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Chapter_2

# Chapter_2 - 2-11 The total potential energy of an object is...

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2-11 The total potential energy of an object is to be determined. Analysis Substituting the given data into the potential energy expression gives kJ 19.6 2 2 2 /s m 1000 kJ/kg 1 m) 20 )( m/s 8 . 9 ( kg) (100 PE mgz 2-17 A river flowing steadily at a specified flow rate is considered for hydroelectric power generation by collecting the water in a dam. For a specified water height, the power generation potential is to be determined. Assumptions 1 The elevation given is the elevation of the free surface of the river. 2 The mechanical energy of water at the turbine exit is negligible. Properties We take the density of water to be = 1000 kg/m 3 . Analysis The total mechanical energy the water in a dam possesses is equivalent to the potential energy of water at the free surface of the dam (relative to free surface of discharge water), and it can be converted to work entirely. Therefore, the power potential of water is its potential energy, which is gz per unit mass, and gz m for a given mass flow rate. kJ/kg 4905 . 0 /s m 1000 kJ/kg 1 m) 50 )( m/s (9.81 2 2 2 mech gz pe e The mass flow rate is kg/s 0,000 24 /s) m 0 )(24 kg/m 1000 ( 3 3 V m Then the power generation potential becomes MW 118 kJ/s 1000 MW 1 kJ/kg) 905 kg/s)(0.4 000 , 240 ( mech mech max e m E W Therefore, 118 MW of power can be generated from this river if its power potential can be recovered completely. Discussion Note that the power output of an actual turbine will be less than 118 MW because of losses and inefficiencies. 2-19C Energy can cross the boundaries of a closed system in two forms: heat and work. 2-31 A car is accelerated from rest to 100 km/h. The work needed to achieve this is to be determined. Analysis The work needed to accelerate a body the change in kinetic energy of the body, kJ 309 2 2 2 2 1 2 2 /s m kg 1000 kJ 1 0 s 3600 m 100,000 kg) (800 2 1 ) ( 2 1 V V m W a River 50 m

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2-33 A man is pushing a cart with its contents up a ramp that is inclined at an angle of 20° from the horizontal. The work needed to move along this ramp is to be determined considering (a) the man and (b) the cart and its contents as the system. Analysis ( a ) Considering the man as the system, letting l be the displacement along the ramp, and letting be the inclination angle of the ramp, kJ 67.0 2 2 2 /s m 1000 kJ/kg 1 m)sin(20) 100 ( ) m/s 8 . 9 )( kg 100 100 ( sin sin mgl Fl W This is work that the man must do to raise the weight of the cart and contents, plus his own weight, a distance of l sin .
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