Find maximum speed at which vehicle can turn round a curve of 20 m rad...
Maximum Speed on a Curve Calculation:
- To find the maximum speed at which a vehicle can turn round a curve of 20 m radius on a level road with a coefficient of friction μs 0.5, we can use the formula for centripetal force:
Centripetal Force Formula:
\[ F_{\text{centripetal}} = \dfrac{mv^2}{r} \]
- Where:
- \( F_{\text{centripetal}} \) = Centripetal force
- \( m \) = Mass of the vehicle
- \( v \) = Velocity of the vehicle
- \( r \) = Radius of the curve
Maximum Speed Formula:
\[ F_{\text{friction}} = \mu_s \cdot m \cdot g \]
- Where:
- \( F_{\text{friction}} \) = Frictional force
- \( \mu_s \) = Coefficient of friction
- \( g \) = Acceleration due to gravity
- At maximum speed, the centripetal force is equal to the frictional force. Therefore:
\[ \dfrac{mv^2}{r} = \mu_s \cdot m \cdot g \]
- Mass \( m \) cancels out from both sides of the equation, leaving us with:
\[ v = \sqrt{\mu_s \cdot g \cdot r} \]
Calculating Maximum Speed:
- Given:
- \( \mu_s = 0.5 \)
- \( g = 9.81 \, m/s^2 \)
- \( r = 20 \, m \)
- Plugging in the values:
\[ v = \sqrt{0.5 \cdot 9.81 \cdot 20} \]
\[ v = \sqrt{98.1} \]
\[ v \approx 9.9 \, m/s \]
Conclusion:
- The maximum speed at which the vehicle can turn round a curve of 20 m radius on a level road with a coefficient of friction \( \mu_s = 0.5 \) is approximately 9.9 m/s.
Find maximum speed at which vehicle can turn round a curve of 20 m rad...
V=?,r=20, v square= urg, =0.5/10×20=5×20 ×10=100=v=√100=10m/s