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

`(3)/(4)`

Step-by-step explanation:

m = Mass of car

3m = Mass of truck

v = Velocity of car

`(1)/(2)v` = Velocity of truck

r = Turn radius

Centripetal force is given by

For car

`F_1=(mv^2)/(r)`

For truck

`F_2=(3m((1)/(2)v)^2)/(r)\\\Rightarrow F_2=(3m(1)/(4)v^2)/(r)`

Dividing the forces we get

`(F_1)/(F_2)=((mv^2)/(r))/((3m(1)/(4)v^2)/(r))\\\Rightarrow (F_1)/(F_2)=(4)/(3)\\\Rightarrow F_2=(3)/(4)F_1`

So, the multiple of the original force is
`(3)/(4)`