## Work and Power

Work is done any time you are transforming one form of energy into another. Power is the rate at which you do work. Learn more and see examples here.

### Work

Work happens when transforming energy into another form.

Gravity does work to convert potential energy to kinetic while a ball falls.  When you lift a ball up, you are do work transforming and storing potential energy back in the ball.

The MKS units for different forms of energy including transforming one to another, or work, is the Joule (J). In this unit, we will talk about mechanical energy that consists of potential and kinetic energy.

### Work and Power Variables and Units

 Name Variable Unit Unit Abbreviation Work W Joules J Power P watt W Time t seconds s ### Work Equation Facts

Only the force component in the direction of motion does work.  When pulling a suitcase, using a handle at an angle, you will only get a portion creating work.  So only get the component in the direction or parallel to the motion goes into work.

The following questions seen in the image are using the basic work equation.

### No Motion Means No Work

When applying force to an object that does not move, there is no work done.  No matter how hard you push a wall, if it does not move, you do no work.

If you climbing upwards you would carry your weight up a distance or height.  Just a reminder that weight (Fw = mg) and g is the acceleration due to gravity (g = g = 9.8 m/s2). ### Example Problems

1. How much work is a stickman doing while pushing a box 5 meters with a force of 12 N forward?

W = (F)(d)

Since the force is in the same direction as motion you plug numbers directly in and don't have to find the parallel component first.

W = (12)(5) = 60 J

(Click on the picture to enlarge it)

2. What is the power output of the stickman that pushes the box 5 meters in 3 seconds with a constant force of 12 N? ### Work and Power When Force is at an Angle

When force is at an angle, you only get the component in the direction of motion applied to work.  The way the picture here is drawn the red arrow would be the component.  Since we are trying to determine the adjacent side, we use the cosine function, which has adjacent, and hypotenuse included.

### 3. How much work do you have when 12 N of force were applied on an object at an angle of 25° above the horizon to move an object 5 meters horizontally?

A) Find the horizontal component of force:

B) Find out how much work is done by this component:

W = (F)(d)

W = (10.9)(5) = 54.5 J

4. What is your power output when applying 12 N of force on an object at an angle of 25° above the horizon to move it 5 meters horizontally in 3 seconds?

Use the work from the previous problem above

W = (F)(d) = (10.9)(5) = 54.5 J

and then solve for power

P = W/t

P = 54.5/3 = 18.2 W

(Click on the picture to enlarge it)

(Click Here for All the Work and Power Example Problems and Solutions) ## Work and Power Practice Quiz

Work and Power Quiz

Do you know your work and power? Take out quiz to find out

1 / 9

What is the unit of energy?

2 / 9

What is the unit of power?

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What is the unit of work?

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What is the power output when it takes a force of 50N forward is applied to move a box 6 meters in the same direction in 6 seconds?

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How much work is done when a force of 50N forward is applied to move a box 6 meters in the same direction?

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How much work would you have done if you pushed on a 2100 kg car with a force of 210N that did not move?

7 / 9

A student lifts a physics book applying a force equal to is 10N weight a distance of 3m up. How much work did the student do on the book?

8 / 9

How much work would a 75 kg student do to climb up a ladder 9 meters?

9 / 9

Sergio pushed a box with 50 Newtons of force forward.  When it did not move he pushed the box even harder with 100 Newtons of force but the box still did not move.  When did Sergio do more work?