A 1200-kg sports car (including the driver) crosses the rounded top of a hill (r
ID: 585423 • Letter: A
Question
A 1200-kg sports car (including the driver) crosses the rounded top of a hill (radius = 95.0 m ) at 23.0 m/s .
Determine the normal force exerted by the road on the car.
Express your answer to three significant figures and include the appropriate units.
Determine the normal force exerted by the car on the 62.0-kg driver.
Express your answer to three significant figures and include the appropriate units.
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.
v =Explanation / Answer
a) Net force, FN acting on the car as it is at the top on the circular path = mv^2/r = (1200 x 23^2)/95 = 6682.1052 N downward
There are only two forces acting on car by earth, FE which is fixed = 1200x9.8 = 11760 N acting downward and adjustable reaction force by road on car upwards, Let this FR. We have
FN = FE - FR or FR = FE - FN= 5077.894 N
b) Applying similar logic on driver we have force of reaction by seat of driver
= 62x9.8 - (62x23^2)/95 =607.6 - 345.242 = 262.358 N
c) Let the velocity of the car be V when the reaction force by seat of driver becomes zero. Thus we have
62x9.8 = (62xV^2)/95 or V^2 = 95x9.8 = V = 30.512 m/s
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