an out of control truck with a mass of 7500kg is traveling at 13 m/s (about 30mi

Question

an out of control truck with a mass of 7500kg is traveling at 13 m/s (about 30mi/hr) when it locks up its brakes and starts decending an icy hill with a 5 degree incline. the coefficient of kinetic friction betwwen the trucks tires and the icy road is .27. use the work- energy theorem to determine a. how farthe truck will slide down the slope with irs brakes locked up before it comes come to rest and stops? b. how far will the truck slide if the truck has the same magnitude of speed but diffrent direction up the hill when the brakes lock up?

Explanation / Answer

a)

X = lenght travel by truck will slide down the slope with irs brakes locked up before it comes come to rest and stops

7500*9.81*X*sin5 - 0.27*7500*9.81*cos5*X + (1/2)*7500*13*13 = 0

6412.484*X - 19789.657*X + 633750 = 0

X = 633750 / 13377.173 = 47.3755 m

b)

Y = lenght travel by truck will slide down the slope with irs brakes locked up before it comes come to rest and stops whwn velocity direction is reversed

- 7500*9.81*Y*sin5 - 0.27*7500*9.81*cos5*Y + (1/2)*7500*13*13 = 0

- 6412.484*Y - 19789.657*Y + 633750 = 0

Y = 633750 / 26202.141 = 24.187 m

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