Answer to Question #246133 in Molecular Physics | Thermodynamics for Kelani

Question

A car of mass m follows a truck of mass 2m around a circular turn. Both vehicles move at speed v.

(a) What is the ratio of the truck's net centripetal force to the car's net centripetal force?

F_truck

____

F_car = 

(b) At what new speed v_truck will the net centripetal force acting on the truck equal the net centripetal force acting on the car still moving at the original speed v? State your answer in terms of v.

v_truck =  

Answer 1

(a) Formula for centripetal force is

$F=\frac{mv^2}{r} \\ F_{truck} = \frac{2mv^2}{r} \\ F_{car} = \frac{mv^2}{r} \\ \frac{F_{truck}}{F_{car}} = 2$

(b)

$F_{car} = \frac{mv^2}{r} \\ F_{truck} = \frac{2mv_{truck}^2}{r} \\ F_{car} = F_{truck} \\ \frac{2mv_{truck}^2}{r} = \frac{mv^2}{r} \\ v_{truck} = \sqrt{\frac{v^2}{2}} \\ = \frac{v}{\sqrt{2}}$