. A car drives over the top of a hill that has a radius of 200 m, as shown. At t

Question

. A car drives over the top of a hill that has a radius of 200 m, as shown. At the top of the hill, the car's speed v = 30 m/s. The 70-kg car driver suddenly brakes hard and starts to skid at this top of the hill. Assume the coefficient of kinetic friction between the car tires and the road surface, ,-0.9. Assume a circular road curve at the top of the hill, as shown. (a) What is the centripetal acceleration of the car driver at the (b) What is the ratio of the apparent weight to the actual (c) What is the tangential acceleration on the car during the (d) Determine the magnitude of the total acceleration on the car as the car starts to skid at the (e) What is the angle between the total acceleration and the tangential acceleration at the top (1) At what critical maximum speed (in mph) can the car travel in order to lose contact with [(a) 4.5 m/s, (b) 54%; (c)-4.8 m/s, (d) 6.6 m'; (e) 43°, (f) 99 mph] given speed at the top of the hill? weight of the driver at this top of the hill? braking? top of the hill? r 200 m on the hill? the road at the top of the hill

Explanation / Answer

4. given r = 200 m

v = 30 m/s

coefficient of kinetic friction, k = 0.9

a. centripital acceelration = v^2/r = 4.5 m/s/s

b. apparent weight = Normal reaction force = N

N + mv^2/r - mg = 0

N = mg - mv^2/r = m(g - 4.5) = 5.31m N

hence

N/mg = 5.31/g = 0.5412

c. tangential acceleration = k*N/m = 0.9*5.31 = 4.779 m/s/s

d. total acceleration = sqroot(4.779^2 + 4.5^2) = 6.564 m/s/s

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