# Work lifting cable and work pumping water

• demonelite123
In summary, when lifting half of a cable hanging from a taller building, the integral must be split up since each small piece of rope in the first half is lifted a variable amount. Similarly, when finding the work done by pumping water out of a container to a depth of 1 ft, the integral may need to be adjusted or split up depending on the limits of integration. This is because the center of mass of the water needs to reach the height of the tank.
demonelite123
so i know that when there is a cable hanging from say a building that is taller than the length of the cable and you want to find the work done lifting half of the cable, you have to split the integral up since each "small piece" of rope in the first half gets lifted up a variable amount while each "small piece" of rope in the 2nd half gets lifted the same amount.

now when you are finding the work done by pumping water, let's say the problem is to find the work done in pumping water out of the top of the container so that only a depth of 1 ft of water remains. would you have to split up the integral in a similar way to the cable problem described above? or could you just adjust the limits of integration accordingly. for example if the tank is 4 ft tall and the limits to find the work to pump out all the water is from 0 to 4. could you change it so that the limits become from 0 to 3 to find the work needed to pump the water out so that 1ft depth remains?

The center of mass of the water you are pumping out has to reach the height of the tank.

## 1. What is a work lifting cable and how does it work?

A work lifting cable is a type of cable used to lift and move heavy objects in various industries. It typically consists of multiple strands of wire twisted together to form a strong and flexible rope. The cable is attached to a lifting mechanism, such as a crane or winch, and the weight of the object is distributed evenly along the cable as it is lifted.

## 2. What factors should be considered when choosing a work lifting cable?

When choosing a work lifting cable, it is important to consider the weight and size of the objects to be lifted, the length and strength of the cable, and the environmental conditions in which it will be used. It is also important to ensure that the cable is properly rated for the intended load and that it is regularly inspected and maintained for safety.

## 3. How do work lifting cables differ from other types of cables?

Work lifting cables are specifically designed to handle heavy loads and are typically made of stronger and more durable materials than other types of cables. They also have a higher breaking strength and are often coated or treated to resist corrosion and wear.

## 4. What is the purpose of work pumping water and how does it work?

Work pumping water is the process of using pumps to move water from one location to another for various purposes, such as irrigation, drainage, or power generation. The pumps create suction or pressure to draw water from a source and push it through pipes or channels to the desired location.

## 5. What are the different types of pumps used for work pumping water?

There are several types of pumps used for work pumping water, including centrifugal pumps, diaphragm pumps, and submersible pumps. Each type has its own unique design and function, and the choice of pump will depend on factors such as the amount of water to be moved, the distance it needs to be pumped, and the desired flow rate or pressure.

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