A car of mass 1500 kg is moving at a constant speed of 20 m/s around a horizonta

Question

A car of mass 1500 kg is moving at a constant speed of 20 m/s around a horizontal track with a radius of 100 meter. a. What is the centripetal acceleration of the car? b. How much centripetal force is required to keep the car moving in a circle? c. What is the required coefficient of friction between the car tires and the road to keep the car moving at 20 m/s? d. Would the required coefficient of friction be higher, lower, or the same for a 2500 kg truck travelling at 20 m/s along the same track? Explain. e. A maniacal roller-coaster designer builds a coaster using cars of 1500 kg completing a vertical loop of radius 100 meters (like the track above on edge). What is the minimum speed needed by the cars at the highest point to complete the loop?

Explanation / Answer

a) v = 20m/s

R = 100m

centripetal acceleration = v2/R = (20)2/100 = 4m/s2

b) centripetal force = mv2/R = 1500x4 = 6000N

c)Let the coefficient of friction be f

mgf = mv2/R

f = v2/gR

= (20x20)/(9.8x100) = 0.408

d) The required coefficient of friction would be same because it is independent of mass of vehicle

e) Minimum speed should be such that the centripetal force is equal to weight of car

mg = mv2/R

v = sqrt(gR)

= sqrt(9.8x100)

= 31.3 m/s

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