Compute the force exerted by the tires on the road:

An automobile of mass 1500 kg traverses a 500 m curve at a constant speed of

50 kmph. Supposing no banking of the curve, compute the force exerted by the tires on the road to maintain motion along the curve.

Solution

Speed of the car = 50 kmph = (50 × 1000)/3600 = 13.89 m / sec

Acceleration acting on the car shall be oriented along the line towards the centre. Therefore,

a_n   = v²/r

= 13.89²/500

= 0.386 m / sec²

 Inertia force

F_i  = - m a = 1500 × 0.386  (by neglecting the sign)

= 579.0 N

Let Free Body Diagram as illustrated Figure (b), we may write equilibrium equations as below :

 ∑ F_x  = 0  ∴ F_i  - F = 0

                                  F = 579.0 N

∑ F_y  = 0  ∴ N - m g = 0

N = 1500 × 9.81 = 14715 N.