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} = v^{2}/r
= 13.89^{2}/500
= 0.386 m / sec^{2}
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.