Question

A 888 kg car is driven clockwise around a flat circular track of radius 59 m. The speed of the car is a constant 7 m/s. Which factor, when doubled, would produce the greatest change in the centripetal force acting on the car? A. Radius of the track B. Weight of the car C. Mass of the car D. Velocity of the car

Answer 1

D. Velocity of the car

Step-by-step explanation:

The centripetal force acting on the car is given by the following formula:

`F_c=ma_c=m(v^2)/(r)` (1)

m: mass of the car = 888 kg

v: tangential speed of the car = 7 m/s

r: radius of the flat circular track = 59 m

By the form of the equation (1) you can notice that the greatest change in the centripetal force is obtained when the velocity v is twice. In fact, you have:

`F_c=m((2v)^2)/(r)=4m(v^2)/(r)=4F_c`

Then, the greatest values of the centripetal force is:

`F_c=4(888kg)((7m/s)^2)/(59m)=2949.96N`

The greatest change in Fc is obtained by changing the value of the speed

answer

D. Velocity of the car