Zack
Lv 7
Zack asked in Science & MathematicsPhysics · 1 year ago

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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  • 1 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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  • 1 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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