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 0.43?

80/40=20

To find the maximum speed at which a car can safely travel around a flat, circular race track, we need to consider the centripetal force provided by friction. The centripetal force is given by the formula:

F = m * (v^2 / r)

Where:
F is the centripetal force,
m is the mass of the car,
v is the velocity of the car,
and r is the radius of the track.

In this case, the centripetal force is provided by friction, so we can write:

F_friction = m * (v^2 / r)

The maximum frictional force can be calculated using the formula:

F_friction_max = μ * N

Where:
F_friction_max is the maximum frictional force,
μ is the coefficient of friction,
and N is the normal force.

The normal force can be calculated as the weight of the car:

N = m * g

Where:
g is the acceleration due to gravity (approximately 9.8 m/s^2).

Combining the equations, we can find the maximum speed at which the car can safely travel:

F_friction_max = μ * N
m * (v^2 / r) = μ * (m * g)
v^2 = μ * (r * g)
v = √(μ * r * g)

Substituting the given values:
μ = 0.43
r = 80.0 m
g = 9.8 m/s^2

v = √(0.43 * 80.0 * 9.8)
v = √(331.52)
v ≈ 18.21 m/s

Therefore, the maximum speed at which the car can safely travel is approximately 18.21 m/s.

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

F = μN

where F is the maximum centripetal force, μ is the coefficient of friction, and N is the normal force. The normal force in this case is equal to the weight of the car, which is given by:

N = mg

where m is the mass of the car and g is the acceleration due to gravity (approximately 9.8 m/s²).

The maximum centripetal force can be expressed as:

F = mv²/r

where v is the velocity of the car and r is the radius of the track.

Substituting the equations for F and N into the first equation, we get:

mv²/r = μmg

Canceling out the mass (m) and rearranging the equation, we achieve:

v² = μgr

Taking the square root of both sides, we have:

v = √(μgr)

Now we can substitute the given values into the equation:

v = √(0.43 * 9.8 * 80.0)

Calculating this, we find:

v ≈ 28.7 m/s

Therefore, the maximum speed at which the car can safely travel is approximately 28.7 m/s.