you are driving a 12,000-kg truck at a constant speed of 65 mi/h down a 6% slope

Question

you are driving a 12,000-kg truck at a constant speed of 65 mi/h down a 6% slope (i.e., an incline that goes down .06 m for every 1 m that one goes along the incline). You suddenly see that a bridge is out 425 ft ahead, and you jam on the brakes. The coefficient of static friction between your tires and the we asphalt road is 0.45, the coefficient of kinetic friction is 0.30, and the cross-sectional area of your truck is 6.6 m^2. Can you stop in time? (Hints: The magnitude of the drag force depends on speed, so it will not be a constant as you slow down. Is the drag force significant? Make plausible estimates for quantities you are not given.)

Explanation / Answer

1 ft = 0.3048 m

425 ft = 129.54 m = 130 m

1mph = 0.4470 m/s

65 mph = 65* 0.4470 = 29.055 m/s

here tan theta = h/d = 0.06 = 3/50

CA = sqrt(9 + 2500) = 50.1

use the kinemtic equations

f = mg sin theta +ma

uKN = mg sin theta + ma

a = uk mg cos theta - mg sin theta /m

also V^2 - U^2 = 2 a

S = u^2/2g *(ukcos theta - sin theta)

S = (29.05)^2/(2*9.8 * 0.3 *50/50.1 - 3/50.1)

S = 179.75 m

instead of 130m , the truck stops at 179.75 m

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