A truck of mass m = 2500 kg is traveling downhill on a road with slope theta = 3

Question

A truck of mass m = 2500 kg is traveling downhill on a road with slope theta = 3.5degree. The driver slams on the brakes and skids to stop, leaving skid marks 30 m long. The coefficient of friction between the truck's wheels and the road is mu = 0.4. (a) Using concepts of work and energy, find an expression for how fast the truck was going just before hitting the brakes. Was the truck exceeding the speed limit of 25 miles per hour? (b) All else being equal, how far would the truck have skidded if the slope of the road were theta = 5degree? Is there a slope angle beyond which the truck would not have been able to stop at all? What is this angle? (c) How dow your answers in (a) and (b) change, if the truck had a mass 4000 kg instead of 2500 kg? Briefly discuss.

Explanation / Answer

a) component of gravity along the track = mgsin3.5   along the displacement

friction force = u N

and N = mgcos@

f = u mg cos3.5   opposite of displacement

using work energy theorem,

work done by gravity + work done by friction = change in KE

mgLsin3.5 - umgLcos3.5 =0 - mv^2 /2

(9.81 x 30 xsin3.5) - (0.4 x 9.81 x 30 x cos3.5) = v^2 /2

v^2 = 199.07

v = 14.11 m/s

b) using work energy theorem again,

mgLsin5 - umgLcos5 =0 - mv^2 /2

(9.81 x L xsin5) - (0.4 x 9.81 x L x cos5) = - 14.11^2 /2   = - 99.53

L = 32.6 m

c) both a and b answer are independent of mass of truck.

so answer will no change if we change the mass of trcuk.

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