Suppose that a 1800 kg car passes over a bump in a roadway that follows the arc

Question

Suppose that a 1800 kg car passes over a bump in a roadway that follows the arc of a circle of radius 19.2 m as in the figure below.

(a) What force does the road exert on the car as the car passes the highest point of the bump if the car travels at 37.5 km/h? (Neglect friction.) NOTE: The "force that the road exerts on the car" is just the Normal force. HINT: Draw the free body diagram for the car. Use the fbd to write out the forces in the Sum of the Forces in the Radial Direction = mv2/r, being careful to notice that the inward direction is positive for the radial direction. Think about where the center of the circle is in this example.

(b) What is the maximum speed the car can have without losing contact with the road as it passes this highest point? HINT: Think about what it means for the normal force if the car loses contact with the road.

Explanation / Answer

part A)

speed of car , v = 37.5 km/hr = 10.41 m/s

normal force = m * g - m * v^2/R

normal force = 1800 * (9.8 - 10.41^2/19.2)

normal force = 7467 N

part B)

let the maximum speed is v

m * v^2/R = m * g

v^2/19.2 = 9.8

v = 13.7 m/s = 49.4 km/hr

the maximum speed is 13.7 m/sor 49.4 km/hr

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