What must be the friction?

Question

Harry Hotrod rounds a corner in his sports car at 50 km/h. The friction force holds him on the road. If he has twice the speed, what must be the friction force to prevent him from skidding off the road?

Answer 1

The friction must counteract (and equal) the outward acceleration defined by:

 

eq 1)    a = v²/r

 

And the friction force can be found with

 

F= ma, subsituting eq 1)    F=mv²/r

 

For this problem mass and radius are constants. 

 

Let F1 equal the friction force at 50 km/h.

Let F2 equal the friction force at 100 km/h  (2x50)

 

If we set this up as a ratio:

 

F1        mv²/r

---- =  -------

F2        m(2v)²/r

 

the m, r and v² cancel from the equation and we are left with 1/4. 

 

The friction force at 100 km/h must be 4 times larger than it was at 50 km/h.

Answer 2

Let f be the friction force. Apply Newton's second law towards to the center of the rotation.

f = mv^2/r, where f is the only force in centrilpetal direction.

If you double v, then f is quadripled.