广州市现正在建设的新电视塔，包括发射天线在内塔高达610m，建成

问题问答题

广州市现正在建设的新电视塔，包括发射天线在内塔高达610m，建成后将成为世界第一高塔，成为现代广州的代表建筑．在新电视塔的工地上有一块底面积为2m²、高为40cm、质量为2t的长方体大理石，一功率为20kW电动起重机用了25s将这块大理石送到20m高的6楼上．g=10N/kg．

求：

（1）大理石的密度．

（2）大理石与地面的接触面积为2m²时，对地面的压强多大？

（3）该电动起重机对大理石做了多少功？

（4）该电动起重机机械效率是多少？

答案

（1）大理石的底面积为2m²、高为40cm，则它的体积为V=2m²×0.4m=0.8m³；

大理石的质量m=2t=2×10³kg，因此大理石的密度为ρ=

2×103kg

0.8m3

=2.5×10³kg/m^{3
答：大理石的密度是2.5×10³kg/m³
（2）大理石的重力G=mg=2×10³kg×10N/kg=2×10⁴N
与地面的接触面积为2m²时，对地面的压强P=
F
S
=2×104N
2m2=1×10⁴Pa
答：大理石与地面的接触面积为2m²时，对地面的压强1×10⁴Pa．
（3）电动起重机将这块大理石送到20m高的6楼上，做的功为
W=Gh=2×10⁴N×20m=4×10⁵J
答：该电动起重机对大理石做了4×10⁵J的功．
（4）起重机消耗的电能W_电=Pt=20×10³W×25s=5×10⁵J
∴电动机的机械效率η=
W
W电
×100%=4×105J
5×105J×100%=80%．
答：该电动起重机机械效率是80%．}

完形填空。
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