Recit%208%2c%20chapters%206-7

Recit%208%2c%20chapters%206-7 - PHY2053 RECITATIONS SPRING...

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PHY2053 RECITATIONS, SPRING 2011 Recitation 8 (Chapters 6-7) Feb. 14-Mar. 18 52. Starting from rest, a 93-kg firefighter slides down a fire pole. The average frictional force exerted on him by the pole has a magnitude of 810 N, and his speed at the bottom of the pole is 3.4 m/s. How far did he slide down the pole? REASONING As the firefighter slides down the pole from a height h 0 to the ground ( h f = 0 m), his potential energy decreases to zero. At the same time, his kinetic energy increases as he speeds up from rest ( v 0 = 0 m/s) to a final speed v f ,. However, the upward nonconservative force of kinetic friction f k , acting over a downward displacement h 0 , does a negative amount of work on him: ( 29 nc k 0 k 0 cos180 W f h f h = = - o (Equation 6.1). This work decreases his total mechanical energy E . Applying the work-energy theorem (Equation 6.8), with h f = 0 m and v 0 = 0 m/s, we obtain ( 29 ( 29 2 2 1 1 nc f f 0 0 2 2 W mv mgh mv mgh = + - + (6.8) { ( 29 ( 29 nc 0 f 2 2 1 1 k 0 f 0 f 0 2 2 0 J 0 J W E E f h mv mgh mv mgh - = + - + = - 1 4 2 4 3 1 442 4 43 (1) SOLUTION Solving Equation (1) for the height h 0 gives ( 29 ( 29 2 2 2 f 1 1 0 k 0 f 0 k f 0 2 2 k or or 2 mv mgh f h mv h mg f mv h mg f - = - = = - The distance h 0 that the firefighter slides down the pole is, therefore, ( 29 ( 29 ( 29 ( 29 2 0 2 93 kg 3.4 m/s 5.3 m 2 93 kg 9.80 m/s 810 N h = = - 61. A truck is traveling at 11.1 m/s down a hill when the brakes on all four wheels lock. The hill makes an angle of 15.0° with respect to the horizontal. The coefficient of kinetic friction between the tires and the road is 0.750. How far does the truck skid before coming to a stop? REASONING
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Recit%208%2c%20chapters%206-7 - PHY2053 RECITATIONS SPRING...

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