ism_ch08

# ism_ch08 - Chapter 8 Potential Energy and Conservative...

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Chapter 8 Potential Energy and Conservative Forces Answers to Even-numbered Conceptual Questions 2. As water vapor rises, there is an increase in the gravitational potential energy of the system. Part of this potential energy is released as snow falls onto the mountain. If an avalanche occurs, the snow on the mountain accelerates down slope, converting more gravitational potential energy to kinetic energy. 4. As the ball falls, gravitational potential energy is converted to kinetic energy. When the ball hits the floor, some of the kinetic energy is converted to sound energy and heat, some to a compression of the ball – like compressing a spring. The ball now rebounds, converting the potential energy of compression back to kinetic energy. Finally, the kinetic energy of the ball is converted back to gravitational potential energy as the ball rises. The final height of the ball is less than its initial height because some energy has left the system in the form of sound and heat. 6. The work done in stretching the spring through a doubled distance is the force times the distance. Both of these quantities increase by a factor of two, and therefore the potential energy of the spring increases by a factor of four. We arrive at the same from the form of the spring potential energy, U = 1 2 kx 2 , which depends on the square of the amount of stretch. 8. The initial mechanical energy of the system is the gravitational potential energy of the mass-Earth system. As the mass moves downward, the gravitational potential energy of the system decreases. At the same time, the potential energy of the spring increases, as it is compressed. Initially, the decrease in gravitational potential energy is greater than the increase in spring potential energy, which means that the mass gains kinetic energy. Eventually, the increase in spring energy equals the decrease in gravitational energy and the mass comes to rest. 10. If a spring is permanently deformed, it will not return to its original length. As a result, the work that was done to stretch the spring is not fully recovered – some of it goes into the energy of deformation. For this reason, the spring force is not conservative during the deformation. If the spring is now stretched or compressed by a small amount about its new equilibrium position, its force is again conservative – though the force constant will be different. 12. (a) The object’s kinetic energy is a maximum when it is released, and a minimum when it reaches its greatest height. (b) The gravitational potential of the system is a minimum when the object is released, and a maximum when the object reaches its greatest height. 14. When the term “energy conservation” is used in everyday language, it doesn’t refer to the total amount of energy in the universe. Instead, it refers to using energy wisely, especially when a particular source of energy – like oil or natural gas – is finite and nonrenewable.

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## This note was uploaded on 04/07/2008 for the course PHYS 105 taught by Professor Klie during the Spring '08 term at Ill. Chicago.

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ism_ch08 - Chapter 8 Potential Energy and Conservative...

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