# 係靜力平衡地問題

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3(最大壓縮力)，2，1(對於B點來說力為零)，4，5，6(對於B點來說，有最大的張力)

### 2 個解答

• 天同
Lv 7
7 年前
最愛解答

(a) The compressive force (壓縮力）on A is maximum and is equal to the weight of the box when the box is placed directly above A.

The force on A is zero when the box is placed directly above B (position 3), as there is no moment (力矩) produced about B.

When the box is to the left of B, it produces a anticlockwise moment about B. Hence, such moment must be balanced by a clockwise moment given by A. That is to say, the force acting on the plank is upward. Then by action-reaction law (Newton's Third Law), A is under a downward compression force.

When the box is placed to the right of B, by taking moment about B, the box gives a clockwise moment. Hence, there must be a downward force given by A on the plank such as to produce a anticlockwise moment about B to balance the clockwise moment given by the box. That is, the the force acting on A is upward (because of action and reaction) which indicates a extension force（張力）　.

The arrangement is:

Compression force: 1 > 2

Zero force: 3

Extension force: 6 > 5 > 4

(b) The force on B is zero when the box is on A (position 1)

By taking moment about A, the box gives a clocwise moment on other positions. Hence, the force acting on the plank given by B must be upward so as to give an anticlockwise moment about A. That is, B is under a compression force. This force is maximum when the box is on B (position 3).

The arragement is,

Zero force: 1

compression force: 3 > 6 > 5 > 4=2

The longer the distance of the box from A, the larger is the moment, hence the greater is the compression force on B.

2013-06-20 16:10:52 補充：

Sorry, I made a mistake in part (b)

Taking moment about A, W.x = R.L

where W is the weight of the box at distance x from A

R is the upward normal force on B, L is the distance between AB

2013-06-20 16:15:25 補充：

cont'd...

Then, R = Wx/L the larger the value of x, the greater the force R

The arrangement is:

6 > 5 > 4 > 3(= W) > 2 > 1(=0)

All of the forces are compression. At positions 4,5 and 6, the force is gretaer than W. At position 2, the force is smaller than W.

2013-06-20 16:16:45 補充：

因字數所限，在[意見]欄繼續

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• 匿名
7 年前

題目有說：

最大壓縮力放在最先，最大張力放在最後

所以關於(b)的答案，我認為是，

依題目要來排列為，

3(最大壓縮力)，2，1(對於B點來說力為零)，4，5，6(對於B點來說，有最大的張力)

我這樣的解答 對嗎? 還是哪裡有錯呢?

謝謝指教：)

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