某建筑工地用如图所示升降机来提升实心砖.升降机货箱的重力是400N,每个滑轮中50N,不计钢丝绳的重力和
\u67d0\u5efa\u7b51\u5de5\u5730\u7528\u5347\u964d\u673a\u63d0\u5347\u5927\u7406\u77f3\u7684\u793a\u610f\u56fe\u5982\u56fe\u6240\u793a\u3002\u5347\u964d\u673a\u8d27\u7bb1\u7684\u91cd\u529b\u662f400N\uff0cg\u53d610N/kg\u3002\u4e0d\u8ba1\u6ed1\u8f6e\u548c\u94a2\u4e1d\u7ef3(1) (2) \uff083\uff09 (1) \u6bcf\u5757\u5927\u7406\u77f3\u91cd\uff1a \uff082\u5206\uff09(2) \u5347\u964d\u673a\u4e00\u6b21\u80fd\u63d0\u8d77\u7684\u5927\u7406\u77f3\u5757\u6570\uff1a \uff081\u5206\uff09(3) \u94a2\u4e1d\u7ef3\u7aef\u79fb\u52a8\u7684\u8ddd\u79bb\uff1a \uff081\u5206\uff09 \u628a\u8d27\u7269\u63d0\u534715 m\u505a\u7684\u529f\uff1a \uff081\u5206\uff09\u5347\u964d\u673a\u7684\u529f\u7387\uff1a \uff081\u5206\uff09\uff081\uff09\u5148\u7531m=\u03c1V\u8ba1\u7b97\u6bcf\u5757\u5927\u7406\u77f3\u7684\u8d28\u91cf\uff0c\u518d\u7531G=mg\u6c42\u51fa\u6bcf\u5757\u5927\u7406\u77f3\u7684\u91cd\u529b\uff1b\uff082\uff09\u7531\u56fe\u53ef\u77e5\u6709\u4e09\u6bb5\u94a2\u4e1d\u63d0\u7740\u8d27\u7bb1\uff0c\u5219\u8d27\u7bb1\u603b\u91cd\u662f\u94a2\u4e1d\u62c9\u529b\u76843\u500d\uff0c\u53bb\u6389\u8d27\u7bb1\u7684\u91cd\u529b\u5c31\u662f\u7816\u7684\u91cd\u529b\uff0c\u4e5f\u5c31\u80fd\u6c42\u51fa\u7816\u7684\u5757\u6570\uff1b\uff083\uff09\u94a2\u4e1d\u7ef3\u79fb\u52a8\u7684\u8ddd\u79bb\u662f\u8d27\u7bb1\u4e0a\u5347\u8ddd\u79bb\u76843\u500d\uff0c\u5229\u7528W=Fs\u6c42\u51fa\u94a2\u4e1d\u7ef3\u505a\u7684\u529f\uff0c\u518d\u5229\u7528 \u5f97\u94a2\u4e1d\u7ef3\u7684\u62c9\u529b\u7684\u529f\u7387\uff0e\u8be5\u9898\u6d89\u53ca\u5230\u5bc6\u5ea6\u3001\u91cd\u529b\u3001\u529f\u3001\u529f\u7387\u3001\u6ed1\u8f6e\u7ec4\u7b49\u7684\u8ba1\u7b97\uff0c\u662f\u4e00\u7efc\u5408\u6027\u8f83\u5f3a\u7684\u9898\uff0c\u5728\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u8981\u6ce8\u610f\u5404\u4e2a\u7269\u7406\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u8003\u67e5\u4e86\u5b66\u751f\u7684\u7efc\u5408\u5e94\u7528\u80fd\u529b\uff0c\u5c5e\u4e8e\u96be\u9898\uff0e\u3010\u8003\u70b9\u3011\u5bc6\u5ea6\u516c\u5f0f\u7684\u5e94\u7528\uff1b\u6ed1\u8f6e\u7ec4\u7ef3\u5b50\u62c9\u529b\u7684\u8ba1\u7b97\uff1b\u91cd\u529b\u7684\u8ba1\u7b97\uff1b\u529f\u7387\u7684\u8ba1\u7b97\uff0e
\u89e3\uff1a\uff081\uff09\u7816\u7684\u5bc6\u5ea6\uff1a\u03c1=2\u00d710 3 kg/m 3 \u6bcf\u5757\u8f6c\u7684\u4f53\u79ef\uff1aV=1.5\u00d710 \ufe633 m 3 \u6bcf\u5757\u7816\u7684\u8d28\u91cf\uff1am=\u03c1V=2\u00d710 3 kg/m 3 \u00d71.5\u00d710 \ufe633 m 3 =3kg \u6bcf\u5757\u7816\u7684\u91cd\u529b\uff1aG=mg=3kg\u00d710N/kg=30N\uff082\uff09\u8d27\u7bb1\u7684\u603b\u91cd\uff1aG \u603b =3\u00d7F \u62c9 =3\u00d72100N=6300N\u7816\u7684\u603b\u91cd\uff1aG \u7816 =G \u603b \ufe63G \u7bb1 =6300N\ufe63300N=6000N \u7816\u7684\u5757\u6570\u662f\uff1a =200\u5757\uff083\uff09\u94a2\u4e1d\u7ef3\u79fb\u52a8\u7684\u8ddd\u79bb\uff1aL=10m\u00d73=30m\u94a2\u4e1d\u7ef3\u7684\u62c9\u529b\uff1aF \u62c9 =2000N \u62c9\u529b\u505a\u7684\u529f\uff1aW=F \u62c9 L=2000N\u00d730m=60000J \u62c9\u529b\u505a\u7684\u529f\u7387\uff1aP= = =1200W
(1)根据ρ=m |
V |
m=ρV=2×103kg/m3×1.5×10-3m3=3kg,
每块砖的重力:
G=mg=3kg×10N/kg=30N;
(2)由图可知,n=3,
∵不计钢丝绳的重力和摩擦,
∴钢丝绳上允许施加的最大拉力:
F=
1 |
n |
1 |
3 |
(3)绳端移动的距离:
s=nh=3×10m=30m,
钢丝绳的拉力做的功:
W=F′s=2000N×30m=60000J,
钢丝绳的拉力的功率:
P=
W |
t |
60000J |
50s |
(4)∵物体提升物体的重力越大,该装置的机械效率越大,
∴当提升物体的重力G=215×30N=6450N时,机械效率最大,
则该装置的最高机械效率:
η=
W有 |
W总 |
Gh |
Fs |
Gh |
Fnh |
G |
nF |
6450N |
3×2300N |
答:(1)每块砖的重力是30N;
(2)钢丝绳上允许施加的最大拉力是2300N;
(3)钢丝绳拉力做功的功率是1200W;
(4)该装置的最高机械效率是93.5%.
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