# Relationship between power and energy physics robots

### What is kinetic energy? (article) | Khan Academy

Solar energy. If you need a robot that can hold its own and avoid being moved, then using dense materials would be to your advantage. When Physics Rules Robotics. Mel Siegel Keywords: robotics, scaling, energy, power, communication The practical connection between them is materials. Fifty universities assemble robots to mine regolith, get to water ice, and on testing power usage, energy losses, and safety features of the electrical system. not only the connection failing, but it may melt the connection together making it.

I'm now going to introduce you to the concepts of work and energy. And these are two words that are-- I'm sure you use in your everyday life already and you have some notion of what they mean. But maybe just not in the physics context, although they're not completely unrelated.

So work, you know what work is. Work is when you do something.

## Introduction to work and energy

You go to work, you make a living. In physics, work is-- and I'm going to use a lot of words and they actually end up being kind of circular in their definitions. But I think when we start doing the math, you'll start to get at least a slightly more intuitive notion of what they all are. So work is energy transferred by a force. So I'll write that down, energy transferred-- and I got this from Wikipedia because I wanted a good, I guess, relatively intuitive definition.

Energy transferred by a force. And that makes reasonable sense to me. But then you're wondering, well, I know what a force is, you know, force is mass times acceleration. But what is energy? And then I looked up energy on Wikipedia and I found this, well, entertaining. But it also I think tells you something that these are just concepts that we use to, I guess, work with what we perceive as motion and force and work and all of these types of things.

But they really aren't independent notions. So Wikipedia defines energy as the ability to do work. So they kind of use each other to define each other. Ability to do work. Which is frankly, as good of a definition as I could find. And so, with just the words, these kind of don't give you much information.

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

So what I'm going to do is move onto the equations, and this'll give you a more quantitative feel of what these words mean. So the definition of work in mechanics, work is equal to force times distance. So let's say that I have a block and-- let me do it in a different color just because this yellow might be getting tedious.

And I apply a force of-- let's say I apply a force of 10 Newtons. And I move that block by applying a force of 10 Newtons.

I move that block, let's say I move it-- I don't know-- 7 meters. So the work that I applied to that block, or the energy that I've transferred to that block, the work is equal to the force, which is 10 Newtons, times the distance, times 7 meters. And that would equal 10 times Newton meters. So Newton meters is one, I guess, way of describing work.

And this is also defined as one joule. And I'll do another presentation on all of the things that soon. But joule is the unit of work and it's also the unit of energy.

## What is kinetic energy?

And they're kind of transferrable. Because if you look at the definitions that Wikipedia gave us, work is energy transferred by a force and energy is the ability to work. So I'll leave this relatively circular definition alone now. But we'll use this definition, which I think helps us a little bit more to understand the types of work we can do. And then, what kind of energy we actually are transferring to an object when we do that type of work.

So let me do some examples. Let's say I have a block. 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. 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.

But the weightlifter on the right is lifting his weight faster. 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.

**Electric Power**

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.

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.