A 1200-kg car rounds a corner of radius r = 45 m. If the coefficient of static friction between tires and the road is 0.93 and the coefficient of kinetic friction between tires and the road is 0.75, what is the maximum velocity the car can have without skidding?

To find the maximum velocity the car can have without skidding, we need to determine the maximum frictional force that can act on the car while it is going around the corner.

The maximum frictional force is given by:

F_max = μ_s * N

where μ_s is the coefficient of static friction and N is the normal force.

The normal force, N, is equal to the weight of the car, which is given by:

N = m * g

where m is the mass of the car and g is the acceleration due to gravity.

In this case, the weight of the car is:

N = 1200 kg * 9.8 m/s^2 = 11760 N

Substituting this value into the equation for the maximum frictional force, we get:

F_max = 0.93 * 11760 N = 10925.8 N

Now, the maximum frictional force can also be written as:

F_max = m * v^2 / r

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

Rearranging the equation, we get:

v^2 = F_max * r / m

Plugging in the values we know, we have:

v^2 = (10925.8 N) * (45 m) / (1200 kg)
v^2 = 409.8725 m^2/s^2

To find the maximum velocity, we take the square root of both sides of the equation:

v = √409.8725 m^2/s^2
v ≈ 20.24 m/s

Therefore, the maximum velocity the car can have without skidding is approximately 20.24 m/s.

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