You and your family take a road trip on a long holiday weekend. In a certain sec

Question

You and your family take a road trip on a long holiday weekend. In a certain section of the trip where the road is particularly uneven, the car goes over a bump that is curved downward with a radius of 16.5 m. See diagram below. The mass of the car and its passengers is 1450 kg.

(a) When the car is at the highest point of the bump its speed is 7.50 m/s. Determine the magnitude and direction of the force exerted by the road on the car at this highest point.

(b) If the speed at the highest point is above a certain maximum value the car will lose contact with the road. Calculate this maximum speed.
m/s

Explanation / Answer

Summing forces,

N - mg = -m v^2 / R

as the acceleration is downward, towards the center of the circle.

Solving for N,

N = 9267 N   [ANSWER, UPWARD]

********************

It will lose contact with the road if N = 0. Thus,

N - mg = -m v^2 / R

0 - mg = -m v^2 / R

Solving for v,

v = 12.72 m/s   [ANSWER]

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