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# Physics question involving circular motion?

A car is racing around a level, circular track moving over the full circumference of 271.4 m. If the coefficient of static friction is 0.5, then what is the fastest speed that the car can be going without slipping?

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- electron1Lv 71 year ago
For the car to move around a circle at a constant speed there must be a centripetal force. In this problem, the friction force is equal to the centripetal force.

Fc = m * v^2 ÷ r

Ff = μ * m *g

m * v^2 ÷ r = μ * m *g

v =√( r * μ * g)

2 * π * r = 271.4

r = 135.7/π

The radius of the circle is approximately 43 meters.

v =√(135.7/π * 0.5 * 9.8)

v = √664.63/π

The maximum speed is approximately 14.5 m/s. I hope this is helpful for you.

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- Some BodyLv 71 year ago
∑F = ma

Nμ = m v² / r

mg μ = m v² / r

g μ = v² / r

v = √(g μ r)

Find radius from circumference then plug in and solve.

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