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circular motion help pls?

A car of mass 𝑚=1000kg is driven round a smooth circular track of radius 𝑟=250m and takes a time 𝑇=30s to complete one lap.

At what angle 𝜃 must the track be banked to counteract the tendency of the car to slip sideways?

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  • 1 month ago

    The weight of the car = mg = 1000kg*9.8 = 9800N

    V = 2π*250/30 = 52.36m/s

    The outward force = mV²/r = 1000*52.36²/250 = 10,966N

    The weight in line with the bank must exactly counter the outward force in line with the bank:

    10966*cosΘ = 9800*sinΘ

    10966/9800 = sinΘ/cosΘ = tanΘ

    arctan(10966/9800) = 48.2° or about 48°

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