homework_26.1_sol

homework_26.1_sol - Solution to Homework Assignment #4 22.1...

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Unformatted text preview: Solution to Homework Assignment #4 22.1 The kinetic energy is 1 K = mv 2 2 1 2000 lb m mile 5280 ft 55 = ton v ) ) )2 ~ ) 2 ) ton ) hour mile 1 = 2 2 hour lb f ) 3600 s ) 32.174 lb m ft/s 2 ) ( 2 ( 4000 lbm ) lb f 80.67 ft ) ) ) 32.174 lb ft/s 2 ) ) s m ( 4.045 105 ft lb f ft lb f 404495 404495 404495 0.001286 Btu o 520.18 Btu ft olb f 1.356 J ~ ft olb f 548495 J 5.485 105 J . 22.2 All the kinetic energy is transferred into thermal energy and released (see above value). 22.3 (a) The component of gravity force accelerating the automobile is F = M g sin q = 4000 lb m ~ 32.174 ( ft/s 2 ) sin 25o and the working distance of this force is 5.44 104 lb f , v L = H / sin q = 100 ft / sin 25o. All the work done by this force converts to the kinetic energy of the car at the bottom of the hill, so 1 FL = mv 2 2 v= 2) 4000 lb m 32.174 ( ft/s 2 ) 100 ft sin 25o 2 FL = m 4000 lb m ) sin 25o 80.217 ft/s . = 2 32.174 ( ft/s 2 ) 100 ft (b) The kinetic energy at the bottom of the hill comes from the potential energy of gravity due to the falling. 1 mgH = mv 2 2 v = 2 gH = 2~ 32.174 ( ft/s 2 ) 100 ft 80.217 ft/s . The two methods are equivalent. 22.4 Assume the comet debris and the earth stay together, thus all the kinetic energy is transferred to thermal energy and released. 1 Q = mv 2 2 2 1 1 pD3r comet vcomet = ) ) ) 2 )6 3 2 3 1 1 p mile 1609 m 7 g/cm3 1000 kg/m mile/s 1609 m = 3 20 2 6 mile g/cm3 mile 2.13 1023 J 2.13 1023 ^J 1 megaton 4.184 1015 J 5.10 107 megaton . 22.13 The work done in the lifting is transferred into potential energy of the load. W = mgh = 1000 lb m 20 ^ ft 32.174 ( ft/s 2 ) lb f = 20000 ft vlb f . 32.174 ( ft/s 2 ) ) lb m Considering the efficiency of the pulley and the motor, the electrical energy required is E= W = hpulley hmotor 20000 ft f lb 1.356 J ft f lb 0.95) 0.6 47579 J . If lifted in 1 minute, the required power is P = E / t = 47579 J / 60 s 792.98 W . ...
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This note was uploaded on 04/26/2009 for the course ENGR 112 taught by Professor V during the Spring '08 term at Texas A&M.

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