# Power time energy relationship developed

### Introduction to work and energy (video) | Khan Academy

Work, Energy, and Power - Lesson 1 - Basic Terminology and Concepts Work has nothing to do with the amount of time that this force acts to cause the. In physics, power is the rate of doing work or transferring heat, the amount of energy transferred The dimension of power is energy divided by time. . The similar relationship is obtained for rotating systems, where TA and ωA are the torque. Is it a unit of power? time? energy? or some other quantity? is related to the electric potential difference established across the ends of the circuit (i.e., The relationship between power, current and electric potential difference can be derived.

In a beeper, electrical energy is transformed into sound energy. And in a motor, electrical energy is transformed into mechanical energy.

An electrical circuit is simply an energy transformation tool. Energy is provided to the circuit by an electrochemical cell, battery, generator or other electrical energy source.

And energy is delivered by the circuit to the load at the location of the load. The rate at which this energy transformation occurs is of great importance to those who design electrical circuits for useful functions. Power - the rate at which mechanical work is done - was introduced in Unit 5 of the Physics Classroom. Here, we will discuss power in electrical terms; while the context has changed, the essential meaning of the concept of power will remain the same. Power is the rate at which electrical energy is supplied to a circuit or consumed by a load.

The electrical energy is supplied to the load by an energy source such as an electrochemical cell. Recall from Lesson 1 that a cell does work upon a charge to move it from the low energy to the high energy terminal. The work done on the charge is equivalent to the electrical potential energy change of the charge.

Thus, electrical power, like mechanical power, is the rate at which work is done. Like current, power is a rate quantity. Its mathematical formula is expressed on a per time basis. Whether the focus is the energy gained by the charge at the energy source or the energy lost by the charge at the load, electrical power refers to the rate at which the charge changes its energy.

In an electrochemical cell or other energy sourcethe change is a positive change i. Thus, power is often referred to as the rate of energy change and its equation is expressed as the energy change per time.

## Power and efficiency

Like mechanical power, the unit of electrical power is the watt, abbreviated W. Quite obviously, it is important that the symbol W as the unit of power not be confused with the symbol W for the quantity of work done upon a charge by the energy source. A watt of power is equivalent to the delivery of 1 joule of energy every second. A watt light bulbs draws joules of energy every second.

### Power (physics) - Wikipedia

The ratio of the energy delivered or expended by the device to time is equal to the wattage of the device. The kilowatt-hour Electrical utility companies who provide energy for homes provide a monthly bill charging those homes for the electrical energy that they used.

A typical bill can be very complicated with a number of line items indicating charges for various aspects of the utility service. But somewhere on the bill will be a charge for the number of kilowatt-hours of electricity that were consumed.

Exactly what is a kilowatt-hour? Is it a unit of power?

And when we pay for the electricity that we use, what exactly is it that we are paying for? A careful inspection of the unit kilowatt-hour reveals the answers to these questions.

**Work, Energy, and Power: Crash Course Physics #9**

A kilowatt is a unit of power and an hour is a unit of time. When an electrical utility company charges a household for the electricity that they used, they are charging them for electrical energy. A utility company in the United States is responsible for assuring that the electric potential difference across the two main wires of the house is to volts. And maintaining this difference in potential requires energy. I have a block of mass m.

I have a block of mass m and it starts at rest.

And then I apply force. Let's say I apply a force, F, for a distance of, I think, you can guess what the distance I'm going to apply it is, for a distance of d.

## Power (physics)

So I'm pushing on this block with a force of F for a distance of d. And what I want to figure out is-- well, we know what the work is. I mean, by definition, work is equal to this force times this distance that I'm applying the block-- that I'm pushing the block. But what is the velocity going to be of this block over here? It's going to be something somewhat faster.

Because force isn't-- and I'm assuming that this is frictionless on here. So force isn't just moving the block with a constant velocity, force is equal to mass times acceleration. So I'm actually going to be accelerating the block. So even though it's stationary here, by the time we get to this point over here, that block is going to have some velocity.

We don't know what it is because we're using all variables, we're not using numbers. But let's figure out what it is in terms of v. So if you remember your kinematics equations, and if you don't, you might want to go back.

Or if you've never seen the videos, there's a whole set of videos on projectile motion and kinematics. But we figured out that when we're accelerating an object over a distance, that the final velocity-- let me change colors just for variety-- the final velocity squared is equal to the initial velocity squared plus 2 times the acceleration times the distance.

And we proved this back then, so I won't redo it now. But in this situation, what's the initial velocity? Well the initial velocity was 0. So the equation becomes vf squared is equal to 2 times the acceleration times the distance. And then, we could rewrite the acceleration in terms of, what? The force and the mass, right? So what is the acceleration? Well F equals ma. Or, acceleration is equal to force divided by you mass.

So we get vf squared is equal to 2 times the force divided by the mass times the distance. And then we could take the square root of both sides if we want, and we get the final velocity of this block, at this point, is going to be equal to the square root of 2 times force times distance divided by mass.

And so that's how we could figure it out. And there's something interesting going on here. There's something interesting in what we did just now. Do you see something that looks a little bit like work? You have this force times distance expression right here.

Force times distance right here. So let's write another equation. If we know the given amount of velocity something has, if we can figure out how much work needed to be put into the system to get to that velocity. Well we can just replace force times distance with work. Because work is equal to force times distance.

So let's go straight from this equation because we don't have to re-square it. So we get vf squared is equal to 2 times force times distance. Took that definition right here. Let's multiply both sides of this equation times the mass. So you get mass times the velocity. And we don't have to write-- I'm going to get rid of this f because we know that we started at rest and that the velocity is going to be-- let's just call it v.

So m times V squared is equal to 2 times the work. Divide both sides by 2. Or that the work is equal to mv squared over 2. Just divided both sides by 2.

- Introduction to work and energy
- Power: Putting Charges to Work

And of course, the unit here is joules. So this is interesting. Now if I know the velocity of an object, I can figure out, using this formula, which hopefully wasn't too complicated to derive.