The coefficient of friction b/n the tyre of the car rotating around horizontal circular road and the road way is 0.5; whate would the minimum radius at w/c acar turn a horizontal road when its speed is 15m/s?(g=10m/s square)
To find the minimum radius at which a car can turn a horizontal road, we need to consider the centripetal force that keeps the car moving in a circular path.
The centripetal force is given by the equation: Fc = m * (v^2 / r), where Fc is the centripetal force, m is the mass of the car, v is the speed of the car, and r is the radius of the circular path.
In this case, we want to find the minimum radius at which the car can turn, which means we need to consider the maximum possible centripetal force. This occurs when the frictional force between the car's tires and the road is at its maximum.
The maximum frictional force is given by the equation: Fmax = μ * N, where μ is the coefficient of friction and N is the normal force.
In this case, the weight of the car provides the normal force. The weight is given by the equation: W = m * g, where W is the weight, m is the mass of the car, and g is the acceleration due to gravity.
Now, let's calculate the minimum radius:
1. Calculate the weight of the car:
W = m * g = m * 10 m/s^2
2. Calculate the maximum frictional force:
Fmax = μ * N = μ * W
3. Calculate the maximum centripetal force:
Fmax = m * (v^2 / r)
Since we want to find the minimum radius, we can equate these two equations:
μ * W = m * (v^2 / r)
4. Rearrange the equation to solve for r:
r = (μ * W * r) / m * v^2
Now, substitute the given values into the equation:
μ = 0.5 (given)
W = m * g = m * 10 m/s^2
v = 15 m/s (given)
r = (0.5 * m * 10 m/s^2 * r) / (m * (15 m/s)^2)
Simplifying the equation further:
r = (5 * r) / (15^2)
r = 5r / 225
225r = 5r
225r - 5r = 0
220r = 0
r = 0
Therefore, the minimum radius is zero. This means that theoretically, the car could turn on a perfectly flat road with a radius of zero and at a speed of 15 m/s. However, in practical situations, there will always be a minimum radius of turn due to various factors such as car design, tire grip, and road conditions.