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22 April, 04:00

When you lift a bowling ball with a force of 61.1 N, the ball accelerates upward with an acceleration a. If you lift with a force of 70.9 N, the ball's acceleration is 2.07a. Calculate the weight of the bowling ball.

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  1. 22 April, 06:02
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    the weight of the ball is w = 51.94 N (mass = 5.3 kg)

    Explanation:

    Following Newton's second law:

    net force = mass * acceleration = weight/gravity * acceleration

    then denoting 1 and 2 as the first and second lift

    F₁ - w = w/g * a₁

    F₂ - w = w/g * a₂ = w/g * 2.07a

    dividing both equations

    (F₂ - w) / (F₁ - w) = 2.07

    (F₂ - w) = 2.07 * (F₁ - w)

    1.07*w = 2.07*F₁ - F₂

    w = (2.07*F₁ - F₂) / 1.07

    replacing values

    w = (2.07*61.1 N - 70.9 N) / 1.07 = 51.94 N

    then the weight of the ball is w = 51.94 N (mass = 5.3 kg)
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