# ch08 - Chapter 8 Potential Energy and Conservation of...

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Chapter 8 Potential Energy and Conservation of Energy In this chapter we will introduce the following concepts: Potential Energy Conservative and non-conservative forces Mechanical Energy Conservation of Mechanical Energy The conservation of energy theorem will be used to solve a variety of problems As was done in Chapter 7 we use scalars such as work ,kinetic energy, and mechanical energy rather than vectors. Therefore the approach is mathematically simpler. (8-1)

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A B g v o h v o Work and Potential Energy: Consider the tomato of mass m shown in the figure. The tomato is taken together with the earth as the system we wish to study. The tomato is thrown upwards with initial speed v o at point A. Under the action of the gravitational force it slows down and stops completely at point B. Then the tomato falls back and by the time it reaches point A its speed has reached the original value v o . Below we analyze in detail what happens to the tomato-earth system. During the trip from A to B the gravitational force F g does negative work W 1 = -mgh . Energy is transferred by F g from the kinetic energy of the tomato to the gravitational potential energy U of the tomato-earth system. During the trip from B to A the transfer is reversed. The work W 2 done by F g is positive ( W 2 = mgh ). The gravitational force transfers energy from the gravitational potential energy U of the tomato-earth system to the kinetic energy of the tomato. The change in the potential energy U is defined as: U W = - (8-2)
A A B B k m Consider the mass m attached to a spring of spring constant k as shown in the figure. The mass is taken together with the spring as the system we wish to study. The mass is given an initial speed v o at point A. Under the action of the spring force it slows down and stops completely at point B which corresponds to a spring compression x . Then the mass reverses the direction of its motion and by the time it reaches point A its speed has reached the original value v o . As in the previous example we analyze in detail what happens to the mass- spring system . During the trip from A to B the spring force F s does negative work W 1 = -kx 2 /2 . Energy is transferred by F s from the kinetic energy of the mass to the potential energy U of the mass-spring system. During the trip from B to A the transfer is reversed. The work W 2 done by F s is positive ( W 2 = kx 2 /2 ). The spring force transfers energy from the potential energy U of the mass-spring system to the kinetic energy of the mass. The change in the potential energy U is defined as: U W = - (8-3)

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m m A B v o f k f k x d Conservative and non-conservative forces. The gravitational force as the spring force are called “conservative” because the can transfer energy from the kinetic energy of part of the system to potential energy and vice versa. Frictional and drag forces on the other hand are called
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## This note was uploaded on 11/21/2011 for the course PHYS 2425 taught by Professor . during the Spring '11 term at San Jacinto.

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ch08 - Chapter 8 Potential Energy and Conservation of...

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