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【求助】大家可不可以帮我看看这两道数学题（已解决，谢谢大家热心帮忙）
iou1985@2004-11-04 01:36
是微积分题来的
想了很9也想不到如何入手，谢谢大家帮忙~~
pojen@2004-11-04 02:06
第一題:
將水塔切成水平的鐵板狀, 移動每一張鐵板所需的能量可輕易算出.
ps. 記得將鐵板寬用畢氏定理改寫為 function of 深.
第二題:
pojen 建議你畫一下圖, V(r) against r. 平均值應不難看出要如何算.
物理理解算法:
1.) 求 flux
2.) 除以其流動切面積
祝好運~
Novia@2004-11-04 05:32
calc?大学的?.....还有和物理联系的啊.......偶8会.............=v=.........
iou1985@2004-11-04 06:08
引用
最初由 pojen 发布
第一題:
將水塔切成水平的鐵板狀, 移動每一張鐵板所需的能量可輕易算出.
ps. 記得將鐵板寬用畢氏定理改寫為 function of 深.
第二題:
pojen 建議你畫一下圖, V(r) against r. 平均值應不難看出要如何算.
物理理解算法:
1.) 求 flux
2.) 除以其流動切面積
祝好運~
偶笨。。。。不是很懂。。。可以说详细一点吗？嘻嘻嘻。。。
pojen@2004-11-04 09:08
看來偶的表達能力有待加強....
1.) 所須能量只和搬動之水量與高度有關係, 換句話說, 搬動每一張鐵板的能量可寫成:
delta 能量 = delta [(鐵板體積(h) * 密度) * 搬動高度(h)]
XX(h) 是搬動高度的 function........ 畫圖後用畢氏定理將鐵板體積寫成 h 的 function.
(... 偶覺得偶有講跟沒講一樣........ = =b)
2.) 第二題偶的做法是先算出每秒流出之總水量, i.e. flux
integral (theta) integral (radious) f(r)
然後除以流出之面積, 就是平均流量了.
....... 偶承認偶的表達能力不佳......... iou1985 試試問同班的同學應該會比較有幫助. (當面畫圖講解會很間單....... 偶不知道為什麼偶講完後反而比原題目還複雜...... = =b)
Ammy@2004-11-04 09:22
Not so sure about it. I believe you do the cross sectional area for this problem. Probably my advice is all wrong.
First, there is work to pump all the water to the top of the cylinder. This is the hard part. We use cross sectional area. I don't remember how since the cylinder is on the side. Once you get the cross sectional area. You do an integral from 0 to some number for the function of the cross sectional area times 1000 times g and y. You integrate the function and then you get the work.
Work = mgh. From the density, we get mass is 1000 kg.
Second, once the water is pump to the top. We have to pump it 1 meters high more. This is the easy part.
You just multiply - 1000 kg times g times 1 meter and that's the work
Last, you add the work up. the work to lift is 1 meters and the work to pump water to the top.
Hoope this helps...
iou1985@2004-11-04 12:20
第一题总算算出来了，谢谢楼上几为朋友～～～
可是第二题还是。。。。。
iou1985@2004-11-04 12:34
第二题的A是不是把v(r)从R到r integrate了，除以（R-r）？
seiyafan@2004-11-04 14:12
引用
最初由 iou1985 发布
第二题的A是不是把v(r)从R到r integrate了，除以（R-r）？
If they ask for average velocity between 0 and R, I think u should integrate from 0 to R, then divided by R-0
seiyafan@2004-11-04 14:14
引用
最初由 Novia 发布
calc?大学的?.....还有和物理联系的啊.......偶8会.............=v=.........
I think these are just Cal AB problems. In college more often than not you use Cal to solve specific problems, rather than using specific problem to learn Cal.
half_angel@2004-11-04 15:24
第1题算起来有点麻烦，第2题很容易啊
(a)无非就是积分的定义，函数的平均值就是函数的积分除以积分上下限的差
(b)求极值，求导就可以了
引用
I think these are just Cal AB problems. In college more often than not you use Cal to solve specific problems, rather than using specific problem to learn Cal
这句话说得好，比起国内的应试教育强多了
aaabbbccc@2004-11-06 03:22
the first one supposed to belong to high school. u can just assume all the mass is at the gravity center(center point of the container).
iou1985@2004-11-06 09:06
算到了，谢谢大家热心帮忙～～～
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