Find the maximum velocity for skidding for a car moving on a circular track of radius 100 m. The coefficient o

Question

Find the maximum velocity for skidding for a car moving on a circular track of radius 100 m. The coefficient of friction between the road and tyre is 0.2.

Accepted Answer

1. **Identify the Principle:** For a car moving on a level circular track, the necessary centripetal force is provided by the force of static friction between the tyres and the road [Source 69].
2. **Formula:** The maximum safe speed ($v_{max}$) to avoid skidding is given by the condition where the maximum static friction equals the centripetal force:
   $$ \frac{mv_{max}^2}{R} = \mu_s mg $$
   $$ v_{max} = \sqrt{\mu_s Rg} $$
   [Source 69, 70]
3. **Calculation:**
   - Coefficient of friction ($\mu_s$) = 0.2
   - Radius ($R$) = 100 m
   - Acceleration due to gravity ($g$) $\approx 9.8 	ext{ m/s}^2$
   Substitute the values:
   $$ v_{max} = \sqrt{0.2 	imes 100 	imes 9.8} $$
   $$ v_{max} = \sqrt{196} $$
   $$ v_{max} = 14 	ext{ m/s} $$

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