Compute the force exerted by the tires on the road, Mechanical Engineering

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,

an   = v2/r

= 13.892/500

= 0.386 m / sec2

 Inertia force

Fi  = - 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 :

 ∑ Fx  = 0  ∴ Fi  - F = 0

                                  F = 579.0 N

∑ Fy  = 0  ∴ N - m g = 0

N = 1500 × 9.81 = 14715 N.

Posted Date: 1/29/2013 2:21:21 AM | Location : United States







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