Work and energy relationship label

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work and energy relationship label

In physics, a force is said to do work if, when acting, there is a displacement of the point of Work transfers energy from one place to another, or one form to another. The relation between the net force and the acceleration is given by the. Kinetic energy is energy possessed by an object in motion. because the earth can pull you down through the force of gravity, doing work in the process. To understand the relationship between work and heat, we need to understand a third, linking factor: the With the interactions of heat, work and internal energy, there are energy transfers and \Delta U=q + w \label{1}\]. with.

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.

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.

work and energy relationship label

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.

Power (video) | Work and energy | Khan Academy

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?

Analysis of Situations in Which Mechanical Energy is Conserved

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.

Work (physics)

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.

work and energy relationship label

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. 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.

I can figure out how much work was imputed into that object to get it to that velocity. And this, by definition, is called kinetic energy.

  • Introduction to work and energy
  • 1st Law of Thermodynamics

And there should be a way to distinguish between what he's doing and what the other slower weightlifter is doing. We can distinguish their actions in physics by talking about power. Power measures the rate at which someone like these weightlifters or something like an automobile engine does work.

To be specific, power is defined as the work done divided by the time that it took to do that work. We already said that both weightlifters are doing 1, joules of work.

The weightlifter on the right takes 1 second to lift his weights, and the weightlifter on the left takes 3 seconds to lift his weights. If we plug those times into the definition of power, we'll find that the power output of the weightlifter on the right during his lift is 1, joules per second.

And the power output of the weightlifter on the left during his lift is joules per second. A joule per second is named a watt, after the Scottish engineer James Watt. And the watt is abbreviated with a capital W. All right, let's look at another example. Let's say a 1, kilogram car starts from rest and takes 2 seconds to reach a speed of 5 meters per second. We can find the power output by the engine by taking the work done on the car divided by the time it took to do that work.

To find the work done on the car, we just need to figure out how much energy was given to the car. In this case, the car was given kinetic energy and it took two seconds to give it that kinetic energy. If we plug in the values for the mass and the speed, we find the engine had a power output of 6, watts.

We should be clear that what we've really been finding here is the average power output because we've been looking at the total work done over a given time interval. If we were to look at the time intervals that got smaller and smaller, we'd be getting closer and closer to the power output at a given moment. And if we were to make our time interval infinitesimally small, we'd be finding the power output at that particular point in time. We call this the instantaneous power.

Dealing with infinitesimals typically requires the use of calculus, but there are ways of finding the instantaneous power without having to use calculus. For instance, let's say you were looking at a car whose instantaneous power output was 6, watts at every given moment.

Work and energy

Since the instantaneous power never changes, the average power just equals the instantaneous power, which equals 6, watts. In other words, the average power over any time interval is going to equal the instantaneous power at any moment.

And that means work per time gives you both the average power and the instantaneous power in this case. Let's say you weren't so lucky, and the instantaneous power was changing as the car progressed.

work and energy relationship label

Then, how would you find the instantaneous power?