1. Chapter 10 Work and Energy

2. Objectives:
Describe work in terms of force and displacement, using the definition of the scalar product.
Solve problems involving concept of work.
Distinguish between the resultant work and the work of a single force.
Define the spring constant and calculate the work done by a varying spring force.

3. Three things are necessary for the performance of work:q x
There must be an applied force F.
There must be a displacement x.
The force must have a component along the displacement.

4. Work = Force component X displacement
Definition of Work
Work is anything that can exert a force through a distance.
a scalar quantity
Work = Force component X displacement
Unit:
1 Nm = 1 Joule (J)

5. Work can be:
Positive, when force applies in the same direction as the displacement. F x
Negative, if the force is opposite displacement direction

6. If a force does not affect displacement, it does no work.
Work done by any force that is at right angles with displacement will be zero (0).
The force F exerted on the pot by the man does work. F W
The earth exerts a force W on pot, but does no work even though there is displacement.
If a force does not affect displacement, it does no work.

7. Resultant Work or Net Work
Resultant work is the algebraic sum of the individual works of each force. F x f
Example: F = 40 N, f = -10 N and x = 4 m
Work = 120 J
Work = (40 N)(4 m) + (-10 N)(4 m) OR
Example: Work = (F - f) x
Work = ( N)(4 m)

8. Note: Work is positive since Fx and x are in the same direction.
Example 1: A lawn mower is pushed a horizontal distance of 20 m by a force of 200 N directed at an angle of 300 with the ground. What is the work of this force?
300
x = 20 m
F = 200 N F
Work = (F cos q ) x
Note: Work is positive since Fx and x are in the same direction.
Work = (200 N)(20 m) Cos 300
Work = 3460 J

9. Graph of Force vs. Displacement
Assume that a constant force F acts through a parallel displacement Dx.
Force, F
The area under the curve is equal to the work done. F x1 x2
Area
Work = F(x2 - x1)
Displacement, x

10. Example for Constant Force
What work is done by a constant force of 40 N moving a block from x = 1 m to x = 4 m?
40 N
Force, F
Displacement, x
1 m
4 m
Area
Work = F(x2 - x1)
Work = (40 N)(4 m - 1 m)
Work = 120 J

11. Work of a Varying Force
Our definition of work applies only for a constant force or an average force.
What if the force varies with displacement as with stretching a spring or rubber band? F x F x

12. Hooke’s Law
When a spring is stretched, there is a restoring force that is proportional to the displacement.
F = -kx F x m
The spring constant k is a property of the spring given by:
K = DF Dx

13. Work Done in Stretching a Spring
Work done ON the spring is positive; work BY the spring is negative. F x m
From Hooke’s law: F = kx
Work = Area of Triangle x F
Area = ½ (base)(height) = ½ (x)(Favg ) = ½ x(kx)
Work = ½ kx2

14. Compressing or Stretching a Spring Initially at Rest:x m
Compressing
Stretching
Two forces are always present: the outside force Fout ON spring and the reaction force Fs BY the spring.
Compression: Fout does positive work and Fs does negative work (see figure).
Stretching: Fout does positive work and Fs does negative work (see figure).

15. General Case for Springs:
If the initial displacement is not zero, the work done is given by: x1 x2 F x1 m x2

16. Power of 1 W is work done at rate of 1 J/s
Power is defined as the rate at which work is done: (P = dW/dt )
Power of 1 W is work done at rate of 1 J/s

17. Units of Power
One watt (W) is work done at the rate of one joule per second.
1 W = 1 J/s and 1 kW = 1000 W
One ft lb/s is an older (USCS) unit of power.
One horsepower is work done at the rate of 550 ft lb/s. ( 1 hp = 550 ft lb/s = 746 W)

18. Recognize that work is equal to the change in kinetic energy:
Example 4: A 100-kg cheetah moves from rest to 30 m/s in 4 s. What is the power?
Recognize that work is equal to the change in kinetic energy:
m = 100 kg
Power Consumed: P = 1.22 kW

19. CONCLUSION: Chapter 10 - Work