如图 所示的是甲、乙两个滑轮组提升重物.物重G1和G2之比是2:1;甲滑轮组中动滑轮重G甲与G1之比是1:5;乙滑轮组中两个动滑轮总重G乙与G2之比是3:5(不计摩擦、绳重)则甲、乙两个滑
问题描述:
如图 所示的是甲、乙两个滑轮组提升重物.物重G1和G2之比是2:1;甲滑轮组中动滑轮重G甲与G1之比是1:5;乙滑轮组中两个动滑轮总重G乙与G2之比是3:5(不计摩擦、绳重)则甲、乙两个滑轮组的机械效率之比是______.
答
由题知,G1:G2=2:1,
设G1=20N,则G2=10N,
∵G甲:G1=1:5,
∴G甲=4N,
∵G乙:G2=3:5,
∴G乙=6N,
∵不计摩擦、绳重,
∴η甲=
=
G1h
(G1+G甲)h
=G1
G1+G甲
=20N 20N+4N
,20N 24N
η乙=
=
G2h
(G2+G乙)h
=G2
G2+G乙
=10N 10N+6N
,10N 16N
∴η甲:η乙=
:20N 24N
=4:3.10N 16N
故答案为:4:3.