Question

Fig. 1.16
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/s)
(Ans : 46.70 m/s, 29.39 m/s)
​

Answer 1

Dear Student,

◆ Answer -

vmax = 46.14 m/s

vopt = 29.39 m/s

● Explanation -

# Given -

r = 500 m

g = 9.8 m/s^2

μ = 0.25

θ = 10°

# Solution -

(i) Maximum speed to avoid slipping -

vmax = √[r.g (μ+tanθ) / (1-μ.tanθ)]

vmax = √[500 × 9.8 (0.25 + tan10) / (1 - 0.25 × tan10)]

vmax = √2129

vmax = 46.14 m/s

(ii) Optimum speed to aboid wear & tear -

vopt = √(r.g.tanθ)

vopt = √(500 × 9.8 × tan10°)

vopt = √864

vopt = 29.4 m/s

Thanks for asking..

Answer 2

Answer:

✔️✔️Hope it helps to u ✔️✔️