Comparing Sideward Static Friction Forces on Cars of Different Masses and Speeds

[courtney1121]

Car 1 with mass m rounds a curve of radius R traveling at a constant speed v. Car 2 with a mass 2m rounds a curve of radius 2R at a constant speed 2v. How does the magnitude F2 of the sideward static friction force acting on car 2 compare with the magnitude F1 of the sideward static friction force acting on car 1?

a. F1 = 4F2
b. F1 = 2F2
c. F1 = F2
d. F2 = 2F1
e. F2 = 4F1

 

[radou]

In order to get some help, you should show some efforts first.

 

[courtney1121]

sorry, I had listed my knowns but it didn't show

Anyways

I know that car 1 has half of everything car 2 has, so wouldn't it make sense that F2 = 2F1?

 

[radou]

Hint: compare the centripetal forces.

 

[courtney1121]

Ok the equation of centripetal forces is mv^2/r. The force of car one is simply mv^2/r and the centripteal force of car 2 would be 4mv^2/2r which equals 2mv^2/r. So Force of car 2 is twice that of force of car 1 so F1=2F2?

 

[radou]

Ok the equation of centripetal forces is mv^2/r. The force of car one is simply mv^2/r and the centripteal force of car 2 would be 4mv^2/2r which equals 2mv^2/r. So Force of car 2 is twice that of force of car 1 so F1=2F2?

The centripetal force exerted on the second car is 2m (2v)^2/(2R) = 4m v^2/R.

 

[courtney1121]

what happened to 2R?

 

[radou]

what happened to 2R?

$$2m \frac{(2v)^2}{2R}= 2m \frac{4v^2}{2R}= 2m \frac{2v^2}{R}= 4m \frac{v^2}{R}$$. I hope you agree on that.

 

[courtney1121]

ok ok i see what you did now

 

[courtney1121]

so then that means F2 = 4F1

 

[radou]

Yes, since the sideward frictional force should balance the centripetal force.