如图所示,一质量M=3.0kg、足够长的木板B放在光滑的水平面上,其上表面放置质量m=l.0kg的小木块A,A、B均 如图所示一质量M=3kg足够长的木板B放在光滑的水平面上,其...

\uff082014?\u5357\u901a\u4e00\u6a21\uff09\u5982\u56fe\u6240\u793a\uff0c\u4e00\u8d28\u91cfM=3.0kg\u3001\u8db3\u591f\u957f\u7684\u6728\u677fB\u653e\u5728\u5149\u6ed1\u7684\u6c34\u5e73\u9762\u4e0a\uff0c\u5176\u4e0a\u8868\u9762\u653e\u7f6e\u8d28\u91cfm=l.0kg

\uff081\uff09\u5f53\u6728\u677f\u56fa\u5b9a\u65f6\uff0cA\u5f00\u59cb\u6ed1\u52a8\u77ac\u95f4\uff0c\u6c34\u5e73\u529bF\u4e0e\u6700\u5927\u9759\u6469\u64e6\u529b\u5927\u5c0f\u76f8\u7b49\uff0c\u5219\uff1aF=f=\u03bcmg\u8bbe\u7ecf\u8fc7t1\u65f6\u95f4A\u5f00\u59cb\u6ed1\u52a8\uff0c\u5219\uff1aF=kt1t1\uff1d\u03bcmgk\uff1d0.3\u00d71\u00d7102s\uff1d1.5s\uff082\uff09t=2s\u65f6\uff0c\u6709\uff1aF=kt=2\u00d72N=4N\u6709\u725b\u987f\u7b2c\u4e8c\u5b9a\u5f8b\u6709\uff1aF-\u03bcmg=maa=F?\u03bcmgm\uff1d4?0.3\u00d71\u00d7101m/s2\uff1d1m/s2\uff083\uff09\u5728t=1s\u65f6\u6c34\u5e73\u5916\u529b\u4e3a\uff1aF=kt=2\u00d71N=2n \u7531\u4e8e\u6b64\u65f6\u5916\u529b\u5c0f\u4e8e\u6700\u5927\u9759\u6469\u64e6\u529b\uff0c\u4e24\u8005\u4e00\u5b9a\u4e0d\u53d1\u751f\u76f8\u5bf9\u6ed1\u52a8\uff0c\u6545\u4e00\u8d77\u505a\u5300\u52a0\u901f\u8fd0\u52a8\uff0c\u4ee5\u6574\u4f53\u4e3a\u7814\u7a76\u5bf9\u8c61\uff0c\u6709\u725b\u987f\u7b2c\u4e8c\u5b9a\u5f8b\u53ef\u5f97\uff1aF=\uff08m+M\uff09a\u2032a\u2032\uff1dFM+m\uff1d21+3m/s2\uff1d0.5m/s2\u5bf9A\u53d7\u529b\u5206\u6790\u4e3a\uff1aF-f=ma\u2032f=F-ma\u2032=2-1\u00d70.5N=1.5N\u7b54\uff1a\uff081\uff09\u82e5\u6728\u677fB\u56fa\u5b9a\uff0c\u5219\u7ecf\u8fc71.5s\u6728\u5757A\u5f00\u59cb\u6ed1\u52a8\uff082\uff09\u82e5\u6728\u677fB\u56fa\u5b9a\uff0c\u6c42t2=2.0s\u65f6\u6728\u5757A\u7684\u52a0\u901f\u5ea6\u5927\u5c0f\u4e3a1m/s2\uff0e\uff083\uff09\u82e5\u6728\u677fB\u4e0d\u56fa\u5b9a\uff0c\u6c42t3=1.0S\u65f6\u6728\u5757A\u53d7\u5230\u7684\u6469\u64e6\u529b\u5927\u5c0f\u4e3a1.5N\uff0e

\u56e0\u4e3a\u6700\u5927\u9759\u6469\u64e6\u529b\u4e0e\u6ed1\u52a8\u6469\u64e6\u529b\u5927\u5c0f\u76f8\u7b49
\u6240\u4ee5\u6700\u5927\u9759\u6469\u64e6\u529bfmax=umg=0.3*0.1*10=0.3N
t3=1.0s\u65f6
F=kt3=2N>fmax
\u6240\u4ee5\uff0ct3=1.0s\u65f6
\u6728\u5757A\u53d7\u5230\u6ed1\u52a8\u6469\u64e6\u529b\uff0c
\u6469\u64e6\u529b\u5927\u5c0f\u662f0.3N\u3002
\u5e0c\u671b\u80fd\u5e2e\u5230\u4f60

(1)当木板固定时,A开始滑动瞬间,水平力F与最大静摩擦力大小相等,则:
F=f=μmg
设经过t 1 时间A开始滑动,则:F=kt 1
t 1 =
μmg
k
=
0.3×1×10
2
s=1.5s

(2)t=2s时,有:
F=kt=2×2N=4N
有牛顿第二定律有:F-μmg=ma
a=
F-μmg
m
=
4-0.3×1×10
1
m/ s 2 =1m/ s 2

(3)在t=1s时水平外力为:F=kt=2×1N=2n
由于此时外力小于最大静摩擦力,两者一定不发生相对滑动,故一起做匀加速运动,以整体为研究对象,有牛顿第二定律可得:
F=(m+M)a′
a′=
F
M+m
=
2
1+3
m/ s 2 =0.5m/ s 2

对A受力分析为:F-f=ma′
f=F-ma′=2-1×0.5N=1.5N
答:(1)若木板B固定,则经过1.5s木块A开始滑动
(2)若木板B固定,求t 2 =2.0s时木块A的加速度大小为1m/s 2
(3)若木板B不固定,求t 3 =1.0S时木块A受到的摩擦力大小为1.5N.


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