1. Work & Energy
Physics, Chapter 5

2. Work
Section 5.1

3. Definition of Work
In Physics, work means more than something that requires physical or mental effort
Work is done on an object when a force causes a displacement of the object
Work is the product of the force applied to an object and the displacement of the object

4. Caution!
Work is done only when a force or a component of a force is parallel to a displacement!

5. Net Work Done by a Constant Net Forceθ
F cos θ d

6. Units of Work The SI unit of work is the joule (J)
Derived from the formula for work
The joule is the unit of energy, thus….
Work is a type of energy transfer!!

7. Sample Problem A
How much work is done on a sled pulled 4.00 m to the right by a force of 75.0 N at an angle of 35.0° above the horizontal? F
Fd cosθ θ d

8. How much work was done by Fg on the sled?FN
Fup F Fy Fx θ Fk d
How much work was done by Fg on the sled?
How much work was done by Fup on the sled?
If the force of kinetic friction was 20.0 N, how much work was done by friction on the sled? Fg

9. The Sign of Work
Work is a scalar quantity and can be positive or negative
Work is positive when the component force & displacement have the same direction
Work is negative when they have opposite directions

10. F
Fup θ Fk d Fg
If the force of kinetic friction was 20.0 N, how much work was done by friction on the sled?
Wf = Fk∙d = (-20.0 N)(4.00 m) = J

11. Graphical Representation of Work
Work can be found by analyzing a plot of force and displacement
The product F∙d is the area underneath and Fd graph

12. Graphical Representation of Work
This is particularly useful when force is not constant (which it normally isn’t)

13. Energy
Section 5.2

14. Kinetic Energy
Kinetic energy is energy associated with an object in motion
KE is a scalar quantity
KE depends upon an objects mass and velocity
SI unit is the joule

15. Sample Problem B
What is the speed of a 145 g baseball whose kinetic energy is 131 J?
Show that the solution is dimensionally consistent.

16. Relationship of Work and Energy
Work is a transfer of energy
Net work done on an object is equal to the change in kinetic energy of the object

17. Proof of W-KE Theorem

18. Importance of W-KE Theorem
Some problems that can be solved using Newton’s Laws turn out to be very difficult in practice
Very often they are solved more simply using a different approach…
An energy approach.

19. Sample Problem C
A 10.0 kg sled is pushed across a frozen pond such that its initial velocity is 2.2 m/s. If the coefficient of kinetic friction between the sled and the ice is 0.10, how far does the sled travel? (Only consider the sled as it is already in motion.) vi FN Fk mg d

20. Fk FN mg d

21. Potential Energy PE is “stored” energy
It has the “potential” to do work
Energy associated with an object due to its position
Gravitational PEg
Due to position relative to earth
Elastic PEe
Due to stretch or compression of a spring

22. Two Types of Potential Energy
Elastic
Gravitational
PEe = ½ kx2
PEg = mgh

23. Gravitational Potential Energy
Gravitational PE is energy related to position
PEg = mgh
Gravitational PE is relative to position
Zero PE is defined by the problem
If PEc is zero, then PEA > PEB > PEC

24. Elastic Potential Energy
PE resulting from the compression or stretching of an elastic material or spring.
PEe = ½ kx2 where…
x = distance compressed or stretched
k = spring constant
Spring constant indicates resistance to stretch.

25. 5.3 Conservation of Energy Objectives
At the end of this section you should be able to
Identify situations in which conservation of mechanical energy is valid
Recognize the forms that conserved energy can take
Solve problems using conservation of mechanical energy

26. Conserved Quantities
For conserved quantities, the total remains constant, but the form may change
Example: one dollar may be changed, but its quantity remains the same.
Example: a crystal of salt might be ground to a powder, but the mass remains the same. Mass in conserved

27. Mechanical Energy Is conserved in the absence of friction MEi = MEf
i.e. initial ME equals final ME
MEi = MEf
If ME = KE + PE
Then KEi + PEi = KEf + PEf
½ mvi2 + mghi = ½ mvf2 + mghf

28. Conservation of Mechanical Energy ( A Falling Egg)
Time (s)
Hght (m)
Spd (m/s) PE
(J) KE ME
0.00
1.00
0.74
0.10
0.95
0.98
0.70
0.04
0.20
0.80
2.00
0.59
0.15
0.30
0.56
2.90
0.41
0.33
0.40
0.22
3.90
0.16
0.58
0.45
4.43
As a body falls, potential energy is converted to kinetic energy
Since ME is conserved (constant)…. ΣPE + KE = ME
In the absence of friction & air resistance, this is true for mechanical devices also

29. Mechanical Energy Is the sum of KE and all forms of PE in the system
ME = ΣKE + ΣPE
sigma (Σ ) indicates “the sum of”

30. Sample Problem 5E
Starting from rest, a child of 25.0 kg slides from a height of 3.0 m down a frictionless slide. What is her velocity at the bottom of the slide?
Could solve using kinematic equations, but it is simpler to solve as energy conservation problem.
MEi = MEf

31. ME may not be conserved
In the presence of friction, mechanical energy is not conserved
Friction converts some ME into heat energy
Total energy is conserved
MEi = MEf + heat

32. Work-Kinetic Energy Theorem
The net work done on an object is equal to the change in kinetic energy of the object
Wnet = ∆KE
The work done by friction is equal to the change in mechanical energy
Wfriction = ∆ME

33. Power Is the rate of work, the rate at which energy is transferred
P = W/∆t
Since W = Fd, P = Fd /∆t or
P = Fvavg
Unit of power = the watt (W)
1 W = 1 J/s
1 hp = 746W horsepower