Question

A car of mass m travels around a particular highway curve at speed v. If a truck of mass 3 m travels around this same corner but at half the speed of the car, then the new centripetal force required must be what multiple of the original force?

Answer 1

Answer:

$\dfrac{3}{4}$

Explanation:

m = Mass of car

3m = Mass of truck

v = Velocity of car

$\dfrac{1}{2}v$ = Velocity of truck

r = Turn radius

Centripetal force is given by

For car

$F_1=\dfrac{mv^2}{r}$

For truck

$F_2=\dfrac{3m(\dfrac{1}{2}v)^2}{r}\\\Rightarrow F_2=\dfrac{3m\dfrac{1}{4}v^2}{r}$

Dividing the forces we get

$\dfrac{F_1}{F_2}=\dfrac{\dfrac{mv^2}{r}}{\dfrac{3m\dfrac{1}{4}v^2}{r}}\\\Rightarrow \dfrac{F_1}{F_2}=\dfrac{4}{3}\\\Rightarrow F_2=\dfrac{3}{4}F_1$

So, the multiple of the original force is $\dfrac{3}{4}$