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21 December, 05:21

A ball is tied to the end of a cable of negligible mass. The ball is spun in a circle with a radius 2.00 m making 0.700 revolutions per second. What is the centripetal acceleration of the ball?

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  1. 21 December, 05:47
    0
    1) find speed (8.8 m/s)

    2) find acceleration (38.7 m/s^2)

    answer is about 38.7 m/s^2
  2. 21 December, 05:49
    0
    Centripetal acceleration = (speed) ² / (radius).

    We know the radius. We have to find the speed.

    Speed around a circle = (circumference) / (time to go around)

    The circumference of the circle is (2 π) (radius) = 4 π meters.

    We don't exactly know the time to go around.

    We know that the ball goes around 0.7 times/second.

    Flip that over, and you have time to go around = second/0.7.

    So now, the centripetal acceleration is

    (speed) ² / (radius).

    = (4π meters · 0.7/sec) ² / (2 meters)

    = (4π · 0.7 / 2) m/s²

    = about 4.4 m/s²
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