A proud new Honda owner drivers her car at a speed of 25 m/s into a corner. The coefficients of friction between the road and the tires are 0.70 (static) and 0.40(kinetic). What is the minimum radius of curvature for the corner in order for the car not to skid?
2007-10-28 13:45:33 · 1 answers · asked by korr 2 in Science & Mathematics ➔ Physics
Just to make things easier, let's let M be the mass of the car. That lets us use the force equations directly, even though M cancels in the end.
So you have two sets of equations:
The centripetal acceleration A is V^2/R so the centripetal force Fc is M x A.
That force has to be balanced by the frictional force. Since the tires are not supposed to slip in the radial direction (this is an idealized world, not reality :-) we use the coefficient of static friction.
Fs = Cs x N
If the road is flat - no banking, etc. N is just the weight of the car:
N = M x g
where g is approximately 9.8 m/s^2
So just substitute back:
Fc = Fs
M x V^2 / R = M x Cs x g
and solve for R.
2007-10-31 13:42:07 · answer #1 · answered by simplicitus 7 · 0⤊ 0⤋