Suppose a 1,950-kg car passes over a bump in a roadway that follows the arc of a

Question

Suppose a 1,950-kg car passes over a bump in a roadway that follows the arc of a circle of radius 20.0 m as in the figure shown 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 8.15 m/s? (Neglect any friction that may occur.)

(b) What is the maximum speed the car can have without losing contact with the road as it passes this highest point?
m/s

magnitude
Your response differs from the correct answer by more than 10%. Double check your calculations. kN direction ---Select--- up left down right

Explanation / Answer

here m = 1950 Kg r = 20 m v = 8.15 m/s

fron newton second law

F = ma = mg - N

N = mg - ma

here a is the centrifugel acceleration so

a = ac = v2 / r

ac = (8.15)2 / 20 = 3.3211 m/s2

so the normal force

N = 1950 ( 9.8 - 3.3211 )

N = 12633.80625 N = 12.6338 KN Ans

here acceleration is in downword so the normal force is also in direction

(b) at the highest point it passes the normal force will zero

N = 0

m (g - a) = 0

g - v2 / r = 0

v2 = 9.8 x 20

V = 14.007 m/s Ans

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