Question

Now assume that two identical cars of mass m drive along a highway. One car approaches a curve of radius 2R at speed v. The second car approaches a curve of radius 6R at a speed of 3v. How does the magnitude F1 of the net force exerted on the first car compare to the magnitude F2 of the net force exerted on the second car? a. F1 = 1/3F2 b. F1 = 3/4F2 c. F1 = F2 d. F1 = 3F2 e. F1 = 27F2

Answer 1

a. F1 = 1/3F2.

Step-by-step explanation:

Given:

Car 1:

Mass = M

R = 2R

V = v

Car 2:

Mass = M

R = 6R

V = 3v

Fc = MV^2/R

F1 = M × v^2/3R

F2 = M × 9v^2/6R

F1 = F2

3R × F1/v^2 = 6R × F2/9v^2

F1 = F2/3

Answer 2

a) F1 is 1/3 of F2

option a is correct

Step-by-step explanation:

The net force for both cars will be the centrifugal force,

The equation for the centrifugal force is:

`F=m(v^2)/(r)`

So for the first car we have

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

For other car we will have

`F_2 = (m(3v)^2)/(6R)`

`F_2 = (3mv^2)/(2R)`

So
`F_2=3F_1,`

which means the magnitude F₁ of the net force exerted on the first car is one third to the magnitude F₂ of the net force exerted on the second car.

F₁ is 1/3 of F₂