The maximum speed that a car can travel around a flat curved road is 18m/s. What would be the maximum speed for that car around a curve with half the radius?

assuming friciton was the same,

original friction=mv^2/r=m18^2/r

original friction2= mV^2/(r/2)

divide the first equation by the second

1=18^2/v^2 (1/2)
solve for v

To find the maximum speed for a car around a curve with half the radius, we can use the concept of centripetal force. The maximum speed around a curve is limited by the friction force between the car's tires and the road, which provides the required inward centripetal force to keep the car moving in a circular path.

The centripetal force is given by the equation:

F = (mv^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 curvature.

Let's assume that the mass of the car remains constant.

In this case, we want to find the maximum speed for a curve with half the radius. We can denote the original radius as 'R' and the new radius as 'R/2'.

Since the mass of the car remains constant, the centripetal force remains the same because the maximum speed is determined by the friction force between the tires and the road. Therefore, we set the two forces equal to each other:

(mv^2) / R = (mv'^2) / (R/2)

Simplifying the equation, we can cancel out the mass 'm' and solve for v':

v^2 / R = v'^2 / (R/2)

Rearranging the equation, we get:

v'^2 = 2v^2

Taking the square root of both sides of the equation, we find:

v' = √(2)v

Now we can substitute the given maximum speed 'v' as 18 m/s:

v' = √(2) * 18

Calculating this value, we find:

v' ≈ 25.45 m/s

Therefore, the maximum speed for the car around a curve with half the radius would be approximately 25.45 m/s.