1. Chapter 11 Work 
Chapter Goal: To develop a more complete understanding of energy and its conservation.
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2. Chapter 11 Preview
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3. Chapter 11 Preview
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4. Chapter 11 Preview
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5. Chapter 11 Preview
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6. Chapter 11 Preview
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7. Chapter 11 Preview
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8. The Basic Energy Model
W > 0: The environment does work on the system and the system’s energy increases.
W < 0: The system does work on the environment and the system’s energy decreases.
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9. The Basic Energy Model
The energy of a system is a sum of its kinetic energy K, its potential energy U, and its thermal energy Eth.
The change in system energy is:
Energy can be transferred to or from a system by doing work W on the system. This process changes the energy of the system: Esys = W.
Energy can be transformed within the system among K, U, and Eth. These processes don’t change the energy of the system: Esys = 0.
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10. Work and Kinetic Energy
The word “work” has a very specific meaning in physics.
Work is energy transferred to or from a body or system by the application of force.
This pitcher is increasing the ball’s kinetic energy by doing work on it.
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11. Work and Kinetic Energy
Consider a force acting on a particle which moves along the s-axis.
The force component Fs causes the particle to speed up or slow down, transferring energy to or from the particle.
The force does work on the particle:
The units of work are N m, where 1 N m = 1 kg m2/s2 = 1 J.
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12. The Work-Kinetic Energy Theorem
The net force is the vector sum of all the forces acting on a particle
The net work is the sum Wnet = Wi, where Wi is the work done by each force .
The net work done on a particle causes the particle’s kinetic energy to change.
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13. An Analogy with the Impulse-Momentum Theorem
The impulse-momentum theorem is:
The work-kinetic energy theorem is:
Impulse and work are both the area under a force graph, but it’s very important to know what the horizontal axis is!
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14. Work Done by a Constant Force
A force acts with a constant strength and in a constant direction as a particle moves along a straight line through a displacement .
The work done by this force is:
Here  is the angle makes relative to .
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15. Example 11.1 Pulling a Suitcase
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16. Example 11.1 Pulling a Suitcase
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17. Tactics: Calculating the Work Done by a Constant Force
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18. Tactics: Calculating the Work Done by a Constant Force
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19. Tactics: Calculating the Work Done by a Constant Force
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20. Example 11.2 Work During a Rocket Launch
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21. Example 11.2 Work During a Rocket Launch
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22. Example 11.2 Work During a Rocket Launch
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23. Example 11.2 Work During a Rocket Launch
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24. QuickCheck 11.6
Which force below does the most work? All three displacements are the same.
The 10 N force.
The 8 N force
The 6 N force.
They all do the same work.
sin60 = 0.87
cos60 = 0.50
Answer: B
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25. QuickCheck 11.6
Which force below does the most work? All three displacements are the same.
The 10 N force.
The 8 N force
The 6 N force.
They all do the same work.
sin60 = 0.87
cos60 = 0.50
Answer: B
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26. QuickCheck 11.7
A light plastic cart and a heavy steel cart are both pushed with the same force for a distance of 1.0 m, starting from rest. After the force is removed, the kinetic energy of the light plastic cart is ________ that of the heavy steel cart.
greater than
equal to
less than
Can’t say. It depends on how big the force is.
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27. QuickCheck 11.7
A light plastic cart and a heavy steel cart are both pushed with the same force for a distance of 1.0 m, starting from rest. After the force is removed, the kinetic energy of the light plastic cart is ________ that of the heavy steel cart.
greater than
equal to
less than
Can’t say. It depends on how big the force is.
Same force, same distance  same work done
Same work  change of kinetic energy
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28. Force Perpendicular to the Direction of Motion
The figure shows a particle moving in uniform circular motion.
At every point in the motion, Fs, the component of the force parallel to the instantaneous displacement, is zero.
The particle’s speed, and hence its kinetic energy, doesn’t change, so W = K = 0.
A force everywhere perpendicular to the motion does no work.
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29. QuickCheck 11.8
A car on a level road turns a quarter circle ccw. You learned in Chapter 8 that static friction causes the centripetal acceleration. The work done by static friction is _____.
positive
negative
zero
Answer: B
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30. QuickCheck 11.8
A car on a level road turns a quarter circle ccw. You learned in Chapter 8 that static friction causes the centripetal acceleration. The work done by static friction is _____.
positive
negative
zero
Answer: B
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31. The Dot Product of Two Vectors
The figure shows two vectors, and , with angle  between them.
The dot product of and is defined as:
The dot product is also called the scalar product, because the value is a scalar.
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32. The Dot Product of Two Vectors
The dot product as  ranges from 0 to 180.
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33. Example 11.3 Calculating a Dot Product
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34. The Dot Product Using ComponentsIf
and ,
the dot product is the sum of the products of the components:
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35. Example 11.4 Calculating a Dot Product Using Components
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36. Work Done by a Constant Force
A force acts with a constant strength and in a constant direction as a particle moves along a straight line through a displacement
The work done by this force is:
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37. Example 11.5 Calculating Work Using the Dot Product
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38. Example 11.5 Calculating Work Using the Dot Product
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39. The Work Done by a Variable Force
To calculate the work done on an object by a force that either changes in magnitude or direction as the object moves, we use the following:
We must evaluate the integral either geometrically, by finding the area under the curve, or by actually doing the integration.
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40. Example 11.6 Using Work to Find the Speed of a Car
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41. Example 11.6 Using Work to Find the Speed of a Car
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42. Example 11.6 Using Work to Find the Speed of a Car
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43. Example 11.6 Using Work to Find the Speed of a Car
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44. Conservative Forces
The figure shows a particle that can move from A to B along either path 1 or path 2 while a force is exerted on it.
If there is a potential energy associated with the force, this is a conservative force.
The work done by as the particle moves from A to B is independent of the path followed.
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45. Nonconservative Forces
The figure is a bird’s-eye view of two particles sliding across a surface.
The friction does negative work: Wfric = kmgs.
The work done by friction depends on s, the distance traveled.
This is not independent of the path followed.
A force for which the work is not independent of the path is called a nonconservative force.
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46. Mechanical Energy
Consider a system of objects interacting via both conservative forces and nonconservative forces.
The change in mechanical energy of the system is equal to the work done by the nonconservative forces:
Mechanical energy isn’t always conserved.
As the space shuttle lands, mechanical energy is being transformed into thermal energy.
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47. Example 11.8 Using Work and Potential Energy
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48. Example 11.8 Using Work and Potential Energy
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49. Example 11.8 Using Work and Potential Energy
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50. Finding Force from Potential Energy
The figure shows an object moving through a small displacement s while being acted on by a conservative force .
The work done over this displacement is:
Because is a conservative force, the object’s potential energy changes by U = −W = −FsΔs over this displacement, so that:
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51. Finding Force from Potential Energy
In the limit s  0, we find that the force at position s is:
The force on the object is the negative of the derivative of the potential energy with respect to position.
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52. Finding Force from Potential Energy
Figure (a) shows the potential-energy diagram for an object at height y.
The force on the object is (FG)y = mg.
Figure (b) shows the corresponding F-versus-y graph.
At each point, the value of F is equal to the negative of the slope of the U-versus-y graph.
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53. Finding Force from Potential Energy
Figure (a) is a more general potential energy diagram.
Figure (b) is the corresponding F-versus-x graph.
Where the slope of U is negative, the force is positive.
Where the slope of U is positive, the force is negative.
At the equilibrium points, the force is zero.
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54. Thermal Energy
Figure (a) shows a mass M moving with velocity with macroscopic kinetic energy Kmacro = ½ Mvobj2.
Figure (b) is a microphysics view of the same object.
The total kinetic energy of all the atoms is Kmicro.
The total potential energy of all the atoms is Umicro.
The thermal energy of the system is:
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55. Dissipative Forces
As two objects slide against each other, atomic interactions at the boundary transform the kinetic energy Kmacro into thermal energy in both objects.
K  Eth
Kinetic friction is a dissipative force.
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56. Dissipative Forces
The figure shows a box being pulled at a constant speed across a horizontal surface with friction.
Both the surface and the box are getting warmer as it slides.
Dissipative forces always increase the thermal energy; they never decrease it.
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57. Example 11.9 Calculating the Increase in Thermal Energy
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58. Conservation of Energy
For a system with both internal interaction forces and external forces, the energy equation is:
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59. Power
The rate at which energy is transferred or transformed is called the power P.
Highly trained athletes have a tremendous
power output.
The SI unit of power is the watt, which is defined as:
1 watt = 1 W = 1 J/s
The English unit of power is the horsepower, hp.
1 hp = 746 W
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60. Example 11.13 Choosing a Motor
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61. Example 11.13 Choosing a Motor
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62. Examples of Power
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63. Power
When energy is transferred by a force doing work, power is the rate of doing work: P = dW/dt.
If the particle moves at velocity while acted on by force , the power delivered to the particle is:
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64. QuickCheck 11.11
Four students run up the stairs in the time shown. Which student has the largest power output?
Answer: B
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65. QuickCheck 11.11
Four students run up the stairs in the time shown. Which student has the largest power output?
Answer: B
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66. Example 11.14 Power Output of a Motor
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67. Example 11.14 Power Output of a Motor
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