# 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.

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#### 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.

Total of twenty questions related to work, energy, power, simple pendulum, electricity, electric power, gravitational potential energy, kinetic energy ,Celsius temperature, Kelvin temperature, specific heat, heat and Ideal gas law.

1. A force of 7.2 N acting on a 1.0-kg object initially at rest moves it through a parallel distance of 2.5 m. How much work is done on the object?

2. Neglecting friction, what is the speed of the object in Question 1 when it has moved 2.5 m?

3. A 0.10-kg ball is dropped from a height of 10 m and rebounds to a height of 8.0 m. How much energy was lost, and what happened to it?

4. A student weighing 700 N climbs a flight of stairs 5.0 m high. Calculate the work done.

5. If the student in Question 4 climbs the stairs in 10 s, what power was required?

6. The bob of a simple pendulum is 0.50 m above the floor at its lowest position. Calculate the maximum speed of the bob when it is held at a maximum height of 2.5 m and released.

7. Given 10 kWh of electricity and assuming no losses, how much work, in joules, could be done?

8. A 5.00-kg object is lifted from the floor to a shelf. The object's new gravitational potential energy relative to the floor is 102 J. What is the height of the shelf?

9. Work in the amount of 280 J is done in lifting an object a distance of 4.0 m in a time of 7.0 s. How much power was required?

10. Car B is traveling twice as fast as Car A, but Car A has twice the mass of Car B. Which car has the greater kinetic energy and by what factor?

11. It is 23 ° F outside. What is the Celsius temperature?

12. For a temperature of − 40 ° F, what are the corresponding temperatures on the Kelvin scale?

13. When 10 kcal of heat is added to 2.0 kg of a substance, its temperature increases 20 C ° . What is the specific heat of the substance?

14. How much heat is required to melt 5.0 kg of ice at 0 ° C to water at 0 ° C?

15. How much heat is necessary to change 20 g of ice at − 10 ° C into water at 20 ° C?

16. How many kcal of heat would be needed to melt 0.12 kg of ice at 0 ° C and increase the temperature to 25 ° C?

17. A constant volume and mass of helium gas at 27 ° C is heated so that the pressure of the gas doubles. What is the new temperature of the gas in degrees Celsius?

18. The number of molecules in a container is tripled and the Kelvin temperature doubled. The volume remains unchanged. The new pressure will be how many times greater than the original pressure?

19. An ideal gas is confined to a container with an adjustable volume. If the number of molecules and temperature are held constant, by what factor will the volume change when the pressure is tripled?

20. The piston of a cylinder containing a quantity of ideal gas is advanced so that the volume of the gas is decreased by one-half. A pressure gauge on the cylinder shows the pressure of the gas to have increased threefold in the process. By what factor does the temperature of the gas change?

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