Concept Summary

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Topic | Discussion | Learning Aids
| 6.1 WORK DONE BY A CONSTANT FORCE The work W done by a constant force acting on an object is |
Work done by constant force |

| (6.1)

where F is the magnitude of the force, s is the magnitude of the displacement, and is the angle between the force and the displacement vectors. Work is a scalar quantity and can be positive or negative, depending on whether the force has a component that points, respectively, in the same direction as the displacement or in the opposite direction. The work is zero if the force is perpendicular to the displacement.
| 6.2 THE WORK–ENERGY THEOREM AND KINETIC ENERGY The kinetic energy KE of an object of mass m and speed v is |
Kinetic energy |

| (6.2)

The work–energy theorem states that the work W done by the net external force acting on an object equals the difference between the object’s final kinetic energy KEf and initial kinetic energy KE0:
Work–energy theorem |

| (6.3)

The kinetic energy increases when the net force does positive work and decreases when the net force does negative work.

Use Self-Assessment Test 6.1 to evaluate your understanding of Sections 6.1 and 6.2.

| 6.3 GRAVITATIONAL POTENTIAL ENERGY The work done by the force of gravity on an object of mass m is |
Work done by force of gravity |

| (6.4)

where h0 and hf are the initial and final heights of the object, respectively.
Gravitational potential energy PE is the energy that an object has by virtue of its position. For an object near the surface of the earth, the gravitational potential energy is given by
Gravitational potential energy |

| (6.5)

where h is the height of the object relative to an arbitrary zero level.
Conservative force Nonconservative force | 6.4 CONSERVATIVE VERSUS NONCONSERVATIVE FORCES A conservative force is one that does the same work in moving an object between two points, independent of the path taken between the points. Alternatively, a force is conservative if the work it does in moving an object around any closed path is zero. A force is nonconservative if the work it does on an object moving between two points depends on the path of the motion between the points.
6.5 THE CONSERVATION OF MECHANICAL ENERGY The total mechanical energy E is the sum of the kinetic energy and potential energy:
Total mechanical energy |

The work–energy theorem can be expressed in an alternate form as
Alternate form for work–energy theorem |

| (6.8)

where Wnc is the net work done by the external nonconservative forces, and Ef and E0 are the final and initial total mechanical energies, respectively.
Principle of conservation of mechanical energy | The principle of conservation of mechanical energy states that the total mechanical energy E remains constant along the path of an object, provided that the net work done by external nonconservative forces is zero. Whereas E is constant, KE and PE may be transformed into one another. |

Use Self-Assessment Test 6.2 to evaluate your understanding of Sections 6.3, 6.4 and 6.5.

| 6.6 NONCONSERVATIVE FORCES AND THE WORK–ENERGY THEOREM, 6.7 POWER Average power is the work done per unit time or the rate at which work is done: |
Average power |

| (6.10a)

It is also the rate at which energy changes:

| (6.10b)

When a force of magnitude F acts on an object moving with an average speed , the average power is given by

| (6.11)

Principle of conservation of energy | 6.8 OTHER FORMS OF ENERGY AND THE CONSERVATION OF ENERGY The principle of conservation of energy states that energy cannot be created or destroyed but can only be transformed from one form to another. |
Work done by a variable force | 6.9 WORK DONE BY A VARIABLE FORCE The work done by a variable force of magnitude F in moving an object through a displacement of magnitude s is equal to the area under the graph of versus s. The angle is the angle between the force and displacement vectors. |

Use Self-Assessment Test 6.3 to evaluate your understanding of Sections 6.6, 6.7, 6.8 and 6.9.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.