Question

Centripetal force Fc acts on a car going around a curve. If the speed of the car were twice as great, the magnitude of the centripetal force necessary to keep the car moving in the same path would be

Answer 1

Answer:

We need 4 times more force to keep the car in circular motion if the velocity gets double.

Explanation:

Lets take the mass of the car = m

The radius of the arc = r

$F=\frac{m\times v^2}{r}$

Given that speed of the car gets double ,v' = 2 v

Then the force on the car = F'

$F'=\frac{m\times v'^2}{r}$  ( radius of the arc is constant)

$F'=\frac{m\times (2v)^2}{r}$

$F'=4\times \frac{m\times v^2}{r}$

We know that $F=\frac{m\times v^2}{r}$

Therefore F' = 4 F

So we can say that we need 4 times more force to keep the car in circular motion if the velocity gets double.