A 1500 kg car is rounding a curve with a radius of 204 meters on a level road. The maximum frictional force the road can exert on the tires of the car totals 4439 N. What is the highest speed at which the car can go to round the curve without sliding?

Answer in m/s.
i need help

f = m v^2 / r ... v = √(f r / m)

what is f

would that be the 4439 N

f is force ... Newtons

To determine the highest speed at which the car can go without sliding, let's first use the concept of centripetal force.

The centripetal force is the force required to keep an object moving in a circular path and is given by the equation:

Fc = (mv^2)/r

Where:
- Fc is the centripetal force
- m is the mass of the car (1500 kg)
- v is the velocity of the car
- r is the radius of the curve (204 meters)

In this case, the maximum frictional force that the road can exert, 4439 N, corresponds to the centripetal force:

Fc = 4439 N

Substituting the known values into the equation, we have:

4439 N = (1500 kg * v^2) / 204 m

Now, we can rearrange the equation to solve for the velocity (v):

v^2 = (Fc * r) / m
v^2 = (4439 N * 204 m) / 1500 kg
v^2 = 605.94 m^2/s^2

Taking the square root of both sides, we find:

v = √(605.94 m^2/s^2)
v ≈ 24.65 m/s

Therefore, the highest speed at which the car can go to round the curve without sliding is approximately 24.65 m/s.