What is the maximum speed (in meters/second) with which a 1400 kg car can round a turn of radius 300 m on a flat road, if the coefficent of friction between tires and road is 0.530 ?

To determine the maximum speed at which the car can round the turn, we can use the concept of centripetal force. The centripetal force is provided by the friction between the car's tires and the road.

The formula for centripetal force is:

F = m * v^2 / r

Where:
F is the centripetal force
m is the mass of the car (1400 kg)
v is the velocity of the car
r is the radius of the turn (300 m)

The maximum frictional force that can be exerted between the tires and the road is determined by the coefficient of friction, which is given as 0.530. The maximum frictional force can be calculated using the formula:

f_max = μ * N

Where:
f_max is the maximum frictional force
μ is the coefficient of friction (0.530)
N is the normal force

The normal force N can be determined using the formula:

N = m * g

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

By substituting these equations, we can solve for the maximum velocity v:

f_max = μ * N
f_max = μ * m * g
m * v^2 / r = μ * m * g
v^2 = μ * r * g
v = sqrt(μ * r * g)

Now, let's substitute the given values into the equation and calculate the maximum velocity:

v = sqrt(0.530 * 300 * 9.8)
v ≈ sqrt(1558.2)
v ≈ 39.48 m/s

Therefore, the maximum speed at which the 1400 kg car can round the turn is approximately 39.48 meters/second.