8. A large tractor-trailer of total mass M = 10 metric tons (10,000 kg) is trave

Question

8. A large tractor-trailer of total mass M = 10 metric tons (10,000 kg) is traveling down I-70 in Colorado, coming down from the Rocky Mountains into Denver. A segment of this road that is 25 kilometers long descends a total of 1000 meters. Suppose that the truck driver wants to drive at a constant speed of v = 50 km/hr. (a) What is the work done on the truck by its brakes during this motion? (Give both the sign and the magnitude.) Does this depend on how fast the truck drives? (b) What is the power applied to the truck by its brakes during this motion? Does this depend on how fast the truck drives? (c) The coefficient of friction of the metal that comprises brake pads decreases as they are heated. If they get too hot, they will not be able to apply the required braking force. Explain why trucks must drive very slowly down a long hill such as this one, but do not need to be so cautious on a short hill

Explanation / Answer

tan(theta) = 1 / 25

theta = 2.3 deg

(A) Work done = F.d

= (10000 x 9.8)(25 x 10^3)(cos(90+2.3))

= - 98.3 x 10^6 J

(B) P = F.v

and v = 50 x 1000 m / 3600s = 13.9 m/s

P = (10000 x 9.8 x sin2.3)(13.9)

P = 54.7 x 10^3 W Or 54.7 kW

(C) because v decreases then power will be less.

so heat will generate slowly and get dissipated.

hence break pads will be safe.

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