Question

A circular race course track has a radius of 500 m and is banked to 10°. If the coefficient of friction between tyres of vehicle and the road surface is 0.25. Compute : (a) the maximum speed to avoid slipping. (b) the optimum speed to avoid wear and tear of tyres. (g = 9.8 m/s²) (Ans : 46.70 m/s, 29.39 m/s)

Answer 1

Answer:

(a) 46.74 m/s

(b) 29.39 m/s

Explanation:

(a) In the question,

We know that the,

Radius of the curve = 500 m

Angle of banking, θ = 10°

Co-efficient of friction between tyres and road surface, μ = 0.25

Now,

The relation between the maximum speed and the banking is given by,

$v^{2}_{max}=\frac{Rg(tan\theta+\mu)}{1-\mu tan\theta}\\So,\\v_{max}=\sqrt{\frac{Rg(tan\theta+\mu)}{1-\mu tan\theta}}$

So,

On putting the value of the respective variables we get,

Maximum speed in case of banking is given by,

$v_{max}=\sqrt{\frac{500\times9.8(tan10+0.25)}{1-0.25 tan10}}\\v_{max}=\sqrt{\frac{2089.002}{0.95591}}\\v_{max}=46.74\ m/s$

Therefore, the maximum speed to avoid slipping is 46.74 m/s.

(b) The optimum speed of the vehicle is given by when the value of co-efficient of friction becomes 0.

So,

μ = 0

We get,

$v_{opt}=\sqrt{Rgtan\theta}\\v_{opt}=\sqrt{500\times 9.8tan10}\\v_{opt}=29.39\ m/s$

Therefore, the optimum speed is given by 29.39 m/s.

Answer 2

Answer:

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