During testing, a 4 wheeled vehicle of mass 1100 kg travelling at 70 km/h must b

Question

During testing, a 4 wheeled vehicle of mass 1100 kg travelling at 70 km/h must be brought to a halt in a distance of 40 m.

a) Calculate what frictional force is required on each of the tyres to bring the vehicle to a halt (assuming the force is constant during the braking and the force is equally distributed over the 4 tyres).

[5 marks]

b) Calculate what minimum value of dynamical coefficient of friction is required for the tyre- road surface interface to give the above test results with the tyres blocked.

[4 marks]

c) Calculate the time taken for the vehicle to come to a halt and hence what power of braking system is required for the above test.

Explanation / Answer

a) initial speed , u = 70 km/h = 70 x 1000m/3600s = 19.44 m/s

final speed = 0

d = 40 m

Using v^2 - u^2 = 2ad

0^2 - 19.44^2 = 2(a)(40)

a = - 4.73 m/s^2

F = ma = 1100 x 4.73 = 5198.7 N in opposite direction

friction force on each tire = 5198.7/4 = 1300 N

b) friction force = u N = u Mg

5198.7 = uk (1100 x 9.8)

uk = 0.48

c) for time,

using v= u + at

0 = 19.44 - 4.73t

t = 4.11 s

P = ( F.d ) / t = (5198.7 x 40) / 4.11 = 50554.47 W

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