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Unformatted text preview: 603 Chapter 7 The Conservation of Energy Conceptual Problems 1 [SSM] Two cylinders of unequal mass are connected by a massless cord that passes over a frictionless pulley (Figure 7-34). After the system is released from rest, which of the following statements are true? ( U is the gravitational potential energy and K is the kinetic energy of the system.) ( a ) U < 0 and K > 0, ( b ) U = 0 and K > 0, ( c ) U < 0 and K = 0, ( d ) U = 0 and K = 0, ( e ) U > 0 and K < 0. Determine the Concept Because the pulley is frictionless, mechanical energy is conserved as this system evolves from one state to another. The system moves and so we know that K > 0. Because K + U = constant , U < 0. ) ( a is correct. 2 Two stones are simultaneously thrown with the same initial speed from the roof of a building. One stone is thrown at an angle of 30 above the horizontal, the other is thrown horizontally. (Neglect effects due to air resistance.) Which statement below is true? ( a ) The stones strike the ground at the same time and with equal speeds. ( b ) The stones strike the ground at the same time with different speeds. ( c ) The stones strike the ground at different times with equal speeds. ( d ) The stones strike the ground at different times with different speeds. Determine the Concept Choose the zero of gravitational potential energy to be at ground level. The two stones have the same initial energy because they are thrown from the same height with the same initial speeds. Therefore, they will have the same total energy at all times during their fall. When they strike the ground, their gravitational potential energies will be zero and their kinetic energies will be equal. Thus, their speeds at impact will be equal. The stone that is thrown at an angle of 30 above the horizontal has a longer flight time due to its initial upward velocity and so they do not strike the ground at the same time. ) ( c is correct. 3 True or false: ( a ) The total energy of a system cannot change. ( b ) When you jump into the air, the floor does work on you increasing your mechanical energy. ( c ) Work done by frictional forces must always decrease the total mechanical energy of a system. ( d ) Compressing a given spring 2.0 cm from its unstressed length takes more work than stretching it 2.0 cm from its unstressed length. Chapter 7 604 ( a ) False. Forces that are external to a system can do work on the system to change its energy. ( b ) False. In order for some object to do work, it must exert a force over some distance . The mechanical energy gained by the jumper comes from the internal energy of the jumper, not from the floor. ( c ) False. The frictional force that accelerates a sprinter increases the total mechanical energy of the sprinter....
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