Question

A car is traveling 30 m/s around a curve of radius 100 m. What is the minimum value of the coefficient of static friction between the tires and the road required to prevent the car from skidding?

Answer 1

The minimum value of the coefficient of static friction is equal to 0.92.

How to determine the minimum value of the coefficient of static friction?

First of all, we would derive an expression for the horizontal and vertical component of forces acting acting on the car.

For the vertical component, we have:

∑Fy = 0

Fn + Fg = 0

Fn - mg = 0

Fn = mg     .....equation 1.

For the horizontal component, we have:

∑Fx = mAc

uFn = m(V²/r)    .....equation 2.

Substituting eqn. 1 into eqn. 2, we have:

umg = m(V²/r)

u = 1/g(V²/r)

u = (V²/gr)

u = (30²/9.8 × 100)

u = 900/980

u = 0.92.

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