A 1000-kg sports car (including the driver) crosses the rounded top of a hill (r

Question

A 1000-kg sports car (including the driver) crosses the rounded top of a hill (radius = 90.0m ) at 22.0m/s .

Part A

Determine the normal force exerted by the road on the car.

Express your answer to three significant figures and include the appropriate units.

Part B

Determine the normal force exerted by the car on the 73.0-kg driver.

Express your answer to three significant figures and include the appropriate units.

Part C

Determine the car speed at which the normal force on the driver equals zero.

Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

a) Net force, FN acting on the car as it is at the top on the circular path = mv^2/r = (1450 x 27^2)/94 = 11245.2 N downward
There are only two forces acting on car by earth, FE which is fixed = 1450x9.8 = 14210 N acting downward and adjustable reaction force by road on car upwards, Let this FR. We have
FN = FE - FR or FR = FE - FN=2964.8 N

b) Applying similar logic on driver we have force of reaction by seat of driver = 77x9.8 - (77x27^2)/94 =754.6 - 597.2 = 157.4 N

c) Let the velocity of teh car be V when the reaction force by seat of driver becomes zero. The we have
77x9.8 = (77xV^2)/94 or V^2 = 94x9.8 = 921.2 or V = 30.4 m/s

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