物理小组的同学用如图所示的实验器材测定重力加速度,实验器材有:底座、带有标尺的竖直杆、光电门1和2组

\u67d0\u540c\u5b66\u5229\u7528\u5149\u7535\u4f20\u611f\u5668\u8bbe\u8ba1\u4e86\u6d4b\u5b9a\u91cd\u529b\u52a0\u901f\u5ea6\u7684\u5b9e\u9a8c\uff0c\u5b9e\u9a8c\u88c5\u7f6e\u5982\u56fe\u6240\u793a\uff0c\u5b9e\u9a8c\u5668\u6750\u6709\u5e26\u6709\u6807\u5ea6\u7684\u7ad6\u76f4\u6746\u3001\u5149\u7535

\uff081\uff09\u6e38\u6807\u5361\u5c3a\u7684\u8bfb\u6570\u7b49\u4e8e7mm+0.05\u00d710mm=7.50mm=0.750cm\uff0e\uff082\uff09\u5c0f\u7403\u901a\u8fc7\u5149\u7535\u95e8\u65f6\u7684\u901f\u5ea6 v= d t \uff0e\u6839\u636ev 2 =2gh\uff0c\u89e3\u5f97g= v 2 2h = d 2 2h t 2 \uff0e\uff083\uff09\u82e5\u67d0\u6b21\u5b9e\u9a8c\u65f6\u5149\u7535\u95e8\u8ba1\u65f6\u5668\u8bb0\u5f55\u4e0b\u5c0f\u94a2\u7403\u7ecf\u8fc7\u5149\u7535\u95e8\u7684\u65f6\u95f4\u4e3a 1 2 t\uff0c\u5219\u901a\u8fc7\u5149\u7535\u95e8\u7684\u901f\u5ea6\u53d8\u4e3a\u539f\u6765\u76842\u500d\uff0c\u6839\u636ev 2 =2gh\u5f97\uff0c\u77e5\u4e0b\u843d\u7684\u9ad8\u5ea6\u53d8\u4e3a\u539f\u6765\u76844\u500d\uff0c\u56e0\u4e3aOD=4OA\uff0c\u6240\u4ee5\u5149\u7535\u95e8\u5e94\u56fa\u5b9a\u5728D\u5904\uff0e\u6545\u7b54\u6848\u4e3a\uff1a\uff081\uff090.750 \uff082\uff09 d t \uff0c d 2 2h t 2 \uff083\uff09D\uff0e

\u8fd9\u9053\u9898\u5efa\u7acb\u7269\u7406\u6a21\u578b\u975e\u5e38\u5173\u952e\uff01
\u5148\u660e\u786e\u4e00\u70b9\uff1a\u4efb\u610f\u4e24\u6ef4\u6c34\u6ef4\u4e4b\u95f4\u7684\u65f6\u95f4\u95f4\u9694\u76f8\u7b49\u3002
\u9996\u5148\u5efa\u7acb\u7b2c\u4e00\u4e2a\u6a21\u578b\uff1a\u7a7a\u4e2d\u6709\u4e09\u6ef4\u6c34\uff0c\u7b2c\u4e00\u5730\u843d\u5230\u76d8\u4e2d\uff0c\u7b2c\u4e8c\u6ef4\u6c34\u5728\u7a7a\u4e2d\u67d0\u4e00\u4f4d\u7f6e\uff0c\u7b2c\u4e09\u6ef4\u6c34\u521a\u597d\u4e0b\u843d\uff0e\u597d\uff01\u5f00\u59cb\u89e3\u7b2c\u4e00\u95ee\u4e86\uff0e\u6839\u636e\u4f60\u6240\u5b66\u8fc7\u7684\u77e5\u8bc6\uff08\u5300\u53d8\u901f\u76f4\u7ebf\u8fd0\u52a8\u7684\u89c4\u5f8b\uff09\uff0c\u5f88\u5bb9\u6613\u5224\u65ad\u51fa\uff0c\u6bd4\u5982\uff1a\u7528\u521d\u901f\u5ea6\u4e3a0\u7684\u5300\u53d8\u901f\u76f4\u7ebf\u8fd0\u52a8\u7684\u63a8\u8bba\uff1a\u521d\u901f\u5ea6\u4e3a0\u7684\u5300\u52a0\u901f\u76f4\u7ebf\u8fd0\u52a8\uff0c\u5728\u8fde\u7eed\u76f8\u7b49\u7684\u65f6\u95f4\u5185\u7684\u4f4d\u79fb\u4e4b\u6bd4\u4e3a1\uff1a3\uff1a5\uff1a\uff0e\uff0e\uff0e\uff0e\uff0e\uff0e\u7b2c\u4e8c\u4e2a\u6c34\u6ef4\u79bb\u5f00\u6c34\u9f99\u5934\u8ddd\u79bb\u662f\uff081/4\uff09H \uff0e
\u5728\u7b2c\u4e00\u4e2a\u6a21\u578b\u7684\u57fa\u7840\u4e4b\u4e0a\uff0c\u6765\u89e3\u4e00\u4e0b\u7b2c\u4e8c\u95ee\uff0e\u6ce8\u610f\u53bb\u5ba1\u9898\uff0e\u201c\u4ece\u7b2c\u4e00\u4e2a\u6c34\u6ef4\u79bb\u5f00\u6c34\u9f99\u5934\u5f00\u59cb\u8ba1\u65f6 \uff0c\u7b2cN \u4e2a\u6c34\u6ef4\u843d\u81f3\u76d8\u4e2d\uff0c\u5171\u7528\u65f6\u95f4T\u201d\uff08\u8fd9\u53e5\u8bdd\u5f88\u5173\u952e\uff01\uff01\uff01\uff09 \u5047\u8bbe\u7b2c\u4e09\u6ef4\u6c34\u843d\u81f3\u76d8\u4e2d\uff0c\u90a3\u4e48\u6709\u51e0\u6bb5\u65f6\u95f4\u95f4\u9694\u5462\uff1f\u7b80\u5355\u60f3\u4e00\u4e0b\uff0c\u662f\u4e0d\u662f4\u6bb5\uff1f\u90a3\u4e48\u7b2cN \u4e2a\u6c34\u6ef4\u843d\u81f3\u76d8\u4e2d\u5c31\u6709\uff08N+1\uff09\u4e2a\u65f6\u95f4\u6bb5\uff0c\u5373(N+1)t=T
\u63a5\u4e0b\u6765\u5217\u51fa\u516c\u5f0f\u6c42\u89e3\u3002
t=T/\uff08N+1\uff09
\uff081/2\uff09g\uff082t\uff09^2=H
\u53ef\u5f97\uff1ag\uff1dH(N+1)^2\uff0f2t^2
\u770b\u770b\u5982\u4f55\uff1f

(1)小球经过光电门2的速度为v,根据运动学公式得从开始释放到经过光电门2的时间t′=
v
g

所以从开始释放到经过光电门1的时间t″=t′-t=
v
g
?t

所以经过光电门1的速度v′=gt″=v-gt;
根据匀变速直线运动的推论得:两光电门间的距离h=
v′+v
2
t=vt?
1
2
gt2

(2)根据h=vt?
1
2
gt2

得,
h
t
=v?
1
2
gt

h
t
?t
图线斜率的绝对值为k,k=
1
2
g

所以重力加速度大小g=2k.
故答案为:(1)vt?
1
2
gt2
,(2)2k.

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