Plz help me

2009-04-04 3:16 am

1. 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 following statements about the basketball is/are corect?

(1) Its potential energy just before collision is four times its potential energy just after collision.
(2) The speed just before collision is two times the speed just after collision.
(3) If the same ratio of kinetic energy were lost in each collision, it would rebound to 1/16 of its original height after the second collision.
(4) Its kinetic energy just before collision is four times its kinetic energy just after collision.

更新1:

For statement 1), I don't understand. The two potential energies are the same, which equal to zero??? Why the PE = 0?

更新2:

Plz help me to answer "Why does the PE = 0??

回答 (1)

天同

2009-04-04 5:01 am

✔ 最佳答案

Except statement (1), the other 3 statements are correct.
(1) Wrong.
The two potential energies are the same, which equal to zero.
(2) correct.
Suppose the object falls from a height H above the ground, and rebound to a height H/4
since kinetic energy (KE) just before hitting the ground = (1/2)mu^2
thus, (1/2)mu^2 = mgH
[where m is the mass of the object and u is the speed before hitting the ground]
u^2 = 2gH
SImilarly, we would have v^2 = 2g(H/4) for the rebound, where v is the speed just after the rebound.
(u/v)^2 = 2gH/2g(H/4) = 4
i.e. u = 2v
(3) correct
Let E be the KE before the first rebound.
After the first rebound, KE = (1/4)E
After the second rebound, KE = (1/4)(1/4)E = E/16
since a KE of E comes from a fall in height of H, hence a KE of (E/16) will give a rebound to a height of H/16
(4) correct
This comes directly from the result in (2)

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