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

Question

Suppose that a 1800 kg car passes over a bump in a roadwaythat follows the arc of a circle of radius 21.6 m as in the figure below. (a) What force does the road exert on the car as the carpasses the highest point of the bump if the car travels at36.0 km/h?
b) What is the maximum speed the car can have without losingcontact with the road as it passes this highest point? Suppose that a 1800 kg car passes over a bump in a roadwaythat follows the arc of a circle of radius 21.6 m as in the figure below. (a) What force does the road exert on the car as the carpasses the highest point of the bump if the car travels at36.0 km/h?
b) What is the maximum speed the car can have without losingcontact with the road as it passes this highest point?

Explanation / Answer

a) v=36.0km/h=36000m/3600s = 10.0m/s F=ma = m(v2 / r) = 1800kg*(10.0m/s)2 /21.6m = 8333.33 N the force is 8333.33N b) at the heighest point, gravitational force F1 = mg if ma = m(v2 / r) <= F1 , the car will not lostcontant with the road,, we have: mg = m(v2/r) =>v = (rg) = (21.6m*9.8m/s2 ) =14.55 m/s as long as v <= 14.55 m/s, the car will not lost contactwith the road.

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