Problem 8.43 The Outlaw Run roller coaster in Branson, Missouri, features a trac

Question

Problem 8.43 The Outlaw Run roller coaster in Branson, Missouri, features a track that is inclined at 82° below the horizontal and that spans a 49.4-m (162 ft) change in height. Part A If the coefficient of friction for the roller coaster is k 0.29, what is the magnitude of the friction force on a 1600-kg coaster train? Express your answer to two significant figures and include appropriate units. O Value Units Submit My Answers Give Up Incorrect; Try Again; 5 attempts remaining Part B How much work is done by friction during the time the coaster train travels along the incline? Express your answer to two significant figures and include appropriate units. alueUnits Submit My Answers Give Up

Explanation / Answer

Here ,

theta = 82 degree

change in height , h = 49.4 m

part A)

uk = 0.29

for the frictional force

frictional force = uk * m * g * cos(theta)

frictional force = 0.29 * 1600 * 9.8 * cos(82 degree)

frictional force = 632 N

part b)

length of incline , L = 49.4/sin(82 degree)

L = 50 m

work done by frictional force = - 632 * 50 J

work done by frictional force = -31527 J

part c)

let the speed at the bottom is v

0.50 * 1600 * v^2 = 1600 * 9.8 * 49.4 - 31527

solving for v

v = 30.5 m/s

the speed of rollercoaster is 30.5 m/s

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