if co-efficient of friction between tyre and road is0.5, what is smallest radious at which car turn on a horizontal road when its speed is 30km/hr?
To determine the smallest radius at which a car can turn on a horizontal road, we need to consider the relationship between the coefficient of friction, the car's speed, and the radius of the turn.
When a car turns, the tires experience a centripetal force that keeps the car moving in a circular path. The centripetal force is provided by the friction between the tires and the road. To calculate the smallest radius, we need to determine the maximum centripetal force that friction can provide.
The centripetal force can be calculated using the following formula:
F = (m * v^2) / r
Where:
F = centripetal force
m = mass of the car
v = velocity of the car
r = radius of the turn
In this case, we know the coefficient of friction between the tires and the road is 0.5, and the car's speed is 30 km/hr. To use this information, we need to convert the speed to meters per second (m/s), since the formula requires the velocity in SI units.
1 km/hr = 1000 m/3600 s ≈ 0.2778 m/s
Therefore, the car's speed is approximately 8.33 m/s.
Now, we can rearrange the formula to solve for the radius:
r = (m * v^2) / F
Since friction provides the centripetal force, we can substitute the formula for friction:
F = µ * N
Where:
µ = coefficient of friction
N = normal force (equal to the weight of the car)
Assuming a flat horizontal road, the normal force is equal to the weight of the car, which is given by:
N = m * g
Where:
g = acceleration due to gravity
Now, we can substitute the values into the formula for the radius:
r = (m * v^2) / (µ * m * g)
Simplifying the equation further, we can cancel the mass of the car:
r = v^2 / (µ * g)
Now, we can plug in the values:
r = (8.33 m/s)^2 / (0.5 * 9.8 m/s^2)
Calculating this equation gives us the radius of the smallest turn the car can make on a horizontal road when its speed is 30 km/hr.