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A 1,100kg car is turning on a flat roadway, moving in a circle with a radius of 12m. The car is going maximum speed through the turn without skidding. If the coefficient of friction between the car and the road is 0.57, find the speed of the car.

speed = ___ m/s (round to the nearest tenth)

User DVG
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1 Answer

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Answer: 20.7 m/s.

Explanation: To find the speed of the car, we need to use the equation for centripetal force, which is:

Fc = m * a = m * v^2 / r

where Fc is the centripetal force, m is the mass of the car, a is the centripetal acceleration, v is the velocity of the car, and r is the radius of the turn.

We know that the coefficient of friction between the car and the road is 0.57

and it is the maximum speed, so the force of friction is equal to the centripetal force.

f = Fc = m * a = m * v^2 / r

f = μ * N = μ * m * g

so

m * v^2 / r = μ * m * g

where g is the acceleration due to gravity.

By substituting the known values into the equation, we get:

(1100 kg) * v^2 / (12 m) = (0.57) * (1100 kg) * (9.8 m/s^2)

Solving for v, we get:

v = sqrt((0.57 * 9.8 * 12 * 1100) / 1100)

v ≈ 20.7 m/s

To the nearest tenth, the speed of the car is 20.7 m/s.

User Nitely
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