1. Chapter 6: Work, energy , and power
6-2 Kinetic energy
6-3 Potential energy and conservative forces
6-4 Dissipative forces
6-9 power
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2. 6-1 Work In physics, work has a very specific meaning.
In physics, work represents a measurable change in a system, caused by a force.
Work is done on a system where an applied force results in some net displacement
A force that results in no displacement does no work
A displacement that results with no applied force has had no work done
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3. Work (force is parallel to distance)
What do forces do?
They change the speed of a mass
They do work on a mass
They change the energy of a mass
Work (force is parallel to distance)
Force (N)
Work (joules)
W = F x d
Distance (m)
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4. Norah Ali Al - moneef
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5. Work… W = F d cos q definition of work
d - the displacement of the point of application of the force
q - is the angle between the force and the displacement vectors
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6. Work Relates force to change in energy Scalar quantity
Independent of time
Units of Work and Energy
SI unit = Joule
1 J = 1 Nm = 1 kgm2/s2
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7. Work…
W = F d cos q
A force does no work on the object if the force does not move through a displacement
The work done by a force on a moving object is zero when the force applied is perpendicular to the displacement of its point of application cos 90 = 0
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8. The Scalar Product of Two Vectors
Our definition of work: W = F d cos q is messy because of the cosine factor
What we are actually doing is performing an operation with two vectors called the scalar product:
It is also called the dot product
q is the angle between A and B
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9. More About Work
The sign of the work depends on the direction of the displacement relative to the force
Work is positive when the projection of F onto d is in the same direction as the displacement
Work is negative when the projection is in the opposite direction
Work zero: W = 0 if q = 90°
Work maximum if q = 0°
Work minimum if q = 180°
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10. W > 0
W < 0
W = 0
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11. Example: When Work is Zero
A man carries a bucket of water
horizontally at constant velocity.
The force does no work on the bucket
Displacement is horizontal
Force is vertical
cos 90° = 0
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12. Work can be positive or negative
Man does positive work lifting box
Man does negative work lowering box
Gravity does positive work when box lowers
Gravity does negative work when box is raised
Work is done on the books when they are being lifted, but no work is done on them when they are being held or carried horizontally.
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13. Work Done by a Constant Force
Example: Work done on the bag by the person..
 Special case: W = 0 J
a) W = F d cos ( 90o )
b) Wg = m g d cos ( 90o )
 Nothing to do with the motion
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14. Norah Ali Al - moneef
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15. example
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16. Work - Example W = F d cos q
The normal force ,, and the gravitational force, mg, do no work on the object
cos q = cos 90° = 0
The force does do work on the object
There is a component along the direction of motion
W = F d cos q
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17. Example :
A horizontal force F pulls a 10 kg carton across the floor at constant speed. If the coefficient of sliding friction between the carton and the floor is 0.30, how much work is done by F in moving the carton by 5m?   
The carton moves with constant speed. Thus, the carton is in horizontal equilibrium.
 F = f = μk N = μk mg.
 Thus F = 0.3 x 10 x 9.8
= 29.4 N
 Therefore work done W = FS
=(29.4 Cos 0o)
=147 J
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18. Norah Ali Al - moneef
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19. Example
Three student push their car which run out of gas. If each student pushes with a force of 500 N and the car pushed a distance of 40 m, find the work done by the student s
A man exert a horizontal force 160 N on a car that moves a distance of 10m calculate the work done by the force
A student pushes on a heavy box with a force of 400 N and moves it a distance of 5 m . If the force applied at an angle of 37 shown below , find the work done by the student
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20. Work Done by a Varying Force
We know that for a constant force the work is just
But if the force is not constant in space we have a problem
We will use an approach similar to that used to determine net displacement given a time varying velocity!
Consider a force in the x-direction with a magnitude that changes depending on the exact position.
We can carve that (the displacement xf-xi) displacement up into a bunch of small (very small) displacements.
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21. Work Done by a Varying Force
For each of these small displacements, the force will be nearly constant, in that case, W1 » FxDx (the area of the rectangle)
This will be true for all the intervals so we can form
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22. Work Done by a Varying Force, cont
Again, we make the intervals vanishingly small;
Therefore,
The work done is equal to the area under the curve
When more than one force acts on an object: or
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23. example
An Eskimo returning pulls a sled as shown. The total mass of the sled is 50.0 kg, and he exerts a force of 1.20 × 102 N on the sled by pulling on the rope. How much work does he do on the sled if θ = 30° and he pulls the sled 5.0 m ?
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24. Work and Multiple Forces
Suppose µk = 0.200, How much work done on the sled by friction, and the net work if θ = 30° and he pulls the sled 5.0 m ?
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25. Energy and Conservation of Energy
Energy is the ability to make things change.
A system that has energy has the ability to do work.
Energy is measured in the same units as work because energy is transferred during the action of work.
What are important kinds of energy?
1. Kinetic Energy
Energy of a mass in motion
Kinetic is moving energy (Dynamics)
Dependant on velocity
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26. Kinetic Energy:
A force F = 10 N pushes a box across a frictionless floor for a distance x = 5 m. The speed of the box is v1 before the push and v2 after the push. x F v1 v2 i m
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27. Kinetic energy and the Work-Kinetic energy theorem
The quantity is so important that we give it a special name.
The kinetic energy K of an object of mass m moving with a speed v is:
Kinetic energy is the energy of a particle due to its motion.
Kinetic energy is a scalar and has the same units as work (Joules)
Kinetic energy and the Work-Kinetic energy theorem
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28. Kinetic Energy Energy of motion is called kinetic energy.
The kinetic energy of a moving object depends on two things: mass and speed.
Kinetic energy is proportional to mass.
Mathematically, kinetic energy increases as the square of speed.
If the speed of an object doubles, its kinetic energy increases four times. (mass is constant)
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29. An object’s kinetic energy depends on its mass and its speed.2
The faster something is moving and the heavier it is, the more work it can do, so …
If ‘v’ tripled
then KE will increase by 9 times.
If ‘v’ quadruples,
then KE will increase by 16 times
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30. example
M= 4 kg
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31. Norah Ali Al - moneef
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32. Kinetic Energy and the Work-Kinetic Energy Theorem
A change in kinetic energy is one possible result of doing work to transfer energy into a system.
If the net work done on a particle is positive, the speed (and hence the kinetic energy) of the particle increases.
If the net work done on a particle is negative, the speed (and hence the kinetic energy) of the object decreases.
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33. Norah Ali Al - moneef
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34. Norah Ali Al - moneef
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35. M=6.00 kg
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36. Norah Ali Al - moneef
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37. Example 3 :
A 6.0-kg block initially at rest is pulled to the right along a horizontal, frictionless surface by a constant horizontal force of 12 N. Find the speed of the block after it has moved 3.0 m.
W =F d cos 0 =12x 3x1 = 36J
Δk = w
0.5m V2 =W =36 J
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38. Example
What acceleration is required to stop a 1000kg car traveling 28 m/s in a distance of 100 meters? .
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39. Example
A car traveling km/h to can brake to a stop within a distance of 20.0 m. If the car is going twice as fast, 120 km/h, what is its stopping distance ?
(a)
(b)
(1) Wnet = F d(a) cos 180o
= - F d(a) = 0 – m v(a)2 / 2
 - F x (20.0 m) = - m (16.7 m/s)2 / 2
(2) Wnet = F d(b) cos 180o
= - F d(b) = 0 – m v(b)2 / 2
 - F x (d ) = - m (33.3 m/s)2 / 2
(3) F & m are common. Thus, d = 80.0 m
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40. example
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41. example
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42. Δ k=
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43. Norah Ali Al - moneef
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44. Potential Energy 6 – 3 potential energy and conservative forces
Potential energy is associated with the position of the object within some system
Potential energy is a property of the system, not the object
A system is a collection of objects or particles interacting via forces or processes that are internal to the system
- Potential is stored energy (Statics) Dependant on height
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45. Height object raised (m)
Potential Energy
Gravitational potential energy is simple to calculate
Gravitational Potential Energy = weight X height
Work done against gravity
Mass (k g)
Height object raised (m)
Work (joules)
W =mgh
Gravity (m/sec2)
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46. Norah Ali Al - moneef
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47. Ball speeds up
Ball slows down
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48. Work Done by Gravity ball up Wg = (mg)(S) S =hf -h0 Wg =-mg(hf-h0)
Yi = hf
ball up
Wg = (mg)(S)
S =hf -h0
Wg =-mg(hf-h0)
= upot,initial – upot,final mg S y
Yi = h0
Yi = h x
,initial
Drop ball
Yf = h0
Wg = (mg)(S)
S =hf -h0
Wg = mg(hf -h0)
= mg(hf -h0)
= Epot, final – Epot, initial y y S x x mg
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Yf = hf

49. Work Done by the Gravitational Force
Work done on the ball by the gravity is:
If an object is moving down,
If an object is moving up,
Work done by the gravity only depends on the change of height, not depends on the path.
Norah Ali Al - moneef
29/07/1438

50. Potential Energy DU = -Dw Ugrav = +mgh DU = -Dw
The change in potential energy is equal to minus the work done BY the conservative force ON the body.
DU = -Dw h
Work done by gravity
= mg.(-h) = -mgh
Therefore change in PE is
DU = -Dw mg
Ugrav = +mgh
Lift mass m with constant velocity
Norah Ali Al - moneef
29/07/1438

51. example
What is the potential energy of a 12 kg mass raised from the ground to a to a height of 25 m?
Potential Energy = weight x height change
Weight = 12 x 10
= 120 N
Height change = height at end - height at start =
= 25 m
Potential energy = 120 x 25
= 3000 J
Norah Ali Al - moneef
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52. example
How much potential energy is lost by a 5Kg object to kinetic energy due a decrease in height of 4.5 m
PE = mgh
PE = (5Kg)(10 m/s2)(4.5 m)
PE = 225 Kg m2/s2
PE = 225 J
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53. example
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54. Norah Ali Al - moneef
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55. Norah Ali Al - moneef
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56. Conservative Forces Same as direct path (-mgh)
A force is conservative if the work done by it on a particle that moves between two points is the same for all paths connecting these points: otherwise the force is non-conservative.
Work done by gravity
w = -mgDh1+ -mgDh2+-mgDh3+…
Each step height=Dh
= -mg(Dh1+Dh2+Dh3 +……)
= -mgh
Same as direct path (-mgh) h
Examples for week 2
Chapter 6
Exercises 9,12, 59
Problems 17, 18, 24, 34, 36, 37, 43, 47, 61, 64, 66, 70
Chapter 7
Exercises 12, 14, 15, 28, 29, 35
Problems 6, 34, 38, 39, 47, 49.
Examples underlined are highly recommended.
The large print, underlined examples are to be handed to your tutor at the tutorial the week after next. -g
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57. Norah Ali Al - moneef
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58. Work done by gravity is independent of path taken between h0 and hf
Slide block down incline h0
Wg = (mg)(S)cos
S = h/cos
Wg = mg(h/cos)cos
Wg = mgh
with h= h0-hf  h S mg hf
Work done by gravity is independent of path taken between h0 and hf
=> The gravitational force is a conservative force.
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59. Norah Ali Al - moneef
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60. Who is going faster at the bottom?
Assume no friction
Assume both have the same speed pushing off at the top
same
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61. Norah Ali Al - moneef
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62. Norah Ali Al - moneef
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63. Doing Work to Decrease Energy
When you catch a ball, its kinetic energy is reduced (or absorbed) by the negative work you do on it
Your muscles do negative work on your limbs and absorb energy when you land from a jump or fall
Average force you must exert to absorb energy in catching a ball or landing from a jump or fall depends on how much energy must be absorbed and the displacement over which the force is absorbed
Safety and protective equipment used in many sports utilizes the work/energy principle to reduce potentially damaging impact forces
Examples of shock absorbing or energy absorbing materials
Landing pads (gymnastics, high jumping, and pole vaulting) increase displacement of the athlete during the impact period
Sand (long jumper), water (diver), midsole material in shoes (runner)
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64. Law of Conservation of Energy
As energy takes different forms and changes things by doing work, nature keeps perfect track of the total.
No new energy is created and no existing energy is destroyed.
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65. DU + DK = 0
Let’s check this for a body of mass m moving under gravity.
Dw = DK = Kf - Ki
DK = ½ mvf2 – ½ mvi2 xf vf h
Dw g= -Du = -mgh
+ve xi vi
Dw = -DU = DK
For motion under gravity you know
v2 = u2 + 2as
 vf2 = vi2 - 2gh
mult by ½ m  ½ m vf2 = ½ mvi2 -mgh mg
so DU + DK = 0
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66. Work-Energy Theorem Work = ΔKE Gives the same answer as above.
The work done on an object is equal to the change in its kinetic energy.
Work = ΔKE
If you know the height of the block, you can predict it’s speed at the bottom of the ramp!
(doesn’t matter how LONG the ramp is)
Gives the same answer as above.
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67. Weight =500 N
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68. example
At B
At C
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69. Example
A skier slides down the frictionless slope as shown. What is the skier’s speed at the bottom?
start
H=40 m
finish
L=250 m
28.0 m/s
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70. A truck of mass 3000 kg is to be loaded onto a ship using a crane that exerts a force of 31 kN over a displacement of 2m.Find the upward speed of truck after its displacement.
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71. Norah Ali Al - moneef
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72. Work-Energy Theorem
If we do work on an object and set it into motion without changing the object’s potential energy, the work done appears as kinetic energy of the object
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73. Work done on a system by external force
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74. Work – Energy Principle & Mechanical Energy Conservation
If we ignore non conservative forces (friction and the such), the implication is that no non-mechanical energies are present (heat, sound, light, etc) therefore…
As energy takes different forms and changes things by doing work, nature keeps perfect track of the total.
No new energy is created and no existing energy is destroyed.
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75. Work and Energy
If a force (other than gravity) acts on the system and does work
Need Work-Energy relation or
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76. Types of Forces There are two general kinds of forces Conservative
Work and energy associated with the force can be recovered
Non conservative
The forces are generally dissipative and work done against it cannot easily be recovered
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77. Conservative Forces
A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the points
The work depends only upon the initial and final positions of the object
Any conservative force can have a potential energy function associated with it
Examples of conservative forces include:
Gravity
Spring force
Electromagnetic forces
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78. Non conservative Forces
A force is non conservative if the work it does on an object depends on the path taken by the object between its final and starting points.
Examples of non conservative forces
kinetic friction
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79. Moving a block against friction at constant velocityd
Work done by me = F.d
Work done by friction = -f.d = -F.d
Total work done =
What happens if I let go?
NOTHING!!
Gravity is Conservative
Friction is NOT!!
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80. Example
Suppose the initial kinetic and potential energies of a system are 75J and 250J respectively, and that the final kinetic and potential energies of the same system are 300J and -25J respectively. How much work was done on the system by non-conservative forces?
1. 0J J J J J
correct
Work done by non-conservative forces equals the difference between final and initial kinetic energies plus the difference between the final and initial gravitational potential energies.
W = (300-75) + ((-25) - 250) = = -50J.
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81. Friction as a Non conservative Force
6-4 Dissipative forces
Friction as a Non conservative Force
The friction force is transformed from the kinetic energy of the object into a type of energy associated with temperature (internal energy)
the objects are warmer than they were before the movement
Internal Energy is the term used for the energy associated with an object’s temperature
Work can be done by friction
The energy lost to friction by an object goes into heating both the object and its environment
Some energy may be converted into sound
For now, the phrase “Work done by friction” will denote the effect of the friction processes on mechanical energy alone
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82. Friction Depends on the Path
The blue path is shorter than the red path
The work required is less on the blue path than on the red path
Friction depends on the path and so is a non-conservative force
Mechanical Energy Conservation with energy lost
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83. example a-
B -
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86. Norah Ali Al - moneef
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87. Norah Ali Al - moneef
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88. example
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89. Norah Ali Al - moneef
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90. Norah Ali Al - moneef
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91. Norah Ali Al - moneef
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92. Another solution
A ) Wgra=Fgra s cos 180 = - (mg sin 20) s =- 10 x 9.8 x5 x sin 20 = J
OR Wgra= -mg ( h-h0 ) = - 10 x 9.8 x s sin 20 = - 10 x9.8 x5 x sin 20= J
B ) wfriction = Ffriction s cos 180= -( mg cos 20 )s = -10 x9.8 x5 cos 20 = J
C ) wapp = F s cos o = 100 x5 = 500 J
wnet= wapp+ Wgra + wfriction= 500 – 168 – 184 = 148 J
D ) Δ K = wnet = 148 J
E ) K –K0 = 148 J
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93. Norah Ali Al - moneef
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94. Norah Ali Al - moneef
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95. Norah Ali Al - moneef
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96. Norah Ali Al - moneef
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97. example s Θ
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98. Norah Ali Al - moneef
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99. Norah Ali Al - moneef
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100. OR
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101. Norah Ali Al - moneef
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102. Norah Ali Al - moneef
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103. Norah Ali Al - moneef
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104. example
You are towing a car up a hill with constant velocity.
A )The work done on the car by the normal force is:
1. positive 2. negative 3. zero W T FN V
correct
The normal force is perpendicular to the displacement,
hence, does no work.
b )The work done on the car by the gravitational force is:
1. positive 2. negative 3. zero
With the surface defined as the x-axis, the x component of gravity is in the opposite direction of the displacement, therefore work is negative.
correct
C ) The work done on the car by the tension force is:
1. positive 2. negative 3. zero
correct
Tension is in the same direction as the displacement.
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105. 6-9 power
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106. Power
Takes more power to run up the stairs than to walk up the stairs, but the energy consumed is the same in either case
Unit is the WATT
A Watt is a newton--meter per second
Bigger units are kilowatts and megawatts
Utility sells energy in kilowatt-hours
1 KWh = 1000 Joules/second times 3600 Seconds = 3.6 X 106 Joule
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107. Norah Ali Al - moneef
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108. Example:
Killer whales are able to accelerate up to 30 mi/h in a matter of seconds. Disregarding the considerable drag force of water, calculate the average power a killer whale with mass 8000 kg would need to generate to reach a speed of 12.0 m/s in 6.00 s?
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109. example
A 100-watt light bulb that is on 10-hours a day for 30 days. How much energy will it use? How much did it cost to operate that lamp if the price is $ per kWh?
· 10 hours per day x 10 days = 300 hours (energy is all about time of operation) · 300 Hours x 100 Watts = 30,000 watt hours (energy is also about connected load or Watts) · A kilowatt (kW) is 1000 watts · 30,000 watt hours ÷ 1000 watts = 30 kilowatt hours (kWh as on the electric bill
30 kWh x $ per kWh = $2.72 cost of operation
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110. Power Delivered by an Elevator Motor
A 1000-kg elevator carries a maximum load of 800 kg. A constant frictional force of 4000 N retards its motion upward. What minimum power must the motor deliver to lift the fully loaded elevator at a constant speed of 3 m/s?
Since the speed is constant, so a = 0
where M = total mass of the system
M= =1800 Kg
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111. example OR
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112. example
A 5 Kg Cart is pushed by a 30 N force against friction for a distance of 10m in 5 seconds. Determine the Power needed to move the cart.
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113. example
In a rifle barrel, a 15.0 g bullet is accelerated from rest to a speed of 780 m/s. a)Find the work that is done on the bullet.?
Using Work-Kinetic Energy Theorem, W = ΔKE W = KEf - KEi W = 1/2(0.015 kg)(780 m/s) W = 4.56 kJ
b) If the rifle barrel is 72.0 cm long, find the magnitude of the average total force that acted on the bullet.
Using W = Fcosθd, F = (4.56 kJ) / (0.72 m) F = 6.33 kN
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114. Example:
The minimum work required to raise a 800 N person up 10 m, is:
W = F d
W = (800 N) (10 m) = 8000 J
If this work is done in 60 sec, then what is the power?
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115. example
A car of mass 500 kg is traveling along a horizontal road .the engine of the car is working at a constant rate of 5kw .the total Resistance to motion is constant and is 250 N . What is the acceleration of the car when its speed is 5 m/s
Fk=
m/s
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116. example
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117. Norah Ali Al - moneef
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118. Summary of Chapter 6 Work: Kinetic energy is energy of motion:
Work-energy principle: The net work done on an object equals the change in its kinetic energy.
Conservative force: work depends only on end points
Gravitational potential energy: Ugrav = mg (h –h0 ).
Total mechanical energy is the sum of kinetic and potential energies.
Additional types of energy are involved when nonconservative forces act.
Total energy (including all forms) is conserved.
Power: rate at which work is done, or energy is transformed:
Δ k = - Δ u
K+u =ko +uo
K+u =ko +uo+ wa or
Norah Ali Al - moneef
29/07/1438