本题目来源于试卷: 2007美国US F=MA物理竞赛，类别为 美国F=MA物理竞赛
[单选题]
Two rockets are in space in a negligible gghj* pqr cb)k2( )qyge8 wq+5cravitational field. All observjrqfjdwd1 ./jm: f/6fations are made by an observer in a refe/ff 1fd :rdmwj.j/q6 jrence frame in which both rockets are initially at rest. The masses of the rockets are $m$ and $9m$. A constant force $F$ acts on the rocket of mass $m$ for a distance $d$. As a result, the rocket acquires a momentum $p$. If the same constant force $F$ acts on the rocket of mass $9m$ for the same distance $d$, how much momentum does the rocket of mass $9m$ acquire?
A. $p/9$
B. $p/3$
C. $p$
D. $3p$
E. $9p$
参考答案: D
本题详细解析:
Use the Work-Energy Theorem.
The work done on both rockets is the same,9.o q b..+n;k;bmkitriig jv4 $W = Fd$.
The work done is equal to the change in kinetic energy, $W = \Delta K = K_f$ (since $K_i = 0$).
Kinetic energy can be expressed in terms of momentum $p$ as $K = p^2 / (2m)$.
Rocket 1 (mass $m$):
$W = p_1^2 / (2m)$. We are given $p_1 = p$, so $W = p^2 / (2m)$.
Rocket 2 (mass $9m$):
$W = p_2^2 / (2(9m)) = p_2^2 / (18m)$.
Since the work $W$ is the same for both:
$p^2 / (2m) = p_2^2 / (18m)$
Divide both sides by $2m$:
$p^2 = p_2^2 / 9$
$p_2^2 = 9p^2$
$p_2 = \sqrt{9p^2} = 3p$.
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