1. Chapter 5
Work and Energy

2. Concept Check - Work
Is it possible to do work on an object that remains at rest?
1. yes
2. no

3. Concept Check - Work
Is it possible to do work on an object that remains at rest?
1. yes
2. no
Work requires that a force acts over a distance. If an object does not move at all, there is no displacement, and therefore no work done on that object.
Does that mean that no work is being done?

4. Work
Isometric exercises do work on the muscle tissue itself without doing work on an external object.

5. Concept Check – Play Ball!!
In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball?
1. catcher has done positive work
2. catcher has done negative work
catcher has done zero work

6. Concept Check – Play Ball!!
In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball?
1. catcher has done positive work
2. catcher has done negative work
catcher has done zero work
The force exerted by the catcher is opposite in direction to the displacement of the ball, so the work is negative. Or using the definition of work (W = F d cos q ), since  = 180o, then W < 0. Note that because the work done on the ball is negative, its speed decreases.

7. Concept Check – Work and Tension
A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension?
1. tension does no work at all
2. tension does negative work
3. tension does positive work v T

8. Concept Check – Work and Tension
A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension?
1. tension does no work at all
2. tension does negative work
3. tension does positive work
No work is done because the force acts in a perpendicular direction to the displacement. Or using the definition of work (W = F d cos q ), since  = 90°, then W = 0. v T
Follow-up: Is there a force in the direction of the velocity?

9. Concept Check – Work and Friction
A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?
1. friction does no work at all
2. friction does negative work
3. friction does positive work Fk Fn Fg
displacement Fa

10. Concept Check – Work and Friction
A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?
1. friction does no work at all
2. friction does negative work
3. friction does positive work
Friction acts in the opposite direction to the displacement, so the work is negative. Or using the definition of work (W = F d cos q ), since  = 180o, then W < 0. Fk Fn Fg
displacement Fa

11. Work = Force × displacement
Definition of Work
In order for mechanical work to be done: Force must act on object Object must move*
Work is a scalar, but it can be + or – (+) if Force and motion are in same direction (–) if Force and motion are in opposite directions
Many forces can do work on the same object. Even friction can do work.
Fn and any other force that is  to the direction of the motion will do no work. Only forces and components that are ∥ to the motion do work.
The simplified form for the equation for work is:
Work = Force × displacement
* Sometimes it appears that no work is being done when it really is, like when you do isometric exercises.

12. Definition of Work
Work is done on an object when a force causes a displacement of the object.
Work is done only by components of a force that are parallel to a displacement.
Work is equal to the product of force and the displacement it produces and the cosine of the angle between their directions.

13. Sample Fg = 1.50 x 103 N Fa = 345 N d = 24.0 m mk = 0.220 Wa = ?
Wk = ?
Wn= ?
Wg = ?
SW = ?
Which ends up in the form of KE

14. Problem – 1
Fg = 5.00 x 109 N
Ft = 5.00 x 103 N
d = 3.00 km = 3.00 x 103 m
Wt = ?

15. Problem – 3
Fa = 35 N
θ = 25°
d = 50.0 m
Wa = ?

16. Problem – 4 Fg Fa d q
Wa = ?
Wk = ?
Wn = ?
Wg = ?
mk = ?

17. Mechanical Energy Mechanical Energy
Work is the transfer of Mechanical Energy from one form to another.
Mechanical Energy
Kinetic Energy
(energy of motion)
Potential Energy
(energy of position)
Gravitational
Elastic
𝐾𝐸= 𝑚𝑣 2
𝑃𝐸 𝑔 =𝑚𝑔ℎ
𝑃𝐸 𝑒 = 𝑘𝑥 2

18. Kinetic Energy
Kinetic energy is energy of motion. It depends on mass and speed.
Kinetic Energy
The energy of an object that is due to the object’s motion is called kinetic energy.

19. Kinetic Energy (Units)
The energy of an object that is due to the object’s motion is called kinetic energy.
These are the same units as for Work! Coincidence? I think not.

20. Gravitational Potential Energy
PEg = mgh
gravitational PE = mass  free-fall acceleration  height
Potential Energy is the energy associated with an object because of the position, shape, or condition of the object.
Gravitational potential energy is the potential energy stored in the gravitational fields of interacting bodies.
Gravitational potential energy depends on height from a zero level.
Given the zero location defined in Diagram A, how much PE would the ball have at points A,B,C,D, and E?

21. Elastic Potential Energy
Elastic potential energy is the energy available for use when a deformed elastic object returns to its original configuration.
The symbol k is called the spring constant, a parameter that measures the spring’s resistance to being compressed or stretched.

22. Springs in a car

23. Energy v. Time for Bouncing Ball
When we say that something is conserved, we mean that it remains constant

24. Conservation of Mechanical Energy
Mechanical energy is the sum of kinetic energy and all forms of potential energy associated with an object or group of objects.
ME = KE + PEg + PEe
Mechanical energy is conserved (remains constant) in the absence of friction even though the individual forms may change and acceleration may not be constant.
MEi = MEf
(KE + PEg + PEe)i = (KE + PEg + PEe)f
The mathematical expression for the conservation of ME depends on the forms of potential energy given in a problem.

25. Sample h = hi = 3.00 m m = 25.0 kg vi = 0.0 m/s hf = 0 m vf = ?
(Top) (Bottom)

26. Conservation of Mechanical Energy
While individual forms of energy may change, the total mechanical energy remains constant (conserved) if there is…
…little or no friction (including air resistance)
…no collision in which significant heat is released
Procedure:
1. Determine the forms of energy present (KE, PEg, PEe) .
2. Write expressions for the various energies at the beginning of the motion (KE + PEg + PEe)i and at the end (KE + PEg + PEe)f , where 𝐾𝐸= 𝑚 𝑣 2 , 𝑃 𝐸 𝑔 =𝑚𝑔ℎ, and𝑃 𝐸 𝑒 = 𝑘 𝑥 2 (identify when some terms will be zero).
3. Use the Law of Conservation of Energy (the total mechanical energy, ME, remains constant) to produce an equation that can be solved for the unknown.

27. Problem – 6 m hi g
vf = ?

28. Problem – 8 hi m g vi
vf = ?

29. Sample m k x
vi = 0
vf = ?
(Initial) (Final)

31. Finding h for a pendulum

32. Problem – 14 m k x g
hf = ?

33. Work and Kinetic Energy
A child on a skateboard is moving at a speed of 2 m/s. After a force acts on the child, her speed is 3 m/s. What can you say about the work done by the external force on the child?
1. positive work was done
2. negative work was done
3. zero work was done

34. Work and Kinetic Energy
A child on a skateboard is moving at a speed of 2 m/s. After a force acts on the child, her speed is 3 m/s. What can you say about the work done by the external force on the child?
1. positive work was done
2. negative work was done
3. zero work was done
The kinetic energy of the child increased because her speed increased. This increase in KE was the result of positive work being done. Or, from the Work-Kinetic Energy Theorem, W = DKE = KEf – KEi. Since we know that KEf > KEi in this case, then the work W must be positive.
Follow-up: What does it mean for negative work to be done on the child?

35. Work and Kinetic Energy
𝐹 𝑎
If an object changes 𝐾𝐸, then Work was done on the object AND
the net work done on the object EQUALS the change in 𝐾𝐸
Σ𝑊=∆𝐾𝐸
net work = change in kinetic energy
This applies regardless of the nature of the forces doing work (i.e. friction)
Work-Kinetic Energy Theorem
The net work done by all the forces acting on an object is equal to the change in the object’s kinetic energy.
The net work done on a body equals its change in kinetic energy.
There are two ways to consider this relationship. The first is that one can find the net work done on an object by simply finding the change in kinetic energy of the object (KEf – KEi). Alternately, one can find the change in KE of an object by determining the net work done by adding together the work done by each force. Since work is a scalar, this is a scalar sum.

36. Sample
Fa DKE
d = ?

37. Sample m = 10.0 kg mk = 0.10 g = 9.81 m/s2 vi = 2.2 m/s vf = 0 m/s
d = ?
Which is the only force that will contribute to the net work?

38. power = work ÷ time interval
Rate at which work is done, or rate at which energy is transferred.
𝑃= 𝑊 ∆𝑡
𝑃= 𝐹𝑑 ∆𝑡 =𝐹 𝑑 ∆𝑡
Power is a quantity that measures the rate at which work is done or energy is transformed.
P = W/∆t
power = work ÷ time interval
An alternate equation for power in terms of force and speed is
P = Fv
power = force  speed
𝑃=𝐹𝑣

39. Simple Machines
Actual Mechanical Advantage (AMA) is the ratio of how much force is applied by the machine to how much force is applied to the machine.

40. Simple Machines
Ideal Mechanical Advantage (IMA) is the ratio of how far the effort moves the machine to how far the machine moves the load.

41. Simple Machines

42. Levers

43. Pulleys
= 𝑑 𝑖𝑛 𝑑 𝑜𝑢𝑡

44. Inclines

45. Zipper

46. Wheel and Axle

47. Wheel and Axle

48. Sample
The efficiency of a squeaky pulley system is _____ %. The pulleys are used to raise a mass to a certain height. What force is exerted on the machine if a rope is pulled _____ m in order to raise a _____ kg mass a height of _____ m?
eff
din
dout m g
Fin = ?