kinetic energy = 1/2 x m x v^2 = 1/2 x 600Kg x 25m/s x 25m/s = 187,500J

Momentum = mass x ...

#### Solution Summary

This solution provides step by step calculations for work, potential energy, and power.