## Tuesday, December 29, 2015

### Power is Rate of Change of Work Done and Problem with Solution

Power is defined as the rate of change of work done. Work done is the format of the energy. If we have energy, we can do  the work and the if we are doing work, it means we are having energy. In the other way work and energy or kind of synonyms which are used in different situations with a similar meaning.

Power is the ability of doing work done. Work done in a specified time gives the ability of power measurement. Power is defined as the work done by time. If we do work more quickly that is in lesser time, we have better power. Power is a kind of efficiency of doing the work.

Power is measured with a unit joule per second and it is also called in the name of watt. We have another unit called horse power unit to measure the power and it is equal to 746 watt.

We have a unit called kilo watt hour. But it is not the unit of power rather it is a unit of energy. It is the commercial unit of energy used in the regular day to day life.

Increase in the power of a motor to increase the water coming out of pipe Problem and Solution

Let us consider a pipe having some area of cross section through which water is coming out. Let the water has some density and mass is varying with time and can be expressed as shown in the video below. We can write the volume of water as the product of area of cross section and variable length of the pipe.

We can express the new power and our aim is to increase the mass of water coming out of the pipe by n times of its initial value. For this to happen, we shall increase the power of the system by n power of three and it is shown in detailed proof in the following video.

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