what is the maximum speed with which a car can round a turn of radius of 80.0m on a flat road if the coefficient of friction between tires and the road is .700?

I don't have a mass.

bobpursley's comment is on the right track, but the equation IS wrong. mg(a.k.a. normal force) x Coefficient of friction = (m x v^2)/r then the normal force breaks down into: m x a(a = 9.8 at sea level) the equation will then look as so: 9.8m x mu = (mv^2)/r the m's will cancel out getting rid of mass. solve from there

Kole is right but how would you find velocity

You solve for velocity

To find the maximum speed at which a car can round a turn, we need to consider the centripetal force acting on the car and compare it to the maximum frictional force between the tires and the road.

The centripetal force required to keep a car moving in a circular path 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 velocity, and r is the radius of the turn.

The maximum frictional force that can be generated between the tires and the road is given by:

Ff = μ * N

where Ff is the maximum frictional force, μ is the coefficient of friction, and N is the normal force between the car and the road.

In this case, since the car is on a flat road, the normal force N is equal to the weight of the car, which is given by:

N = m * g

where g is the acceleration due to gravity.

To find the maximum speed, we need to find the velocity v when the centripetal force is equal to the maximum frictional force:

Fc = Ff

Substituting the equations for Fc and Ff:

(m * v^2) / r = μ * N

(m * v^2) / r = μ * (m * g)

Now, let's plug in the given values:

m = mass of the car
r = radius of the turn = 80.0 m
μ = coefficient of friction = 0.700
g = acceleration due to gravity = 9.8 m/s^2

Now we need to solve for v:

(v^2) / r = μ * g

v^2 = μ * g * r

v = sqrt(μ * g * r)

Now we can calculate the maximum speed:

v = sqrt(0.700 * 9.8 * 80.0)

v ≈ 26.92 m/s

Therefore, the maximum speed at which the car can round the turn of radius 80.0 m is approximately 26.92 m/s.

It matters if the road is banked. If unbanked, then force friction=centripetalForce

mg*mu=1/2 m v^2 / r
solve for v.