1. The Work Energy Principle
By Heather Britton

2. What is the meaning of work?
Work in the world of physics does not have the same definition as in everyday life
In physics we define work as a force applied over a distance
To put work in terms of an equation it would read
Work = force x distance

3. W = F x Work (W) is measured in Joules (J)
Force (F) is measured in Newtons (N)
Delta x (final position - initial position) is measured in meters (m)
Therefore one J = 1Nm

4. Work is Scalar
Work is a scalar quantity so it only has magnitude (how much)
If the force is directed along the line of motion, work is positive
If the force is directed opposite the line of motion, work is negative

5. Example 1
If a person must exert a force of 20 N to move a box 5 m, how much work did the person do?
Answer
F = 20 N
W = F(x)
x = 5 m
W = 20 N (5 m)
W = 100 J

6. Force Applied at an Angle
Recall from Newton’s Laws that a force applied at an angle has an x component and a y component
Using trig functions of sine and cosine we can resolve that force into its components
x = cos θ
y = sin θ

7. Force at an Angle
The force applied to an object must be in the plane of displacement to calculate work
When a box is picked up off the floor, the force is directed upward. The box moves in the direction of the force, and work is done
When the box is carried across the room the force is still upward to counteract gravity. The displacement is horizontal, so no work is done

8. Practice

9. Example 2
A 25 N force is applied to a crate at an angle of 30 degrees, and the crate moves 10 meters. What is the magnitude of work done on the crate?
Answer
216.5 J

10. Example 3
A weightlifter is bench pressing a total mass of 100 kg. He lifts the mass up 0.8 meters, and then lowers it back to his chest 0.8 meters. How much work is done in (a)lifting the mass, (b) lowering the mass, and (c) what is the total amount of work?
Answer
(a) 784 J (b) -784 J (c) 0

11. Friction and Work
Friction is a force, therefore when it acts over a distance it has the ability to do work
Since friction opposes motion it does negative work
To find the total work the two must be added together.

12. Example 4
A person applies a force of 200 N to move a 75 N couch across the room (total displacement = 6 m). How much work is done on the couch if the coefficient of friction between the couch and carpet is 0.5?
Answer
975 J