? 發問於 科學及數學其他 - 科學 · 1 十年前

Collision....高手..請進..Please show your workings...THX ^^

A basketball falls freely from rest and hits the ground .It then rebounds to 1/4 of its original height .Neglecting air resistance .Which of the follwing staments about the basketball is/are correct ?

(1) Its kinetic energy just before collision is four times its kinetic energy just after collision.

(2) Its potential energy just before collision is four times its potential energy just after collision.

(3) Its speed just before collision is four times its speed just after collision.

1 個解答

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  • 1 十年前
    最愛解答

    Let original P.E. = mgH.

    As the ball rebounds 1/4 of its original height (i.e. 1/4 × H), P.E. at 1/4 of original height = mg(1/4 × H) = 1/4 × mgH = 1/4 of original P.E.

    By conservation of energy, K.E. just before collision = mgH

    By conservation of energy, K.E. just after collision = 1/4 × mgH

    Therefore, K.E. before collision / K.E. after collision = 4

    Only (1) is correct.

    (2) is incorrect because P.E. just before collision = P. E. just after collision = 0 (because of zero height on ground)

    (3) incorrect.

    Let u and v be speed before and after collision

    K.E. before collision = 1/2 × mu^2

    K.E. after collision = 1/2 × mv^2

    Therefore, from above, u^2/v^2 = 4, u/v = 2, not 4

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