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1 April, 20:41

A car with a mass of 1200 kg is moving around a circular curve at a uniform velocity of 20 meters per second. the centripetal force on the car is 6000 newtons. what is the radius of the curve?

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  1. 1 April, 21:08
    0
    Well, first of all, the car is not moving with a uniform velocity.

    It's on a part of a circle, so the direction of its motion is constantly

    changing. Its speed may be constant, but its velocity is constantly

    changing, because direction is a big part of velocity.

    OK. So its mass is 1200 kg, its speed is 20 m/s, and 6000N of

    centripetal force is enough to keep it on a circular path.

    The centripetal force on an object moving in a circle is

    F = (mass) x (speed) ² / (radius)

    6,000 N = (1,200 kg) x (20 m/s) ² / (radius)

    Multiply each side

    by (radius) : (6000 N) x (radius) = 24000 kg-m²/s²

    Divide each side

    by (6000 N) : radius = (24,000 kg-m²/s²) / (6000 N)

    = (24,000 kg-m²/s²) / (6000 kg-m/s²)

    = 4 meters.

    In the real world, this is an absurd situation. But I think

    my Physics and my Math here are OK.

    It just says that if you were in a car that weighs 2,645 pounds,

    and you were cruising along at 45 miles per hour, then if you

    could somehow arrange for a centripetal force of 1,350 pounds,

    it would be enough centripetal force to keep your car on a circular

    track that's only 26 feet across!
  2. 1 April, 21:10
    0
    F = m v^2 / r

    r = m v^2 / F

    r = 1200 * 400 / 6000 = 120 * 4 / 6 = 20 * 4 = 80

    Units are left as an excersise.
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