# Power and energy relationship

### Work, Energy and Power

The energy used is the time integral of the electric power. Learning Objectives. Formulate the relationship between the energy usage and the electric power. Work, Energy, and Power - Lesson 1 - Basic Terminology and Concepts to do with the rate at which a certain amount of work is done is known as the power. Energy can be converted between different forms. Let's start with a different example though, to understand the relation between power and.

Like all rate quantities, power is a time-based quantity. Power is related to how fast a job is done.

Two identical jobs or tasks can be done at different rates - one slowly or and one rapidly. The work is the same in each case since they are identical jobs but the power is different. The equation for power shows the importance of time: Special attention should be taken so as not to confuse the unit Watt, abbreviated W, with the quantity work, also abbreviated by the letter W.

Combining the equations for power and work can lead to a second equation for power.

A few of the problems in this set of problems will utilize this derived equation for power. Mechanical, Kinetic and Potential Energies There are two forms of mechanical energy - potential energy and kinetic energy.

### What is the relationship between power and energy? - Physics Stack Exchange

Potential energy is the stored energy of position. In this set of problems, we will be most concerned with the stored energy due to the vertical position of an object within Earth's gravitational field. Kinetic energy is defined as the energy possessed by an object due to its motion. An object must be moving to possess kinetic energy. The amount of kinetic energy KE possessed by a moving object is dependent upon mass and speed.

The total mechanical energy possessed by an object is the sum of its kinetic and potential energies. Work-Energy Connection There is a relationship between work and total mechanical energy.

## Mechanics: Work, Energy and Power

The final amount of total mechanical energy TMEf possessed by the system is equivalent to the initial amount of energy TMEi plus the work done by these non-conservative forces Wnc. The mechanical energy possessed by a system is the sum of the kinetic energy and the potential energy.

Positive work is done on a system when the force doing the work acts in the direction of the motion of the object. Negative work is done when the force doing the work opposes the motion of the object.

When a positive value for work is substituted into the work-energy equation above, the final amount of energy will be greater than the initial amount of energy; the system is said to have gained mechanical energy. When a negative value for work is substituted into the work-energy equation above, the final amount of energy will be less than the initial amount of energy; the system is said to have lost mechanical energy. There are occasions in which the only forces doing work are conservative forces sometimes referred to as internal forces.

Typically, such conservative forces include gravitational forces, elastic or spring forces, electrical forces and magnetic forces. When the only forces doing work are conservative forces, then the Wnc term in the equation above is zero. In such instances, the system is said to have conserved its mechanical energy. The proper approach to work-energy problem involves carefully reading the problem description and substituting values from it into the work-energy equation listed above.

Mathematically, it is computed using the following equation. As is implied by the equation for power, a unit of power is equivalent to a unit of work divided by a unit of time. For historical reasons, the horsepower is occasionally used to describe the power delivered by a machine. One horsepower is equivalent to approximately Watts.

Most machines are designed and built to do work on objects. All machines are typically described by a power rating. The power rating indicates the rate at which that machine can do work upon other objects.

A car engine is an example of a machine that is given a power rating. The power rating relates to how rapidly the car can accelerate the car. If this were the case, then a car with four times the horsepower could do the same amount of work in one-fourth the time.

## Power (physics)

The point is that for the same amount of work, power and time are inversely proportional. The power equation suggests that a more powerful engine can do the same amount of work in less time. A person is also a machine that has a power rating. Some people are more power-full than others. That is, some people are capable of doing the same amount of work in less time or more work in the same amount of time. A common physics lab involves quickly climbing a flight of stairs and using mass, height and time information to determine a student's personal power.

Despite the diagonal motion along the staircase, it is often assumed that the horizontal motion is constant and all the force from the steps is used to elevate the student upward at a constant speed.

Thus, the weight of the student is equal to the force that does the work on the student and the height of the staircase is the upward displacement. Suppose that Ben Pumpiniron elevates his kg body up the 2. If this were the case, then we could calculate Ben's power rating. It can be assumed that Ben must apply an Newton downward force upon the stairs to elevate his body.