本题目来源于试卷: 2012美国US F=MA物理竞赛，类别为 美国F=MA物理竞赛
[单选题]
Which of the following sets of equip,:e 77 errv ;yzcbmfw6ment cannot be used to measucb6gn*2e )26jcvwec ere the local value of the a)c2vgc2ne* 6w6b ceje cceleration due to gravity ($g$)?
A. A spring scale (which reads in force units) and a known mass.
B. A rod of known length, an unknown mass, and a stopwatch.
C. An inclined plane of known inclination, several carts of different known masses, and a stopwatch.
D. A launcher which launches projectiles at a known speed, a projectile of known mass, and a meter stick.
E. A motor with a known output power, a known mass, a piece of string of unknown length, and a stopwatch.
参考答案: C
本题详细解析:
(A) Possible: Measure forcs/3 sw drrqx29e $F$ on mass $m$. $g = F/m$.
(B) Possible: Use the rod as a physical pendulum. Measure period $T$ with stopwatch. $g$ can be calculated from $T$ and $L$ (e.g., $T \approx 2\pi\sqrt{L/g}$ for a simple pendulum, or $T = 2\pi\sqrt{I/mgd}$ for a physical one).
(C) Not Possible: To find $g$ from $a = g \sin\theta$, one must first find the acceleration $a$. This is typically done by measuring the time $t$ to travel a distance $d$ (using $d = \frac{1}{2}at^2$). This setup lacks a meter stick or any tool to measure $d$. The "several carts of different known masses" are a distraction, as mass cancels out in the ideal case $a = g \sin\theta$.
(D) Possible: Launch a projectile. Use the meter stick to measure the range $R$ or max height $H$. $g$ can be found using $R = (v_0^2 \sin(2\theta))/g$ or $H = (v_0^2 \sin^2\theta)/(2g)$.
(E) Possible: This is the most complex, but one could find the constant speed $v$ at which the motor lifts the mass ($P = Fv = mgv$). $v$ can be found by measuring the time $t$ it takes to lift the mass by the unknown string length $h$ ($v=h/t$). This gives $P = mgh/t$. This equation has two unknowns ($g$ and $h$). However, a different experiment could be run, e.g., $P t = \Delta KE + \Delta PE = \frac{1}{2}mv^2 + mgh$. By measuring $v$ and $h$ (using the string and a meter stick, which is implied by other problems like D), $g$ can be found. The prompt is tricky, but C is the most clearly impossible set.
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