Lecture Power Point Physics for Scientists and Engineers

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Lecture Power. Point Physics for Scientists and Engineers, 3 rd edition Fishbane Gasiorowicz Thornton

Lecture Power. Point Physics for Scientists and Engineers, 3 rd edition Fishbane Gasiorowicz Thornton © 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials.

Chapter 6 Work and Kinetic Energy

Chapter 6 Work and Kinetic Energy

Main Points of Chapter 6 • Kinetic energy and the work-energy theorem • Work

Main Points of Chapter 6 • Kinetic energy and the work-energy theorem • Work in more than one dimension • Variable forces • Conservative and nonconservative forces • Power • Kinetic energy at very high speeds

6 -1 Kinetic Energy, Work, and the Work–Energy Theorem Definition of kinetic energy: (6

6 -1 Kinetic Energy, Work, and the Work–Energy Theorem Definition of kinetic energy: (6 -2) Q. Why do we define this? A. It turns out to make our calculations easier!

6 -1 Kinetic Energy, Work, and the Work–Energy Theorem The work-energy theorem: the net

6 -1 Kinetic Energy, Work, and the Work–Energy Theorem The work-energy theorem: the net work done on an object is equal to its change in kinetic energy (6 -6)

6 -1 Kinetic Energy, Work, and the Work–Energy Theorem Q. So, why does defining

6 -1 Kinetic Energy, Work, and the Work–Energy Theorem Q. So, why does defining kinetic energy make calculations easier? A. Kinetic energy is a scalar and can be simply added. Work is a scalar too but it’s a dot product – you need more information to calculate it.

6 -1 Kinetic Energy, Work, and the Work–Energy Theorem • Work may be positive

6 -1 Kinetic Energy, Work, and the Work–Energy Theorem • Work may be positive or negative. • If force has a component in the direction of the velocity, work is positive.

6 -1 Kinetic Energy, Work, and the Work–Energy Theorem • Work may be positive

6 -1 Kinetic Energy, Work, and the Work–Energy Theorem • Work may be positive or negative. • If force has a component opposite to the direction of the velocity, work is negative.

6 -1 Kinetic Energy, Work, and the Work–Energy Theorem Units of work and energy:

6 -1 Kinetic Energy, Work, and the Work–Energy Theorem Units of work and energy: 1 joule (J) = 1

6 -1 Kinetic Energy, Work, and the Work–Energy Theorem Work Done by Individual Forces

6 -1 Kinetic Energy, Work, and the Work–Energy Theorem Work Done by Individual Forces For each force, Therefore, one can find the net work done in two ways: 1. Find the vector sum of the forces and multiply it by the displacement, or 2. Find the work done by each individual force and add them.

6 -2 Constant Forces in More than One Dimension • Each Cartesian direction can

6 -2 Constant Forces in More than One Dimension • Each Cartesian direction can be treated separately (x, y, z) • Now the angle between the force and the displacement needs to be used

6 -2 Constant Forces in More than One Dimension Component equations for FΔr: (6

6 -2 Constant Forces in More than One Dimension Component equations for FΔr: (6 -8 a) (6 -8 b) Combining, (6 -9, 11)

6 -2 Constant Forces in More than One Dimension This leads to the general

6 -2 Constant Forces in More than One Dimension This leads to the general expression for work done by a constant force: (6 -12)

6 -3 Forces that Vary with Position Variable forces in one dimension: • Divide

6 -3 Forces that Vary with Position Variable forces in one dimension: • Divide displacement into small enough pieces that the force is almost constant • Do the usual calculation of work for each piece • Add them all up

6 -3 Forces that Vary with Position If you know the force as a

6 -3 Forces that Vary with Position If you know the force as a function of displacement, you can make the pieces infinitesimally small and integrate. (6 -14)

6 -3 Forces that Vary with Position Work Done by a Spring force: (6

6 -3 Forces that Vary with Position Work Done by a Spring force: (6 -15) • k is the spring constant • restoring force – always in the direction of x = 0 • force varies with x

6 -3 Forces that Vary with Position Work Done by a Spring Integrating gives

6 -3 Forces that Vary with Position Work Done by a Spring Integrating gives the work done to stretch the spring from 0 to L:

6 -3 Forces that Vary with Position Forces that Vary in both Magnitude and

6 -3 Forces that Vary with Position Forces that Vary in both Magnitude and Direction • Now need to combine both the previous results • magnitude variation means integration • direction variation means dot product

6 -3 Forces that Vary with Position So we need to calculate the work

6 -3 Forces that Vary with Position So we need to calculate the work at every point on the path: (6 -16) Now you see why using the work-energy theorem is so much easier!

6 -3 Forces that Vary with Position No Work Is Done in Uniform Circular

6 -3 Forces that Vary with Position No Work Is Done in Uniform Circular Motion Remember that: (6 -16) At every point on a circle: Therefore, no work!

6 -4 Conservative and Nonconservative Forces • A conservative force is one where the

6 -4 Conservative and Nonconservative Forces • A conservative force is one where the work done does not depend on the path taken. • Gravity is a conservative force.

6 -4 Conservative and Nonconservative Forces • A nonconservative force is one where the

6 -4 Conservative and Nonconservative Forces • A nonconservative force is one where the work done depends on the path taken. • Friction is a nonconservative force.

6 -5 Power P is the rate at which work is done: (6 -18)

6 -5 Power P is the rate at which work is done: (6 -18) This result can be generalized: (6 -20)

6 -5 Power The units of power are watts: 1 W = 1 J/s

6 -5 Power The units of power are watts: 1 W = 1 J/s In the English system, power is measured in horsepower: 1 hp = 550 ft-lb/s = 746 W The kilowatt-hour, power multiplied by time, is a measure of energy use: 1 k. Wh = 3. 6 x 106 J

6 -6 Kinetic Energy at Very High Speeds • When objects approach the speed

6 -6 Kinetic Energy at Very High Speeds • When objects approach the speed of light, many strange things happen. • One is that the kinetic energy can become very large. (6 -21) • The speed of light c = 3 x 108 m/s • As v approaches c, K approaches infinity

Summary of Chapter 6 • Definition of kinetic energy: • Work-energy theorem: (6 -6)

Summary of Chapter 6 • Definition of kinetic energy: • Work-energy theorem: (6 -6) • For more than one dimension, each coordinate must be calculated separately. • Work done by variable forces is found by integrating.

Summary of Chapter 6, cont. • Conservative force: work does not depend on path

Summary of Chapter 6, cont. • Conservative force: work does not depend on path • Nonconservative force: work depends on path • Power is the rate at which work is done