如图所示,某建筑工地用升降机提升大理石.当货箱内物体质量是360kg时,滑轮组的机械效率是80%,不计滑轮
\u5982\u56fe\u6240\u793a\u662f\u67d0\u5efa\u7b51\u5de5\u5730\u7528\u5347\u964d\u673a\u63d0\u5347\u5927\u7406\u77f3\u7684\u6ed1\u8f6e\u7ec4\u793a\u610f\u56fe\uff0e\u6ed1\u8f6e\u7ec4\u901a\u8fc7\u56fa\u5b9a\u67b6\u88ab\u56fa\u5b9a\u4f4f\uff0c\u6ed1\u8f6e\u7ec4\u4e2d\u7684\u4e24\u4e2a\u5b9a\u6ed1\uff081\uff09\u7531\u03c1=mV\u5f97\u6bcf\u5757\u5927\u7406\u77f3\u7684\u8d28\u91cf\uff1am=\u03c1V=2.8\u00d7103kg/m3\u00d71.0\u00d710-2m3=28kg\u6bcf\u5757\u5927\u7406\u77f3\u91cd\uff1aG=mg=28kg\u00d710N/kg=280N\uff1b\u5347\u964d\u673a\u4e00\u6b21\u80fd\u591f\u63d0\u8d77\u7684\u603b\u91cd\u4e3aG\u603b=3\u00d7F\u6700\u5927=3\u00d72000N=6000N\u5347\u964d\u673a\u4e00\u6b21\u80fd\u63d0\u8d77\u7684\u5927\u7406\u77f3\u7684\u603b\u91cd\u4e3aG\u77f3=G\u603b-G0=6000N-300N=5700N\u5347\u964d\u673a\u4e00\u6b21\u80fd\u63d0\u8d77\u7684\u5927\u7406\u77f3\u7684\u5757\u6570\u4e3an=G\u77f3G=5700N280N\u224820\uff08\u5757\uff09\uff0c\u6545A\u9519\uff1b\uff082\uff09\u63d0\u534715\u5757\u5927\u7406\u77f3\u7684\u8fc7\u7a0b\u4e2d\uff0c\u94a2\u4e1d\u7ef3\u7aef\u79fb\u52a8\u7684\u8ddd\u79bb\uff1as=3h=3\u00d715m=45mF=13\uff08G+G0\uff09=13\uff0815\u00d7280N+300N\uff09=1500N\uff0c\u6545B\u9519\uff1b\uff083\uff09\u628a\u8d27\u7269\u63d0\u534715m\u62c9\u529b\u505a\u7684\u529f\uff1aW=Fs=1500N\u00d745m=6.75\u00d7104J\u5347\u964d\u673a\u7684\u529f\u7387\u4e3aP=Wt=6.75\u00d7104J60s=1125W\uff1b\u6545C\u6b63\u786e\uff1b\uff084\uff09W\u6709\u7528=Gh=15\u00d7280N\u00d715m=6.3\u00d7104J\uff0c\u03b7=W\u6709\u7528W\u603b\u00d7100%=6.3\u00d7104J6.75\u00d7104J\u00d7100%\u224893.3%\uff0c\u6545D\u9519\uff0e\u6545\u9009C\uff0e
\uff081\uff09\u7531\u03c1=mV\u5f97\u6bcf\u5757\u5927\u7406\u77f3\u7684\u8d28\u91cf\uff1am1=\u03c1V=2.7\u00d7103kg/m3\u00d71.0\u00d710-2m3=27kg\u6bcf\u5757\u5927\u7406\u77f3\u91cd\uff1aG1=m1g=27kg\u00d710N/kg=270N\uff1b\uff082\uff0910\u5757\u5927\u7406\u77f3\u7684\u603b\u91cd\u529b\uff1aG=10G1=10\u00d7270N=2700N\uff0c\u7531\u56fe\u77e5\uff0cn=3\uff0c\u5219\u5347\u964d\u673a\u7684\u6548\u7387\uff1a\u03b7=W\u6709\u7528W\u603b\u00d7100%=GhFs\u00d7100%=GhF3h\u00d7100%=G3F\u00d7100%=2700N3\u00d71000N\u00d7100%=90%\uff1b\u2235\u4e0d\u8ba1\u94a2\u4e1d\u7ef3\u7684\u91cd\u529b\u548c\u6469\u64e6\uff0c\u2234F=13\uff08G+G\u52a8+G\u7bb1\uff09\uff0c\u5373\uff1a1000N=13\uff082700N+G\u52a8+200N\uff09\u52a8\u6ed1\u8f6e\u7684\u91cd\u529b\uff1aG\u52a8=100N\uff1b\uff083\uff09\u5f53\u94a2\u4e1d\u7ef3\u7684\u62c9\u529bF\u2032=1540N\u65f6\uff0c\u5373\uff1aF\u2032=13\uff08G\u2032+G\u52a8+G\u7bb1\uff09\uff0c1540N=13\uff08G\u2032+100N+200N\uff09\u89e3\u5f97\uff1aG\u2032=4320N\uff1b\u5927\u7406\u77f3\u7684\u5757\u6570\uff1aN=4320N270N=16\uff08\u5757\uff09\uff1b\u6709\u7528\u529f\u7387\uff1aP\u6709\u7528=W\u6709\u7528t=G\u2032ht=4320N\u00d715m60s=1080W\uff0e\u7b54\uff1a\uff081\uff09\u6bcf\u5757\u5927\u7406\u77f3\u7684\u91cd\u529b\u662f270N\uff1b\uff082\uff09\u5347\u964d\u673a\u6548\u7387\u4e3a90%\uff1b\uff083\uff09\u63d0\u5347\u5927\u7406\u77f316\u5757\uff0c\u5347\u964d\u673a\u7684\u6709\u7528\u529f\u7387\u662f1080W\uff0e
(1)货箱内物体质量m=360kg,
G=mg=360kg×10N/kg=3600N,
由图知,n=3,则拉力端移动的距离s=3h,
∵η=
W有用 |
W总 |
Gh |
Fs |
Gh |
F3h |
G |
3F |
∴拉力F=
G |
3η |
3600N |
3×80% |
(2)由题知,n=3,并且不计滑轮和钢丝绳的重力、不计摩擦,则拉力:
F=
1 |
3 |
即:1500N=
1 |
3 |
货箱重G货箱=900N,
当最大拉力F最大=2000N时,升降机提升的最大货物重G最大,则:
F最大=
1 |
3 |
即:2000N=
1 |
3 |
解得:
G最大=5100N;
(3)由(2)的计算可知,当拉力F=2000N,货物重G=5100N,
由图知,n=3,则s=3h=3×15m=45m,
有用功:
W有用=Gh=5100N×15m=76500J,
钢丝绳的拉力做的总功:
W总=Fs=2000N×45m=90000J,
钢丝绳的拉力的功率:
P=
W总 |
t |
90000J |
60s |
滑轮组的机械效率:
η=
W有用 |
W总 |
76500J |
90000J |
答:(1)拉力的大小是为1500N;
(2)该升降机一次最多能匀速提升5100N的货物;
(3)钢丝绳的拉力的功率是1500W;滑轮组的机械效率是85%.
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