Friction provides the force needed for a car to travel around a flat, circular race track. What is the maximum speed at which a car can safely travel if the radius of the track is 80.0 m and the coefficient of friction is 0.38?
At the maximum safe speed V, the maximum possible static friction force equals the centripetal force.
M V^2/R = M g*0.38
Cancel the M and solve for V
V = sqrt(0.38 g R)
To find the maximum speed at which a car can safely travel around a flat, circular race track, we can use the principle of centripetal force.
The centripetal force acting on the car is provided by friction and is given by the equation:
Fc = μ * N
Where Fc is the centripetal force, μ is the coefficient of friction, and N is the normal force.
The normal force is the force exerted by the track on the car perpendicular to the track's surface. In this case, it is equal to the car's weight, which can be calculated as:
N = m * g
Where m is the mass of the car and g is the acceleration due to gravity.
The centripetal force can also be expressed as:
Fc = m * (v^2 / r)
Where v is the velocity of the car and r is the radius of the track.
By equating these two expressions for Fc and solving for v, we can find the maximum speed at which the car can safely travel:
μ * N = m * (v^2 / r)
μ * m * g = m * (v^2 / r)
μ * g = v^2 / r
v^2 = μ * g * r
v = sqrt(μ * g * r)
Now, we can plug in the given values:
μ = 0.38 (coefficient of friction)
g ≈ 9.8 m/s^2 (acceleration due to gravity)
r = 80.0 m (radius of the track)
v = sqrt(0.38 * 9.8 * 80.0)
v = sqrt(296.8)
v ≈ 17.2 m/s
Therefore, the maximum speed at which the car can safely travel on this track is approximately 17.2 m/s.
To find the maximum speed at which a car can safely travel, we can use the centripetal force formula:
F = m * a
Where:
F = Centripetal force
m = Mass of the car
a = Centripetal acceleration
The centripetal force is provided by the frictional force:
F = frictional force
The frictional force can be calculated using the formula:
frictional force = coefficient of friction * normal force
The normal force acting on the car can be calculated by:
normal force = m * g
Where:
g = acceleration due to gravity
Now, we can combine these equations to find the maximum speed.
1. Find the normal force:
normal force = m * g
2. Calculate the frictional force:
frictional force = coefficient of friction * normal force
3. Determine the centripetal force:
F = frictional force
4. Calculate the centripetal acceleration:
a = F / m
5. Use the centripetal acceleration formula to find the maximum speed:
v = √(r * a)
Let's calculate it step by step.
Given:
Radius (r) = 80.0 m
Coefficient of friction (μ) = 0.38
First, we need the mass of the car. Since it is not provided, we cannot proceed with the calculation. We need the mass of the car to find the normal force.