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Phys 141_HW Sol_Ch10_W08

# Phys 141_HW Sol_Ch10_W08 - Cal Poly State University SLO...

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Cal Poly State University, SLO D. Niebuhr Physics Department Winter 2008 Phys 141 Homework Solutions Chapter 10 Assigned Problems: Ch. 10: 2, 5, 9, 12, 16, 18, 23, 30, 31, 42, 47, 54 10.2. Model: Model the hiker as a particle. Visualize: The origin of the coordinate system chosen for this problem is at sea level so that the hiker’s position in Death Valley is 0 8.5 m. y = - Solve: The hiker’s change in potential energy from the bottom of Death Valley to the top of Mt. Whitney is gf gi f i f i 2 6 ( ) (65 kg)(9.8 m/s )[4420 m ( 85 m)] 2.87 10 J U U U mgy mgy mg y y = - = - = - = - - = × Assess: Note that U is independent of the origin of the coordinate system. 10.5. Model: Model the car (C) as a particle. This is an example of free fall, and therefore the sum of kinetic and potential energy does not change as the car falls. Visualize: Solve: (a) The kinetic energy of the car is 2 2 5 C C C 1 1 (1500 kg)(30 m/s) 6.75 10 J 2 2 K m v = = = × (b) Let us relabel K C as K f and place our coordinate system at f 0 y = m so that the car’s potential energy U gf is zero, its velocity is v f , and its kinetic energy is K f . At position y i , i i 0 m/s or 0 J, v K = = and the only energy the car has is gi i . U mgy = Since the sum K + U g is unchanged by motion, f gf i gi K U K U + = + . This means

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Cal Poly State University, SLO D. Niebuhr Physics Department Winter 2008 Phys 141 f f i i f i i 5 f i i 2 0 ( ) (6.75 10 J 0 J) 45.9 m (1500 kg)(9.8 m/s ) K mgy K mgy K K mgy K K y mg + = + + = + - × - = = = (c) From part (b), ( 29 2 2 2 2 f i f i f i i 1 1 ( ) 2 2 2 mv mv v v K K y mg mg g - - - = = = Free fall does not depend upon the mass. 10.9. Model: Model the skateboarder as a particle. Assuming that the track offers no rolling friction, the sum of the skateboarder’s kinetic and gravitational potential energy does not change during his rolling motion. Visualize: The vertical displacement of the skateboarder is equal to the radius of the track. Solve: The quantity K + U g is the same at the upper edge of the quarter-pipe track as it was at the bottom. The energy conservation equation f gf i gi K U K U + = + is 2 2 2 2 f f i i i f f i 2 2 2 i i 1 1 2 ( ) 2 2 (0 m/s) 2(9.8 m/s )(3.0 m 0 m) 58.8 m/s 7.67 m/s mv mgy mv mgy v v g y y v v + = + = + - = + - = = Assess: Note that we did not need to know the skateboarder’s mass, as is the case with free-fall motion. 10.12.
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Phys 141_HW Sol_Ch10_W08 - Cal Poly State University SLO...

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