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 77.0 m and the coefficient of friction is 0.36?

For a flat track, equate the maximum friction force to the required centripetal force.

0.36 M g = M V^2/R

The M's cancel. Solve for V

The friction coefficient you are using is the static one, since the tires (although rolling) are not skidding.

5.3

To find the maximum speed at which a car can safely travel around a flat, circular race track, we can use the equation:

Centripetal force = Frictional force

The centripetal force can be expressed as:

Centripetal force (Fc) = (mass of the car) * (velocity of the car)^2 / (radius of the track)

Frictional force (Ff) = (coefficient of friction) * (normal force)

In this case, the normal force is equal to the weight of the car, which can be expressed as:

Normal force (N) = (mass of the car) * (acceleration due to gravity)

Therefore, we have:

Fc = Ff

(mass of the car) * (velocity of the car)^2 / (radius of the track) = (coefficient of friction) * (mass of the car) * (acceleration due to gravity)

Simplifying the equation, we get:

(velocity of the car)^2 = (coefficient of friction) * (radius of the track) * (acceleration due to gravity)

Now, we can solve for the maximum speed (velocity) of the car by taking the square root of both sides of the equation:

velocity of the car = √[(coefficient of friction) * (radius of the track) * (acceleration due to gravity)]

Plugging in the given values:

velocity of the car = √[(0.36) * (77.0 m) * (9.8 m/s^2)]

velocity of the car ≈ √(268.392) m/s ≈ 16.4 m/s

Therefore, the maximum speed at which the car can safely travel is approximately 16.4 m/s.

To find the maximum speed at which a car can safely travel on a flat, circular race track, we need to consider the forces acting on the car. In this case, the centripetal force required to keep the car in circular motion is provided by the friction force between the tires and the track surface.

The centripetal force is given by the equation:

Fc = mv^2 / r

where Fc is the centripetal force, m is the mass of the car, v is the velocity, and r is the radius of the track.

The friction force can be calculated using the equation:

Ffriction = μ * N

where Ffriction is the friction force, μ is the coefficient of friction, and N is the normal force.

Since the car is on a flat track, the normal force is equal to the gravitational force acting on the car, which is given by:

N = mg

where m is the mass of the car and g is the acceleration due to gravity.

Combining these equations, we can express the maximum velocity as:

v = √(μ * g * r)

To find the maximum speed, we need to substitute the given values:

μ = 0.36 (coefficient of friction)
r = 77.0 m (radius of the track)
g ≈ 9.8 m/s^2 (acceleration due to gravity)

Calculating:

v = √(0.36 * 9.8 * 77.0)
v = √(27.936)
v ≈ 5.29 m/s

Therefore, the maximum speed at which the car can safely travel on the track is approximately 5.29 m/s.