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]
A point-like mass moves horizontak s7d(dpd4 6x w7qkc ; rkr2sc09v.mrilly between cxd/szg fj6uo::/y /,mir8aw two walls on a frictionless surface with iraw 6yz8 /:co/ugdsi/:,jx mfnitial kinetic energy $E$. With every collision with the walls, the mass loses $\frac{1}{2}$ its kinetic energy to thermal energy. How many collisions with the walls are necessary before the speed of the mass is reduced by a factor of 8?
A. 3
B. 4
C. 6
D. 8
E. 16
参考答案: C
本题详细解析:
Initial kinetic energjpez z+5s rb+uhz6tul0i : x:yc3x )2oy $E_0 = \frac{1}{2}mv_0^2$.
The final speed is $v_f = v_0 / 8$.
The final kinetic energy $E_f = \frac{1}{2}m(v_f)^2 = \frac{1}{2}m(v_0/8)^2 = \frac{1}{64} \left( \frac{1}{2}mv_0^2 \right) = E_0 / 64$.
If the mass *loses* $\frac{1}{2}$ its KE on each collision, it *retains* $\frac{1}{2}$ its KE.
Let $E_n$ be the kinetic energy after $n$ collisions. This forms a geometric progression:
$E_n = E_0 \times (\frac{1}{2})^n$.
We want to find $n$ such that $E_n = E_f = E_0 / 64$.
$E_0 (\frac{1}{2})^n = E_0 / 64$
$(\frac{1}{2})^n = 1/64$
$2^n = 64$
Since $2^5 = 32$ and $2^6 = 64$, the number of collisions is $n=6$.
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