题目
4.
Figure 1 shows a large bucket used by a crane on a building site to move materials between the ground and the top of the building. The mass of the bucket is .
The bucket is attached to a vertical cable with the bottom of the bucket horizontal.
The cable is modelled as light and inextensible.
When the bucket is on the ground, a bag of cement of mass is placed in the bucket.
The bucket with the bag of cement moves vertically upwards with constant acceleration . Air resistance is modelled as being negligible.
(a) Find the tension in the cable.
At the top of the building, the bag of cement is removed. A box of tools of mass is now placed in the bucket.
Later on the bucket with the box of tools is moving vertically downwards with constant deceleration . Air resistance is again modelled as being negligible.
(b) Find the magnitude of the normal reaction between the bucket and the box of tools.
题目中文翻译
图 1 显示建筑工地起重机使用的一个大吊桶，用来在地面和楼顶之间搬运物料。吊桶的质量为 。
吊桶连接在一根竖直缆绳上，桶底保持水平。将缆绳视为轻且不可伸长的绳。
吊桶位于地面时，将一袋质量为 的水泥放入桶内。
吊桶连同水泥袋以恒定加速度 竖直向上运动。将空气阻力视为可忽略。
(a) 求缆绳中的张力。
到达楼顶后，取出水泥袋，将一个质量为 的工具箱放入桶内。
之后，吊桶连同工具箱竖直向下运动，恒定减速度为 。仍将空气阻力视为可忽略。
(b) 求吊桶与工具箱之间法向反作用力的大小。
解答
(a)
解法一
思路
展开
把桶和水泥作为整体，内部接触力互相抵消。向上加速，所以拉力必须大于整体重力。
答题过程
展开
Treat the bucket and cement as one system of mass kg. Taking upwards as positive, Newton’s second law gives
(b)
解法一
思路
展开
向下运动但正在减速，因此加速度向上。要求的是桶与工具箱之间的支持力，应只对工具箱列方程。
答题过程
展开
The tools are moving downwards but slowing down, so their acceleration is upwards.
Let be the upward normal reaction on the 12 kg box of tools. Taking upwards as positive,
The required magnitude is (3 s.f.).