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# F4 Momentum

Two objects A and B of masses m and 2m respectively are initially at rest on a smooth, horizontal surface. If each of them is acted upon by the same force for the same period of time. What is the ratio of the gain in kinetic energy of A to that of B ?

個答案我計黎計去都係 2:1 但係個model ans 就係1:2 。究竟點計？

### 2 Answers

- choyLv 59 years agoFavorite Answer
Since both A and B are at rest initially, the initial momentum of both of them are zero.

As A and B are acted upon by same force for the same period of time, the change in momentum, i.e. impulse on them are the same.

Therefore, the final momentum of A and B are the same.

Let the final momentum of A and B be mv and 2mV respectively.

mv = 2mV

v = 2V

V = v/2

final KE of A = 1/2(m)v^2

final KE of B = 1/2(2m)(v/2)^2 = 1/2(2m)(1/4)v^2 = 1/2 of KE of A

2011-05-26 00:23:13 補充：

since both A and B are at rest initially at rest, their initial K.E. are both zero.

ratio of the gain in kinetic energy of A to that of B = 2 to 1

Therefore, the so-called model answer is wrong.