The next two questions are about the following situation 100 m A car, which weig

Question

The next two questions are about the following situation 100 m A car, which weighs 20 N,travels over a bumpy road with a constant speed. Gravity acts. The road at point B is in the shape of a circle with a radius of 100 meters. 10. Which statement correctly relates the force of the car on the road at points A (a valley) and B (the top of a hill). a·The magnitude of the force of the car on the road is less at point A than it is at point B b·The magnitude of the force of the car on the road is less at point B than it is at point A. c. You need to know the road radius at point A to answer this question. 11. With what speed must the car travel such that the force that it exerts on the road at point B is a. 9.8 m/s b. 15.5 m/s c. 22.1 m/s d. 26.2 m/s e. 31.3 m/s

Explanation / Answer

10) The paths are curved in nature and hence they will have radius of curvature R

On a curved path, the car will experience centripetal/ centrifugal force ( depending on frame of observer)

This force is (MV2 / R) ; M is, mass of the car ; V is , velocity of the car.

So the path with higher radius of curvature will have lower force and vice versa.

To compare two such forces we need the value of both the radius of curvatures.

11) Here force is 600N

==> 600 = (MV2 / R) ==> V = (600*R/M)0.5 ; Mass of the car is 2000/g ; g = 9.81 m/s2

We get V = 17.1551 m/s

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