A flat (unbanked) curve on a highway has a radius of 230.0 . A car rounds the curve at a speed of 28.0 .What is the minimum coefficient of friction that will prevent sliding?
0.35
To find the minimum coefficient of friction required to prevent sliding, we can use the centripetal force equation:
Fc = μ*mg
Where:
Fc is the centripetal force,
μ is the coefficient of friction,
m is the mass of the car,
and g is the acceleration due to gravity.
First, we need to find the centripetal force acting on the car. The centripetal force is given by:
Fc = m*v^2 / R
Where:
v is the velocity of the car,
and R is the radius of the curve.
Given:
v = 28.0 m/s
R = 230.0 m
Substituting these values into the equation, we have:
Fc = (m*28.0^2) / 230.0
Now, we can set up an equation using the centripetal force equation and the weight of the car:
μ*mg = (m*28.0^2) / 230.0
Simplifying the equation:
μ*g = (28.0^2) / (230.0*g)
We can cancel out the mass of the car.
μ = (28.0^2) / (230.0*g)
Finally, we need to substitute the value of g (acceleration due to gravity):
μ = (28.0^2) / (230.0*9.8)
Calculating the numerator:
28.0^2 = 784
μ = 784 / (230.0*9.8)
Calculating the denominator:
230.0*9.8 = 2254.0
Finally, plugging in the values:
μ = 784 / 2254.0
Calculating the value of μ:
μ ≈ 0.347
Therefore, the minimum coefficient of friction required to prevent sliding is approximately 0.347.
To determine the minimum coefficient of friction that will prevent sliding, we can use the following formula:
μ ≥ (v^2) / (g * r)
Where:
μ - Coefficient of friction
v - Velocity of the car
g - Acceleration due to gravity (approximately 9.8 m/s^2)
r - Radius of the curve
Let's substitute the given values into the formula:
μ ≥ (28.0^2) / (9.8 * 230.0)
1. Calculate the numerator:
(28.0^2) = 784.0
2. Calculate the denominator:
9.8 * 230.0 = 2254.0
3. Divide the numerator by the denominator:
784.0 / 2254.0 ≈ 0.3474
Therefore, the minimum coefficient of friction that will prevent sliding is approximately 0.347.