Two balls are thrown against a wall. Ball 1 has a much higher speed than ball 2. Explain how the energy of the two balls is different

Question

Two balls are thrown against a wall. Ball 1 has a much higher speed than ball 2.
Explain how the energy of the two balls is different.

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Khoii Minh 6 months 2021-07-15T02:42:10+00:00 1 Answers 51 views 0

Answers ( )

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    2021-07-15T02:43:55+00:00

    Let both the balls have the same mass equals to m.

    Let v_1 and v_2 be the speed of the ball1 and the ball2 respectively, such that

    v_1>v_2\;\cdots(i)

    Assuming that both the balls are at the same level with respect to the ground, so let h be the height from the ground.

    The total energy of ball1= Kinetic energy of ball1 + Potential energy of ball1. The Kinetic energy of any object moving with speed, v, is \frac 12 m v^2

    and the potential energy is due to the change in height is mgh [where g is the acceleration due to gravity]

    So, the total energy of ball1,

    =\frac 12 m v_1^2 + mgh\;\cdots(ii)

    and the total energy of ball1,

    =\frac 12 m v_2^2 + mgh\;\cdots(iii).

    Here, the potential energy for both the balls are the same, but the kinetic energy of the ball1 is higher the ball2 as the ball1 have the higher speed, refer equation (i)

    So, \frac 12 m v_1^2 >\frac 12 m v_2^2

    Now, from equations (ii) and (iii)

    The total energy of ball1 hi higher than the total energy of ball2.

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