A 2000 kg car negotiates a curve of radius 40.0m on a level road. The static friction coefficient between the tires and the pavement is 0.7. Calculate the maximum force of static friction for the car and the maximum speed with which it will be able to negotiate the curve.

The maximum static frioction force is the weight of the car (M g) multiplied by the static friction coefficient (0.7). Set that equal to the centripetal force (M V^2/R) to solve for the maximum speed. The car's mass M will cancel out

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To find the maximum force of static friction for the car, we need to use the formula:

Fs_max = μs * N

Where Fs_max is the maximum force of static friction, μs is the static friction coefficient, and N is the normal force.

The normal force is the force exerted by a surface to support the weight of an object resting on it. On a level road, the normal force is equal to the weight of the car.

N = mg

Where m is the mass of the car (2000 kg) and g is the acceleration due to gravity (9.8 m/s^2).

N = (2000 kg) * (9.8 m/s^2) = 19,600 N

Now we can calculate the maximum force of static friction:

Fs_max = (0.7) * (19,600 N) = 13,720 N

So, the maximum force of static friction for the car is 13,720 N.

To find the maximum speed with which the car will be able to negotiate the curve, we can use the formula for centripetal force:

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 curve.

The centripetal force is provided by the static friction force, so Fc = Fs_max.

Plugging in the values:

13,720 N = (2000 kg) * v^2 / 40.0 m

To find the maximum speed, we rearrange the equation to solve for v:

v^2 = (13,720 N * 40.0 m) / (2000 kg)

v^2 = 274,400 Nm / 2000 kg

v^2 = 137.2 m^2/s^2

v = √(137.2 m^2/s^2) = 11.7 m/s

So, the maximum speed with which the car will be able to negotiate the curve is 11.7 m/s.