Key Concepts of Work, Energy, Power

In this video, we'll be reviewing how to calculate work, energy, and power. We're going to start with this box. And let's say we pull it at an angle, F here, with a certain amount of force. And it moves across the ground with a certain amount of displacement. In physics, we have a term called work. And work can be very useful in analyzing problems like this. And it's equal to the component of the force times the displacement. component of the force in the direction of the displacement. And if it's not in the direction of displacement, then we're going to multiply by cosine theta. And this will give us, f cosine theta will give us a component of the force in the direction of the displacement. So let's say that this force is 20 newtons. And let's say that the displacement is 3 meters. And our angle, angle theta, is going to be 30 degrees. So to calculate the work, It's just going to be 20 times 3 times cosine 30 degrees. Get rounded 52 joules. Now work can be positive, zero, or negative. So let me start with a situation where the work is positive. So work is positive if the force and the displacement are in the same direction. So using our previous example where we have a box. But this time it's getting pulled in the same direction as its displacement. The work is going to just be the force times the force 20 newtons times the displacement of 3 meters and we get 60 joules. Work can also be 0. If you exert a force on an object, let's say the box we... Or we're just holding it up. There's a force that we're pushing it up on and the displacement is zero. Let's say the displacement here is zero. It's not it's not moving up. We're just holding on to it. Maybe it's on our palm and we're just holding up. The work would be zero because there's no displacement. Or let's say that we are holding it up, but our displacement is sideways. We're just going across the room. So it's just this sideways in this case. Work would also be zero work can also be negative if The force is in the opposite direction of the displacement so example of that would be friction So let's say here we have friction and let's say friction Was 10 newtons and this box was going to the right has a displacement of going to the right of? 1.5 meters And let's say we're making right positive. So right is positive. So in this case, our work is negative 10 force times the displacement 1.5 and we get negative 15 joules. So work can be positive, zero or negative. We'll see the significance of this in just a little bit. Work can also be represented graphically on a force-verse position graph. So on the left here, we have an object that's being pulled at a constant 3 newton amount of force from position 2 to 4. And the area under the curve right here, this represents the work that was done by this force. So we have work is going to be equal to, I'm going to calculate the area under the curve, which is going to be 3 times 2. And we get 6 joules. On the right here, we could do the same method as well. So except this time, the force is not constant. It's going from 3 to 5 newtons over the same amount of displacement here. And so once again, I'm going to find the area under the curve here. Now, I'm going to break this up into two parts, into a triangle, and then also break it up into a rectangle. So this... is going to be 1 half area of a triangle, 1 half base times height, so 1 half 2 times 2, I get 2 joules. And then down here I get, it's a rectangle, so base times height, 2 times 3, and I get 6 joules. And if I combine the two, if I combine these two, I get 6 plus 2, I get a total of 8 joules of work done by this force. Sometimes there are more than one force acting on our system. Each of those forces can be doing work on the system. The sum of those work is our net work. Here in our example we have an applied force to the right and a friction to the left. This box has a displacement of 3 meters to the right. To calculate the net, We can calculate the work for each of the individual forces in atom up or what we could do is to use the net force times the displacement cosine theta. In this case, our applied force is 20 newtons and we have a friction of 10 newtons. And so our net. force is 20 minus 10 would be 10 newtons the displacement is 3 and the cosine we don't have to worry about that because the net force is parallel is in the same direction as its displacement so we're just going to leave that alone so 10 times 3 we get 30 joules so now that we've defined what work is we're going to combine it with One of our kinematic equations to derive what's called the energy, the work energy theorem, and this is the big payoff. And this is the reason why we define work the way we do, because then it gives a relationship between work and kinetic energy, which we'll see in a moment. So we're going to start with our definition of work, which is work is equal to force. And we're talking about the net work. It's going to be equal to the net force. times displacement. We're going to assume the net force here is parallel or in the same direction as displacement, so I'm not going to worry about the cosine at this moment. So using F equals ma Newton's second law, I can substitute ma for the net force is equal to d. Next, I'm going to substitute one of our kinematic equations, which is VF squared equals VI squared. plus 2a times the displacement. And I'm going to divide 2d on both sides, so I get vf squared minus vi squared divided by 2d is equal to the acceleration. I'm going to substitute the acceleration in here. So I have m times vf squared minus vi squared divided by 2d. And there's going to be another D and you'll notice that the D's will cancel out and that leaves me with 1 over 2 mv final squared minus 1 over 2 mv initial squared. And all of that is equal to the net network and we have a special name for 1 over 2. mv squared and we call that kinetic energy so 1 over 2 mv squared and so we can also rewrite this as the net work the net work is equal to the final kinetic energy minus the initial kinetic energy and this is what we call the work energy theorem so the work energy theorem tells us. that the net work on a system is equal to the change in the system's kinetic energy. So let's apply this equation to our problem that we just solved in our previous example. So we have this box that's moving to the right, has a displacement of 3 meters, and the net work done on it, which we calculated, was 30 joules. And this is work done from the applied minus the work done by friction. And let's say that the initial velocity was 0. And now we want to find out what is the final velocity. So to calculate that, we can use our equation. And we can substitute 30 joules for the work that was done, which is equal to the final kinetic energy, which is going to be 1 over 2 m v final squared minus. And the initial is going to be 0 starting from rest, so 0. And we want to find VF. So let's say that the mass was 10 kilograms. The box was 10 kilograms. OK. So to find, to calculate this, we can just take 30 is equal to 1 over 2 times 10. And we're looking for VF squared. So we have 30 equals to 5. VF squared, 30 divided by 5 is 6. Equals VF squared we're going to square root both sides and we get that the VF is about 2.4 meters per second so this is telling us that after pushing the box 3 meters with a net work of 30 Joules that the box will end up with a final velocity of 2.4 meters per second so now we'll look at a special case of doing work against gravitational force so taking our same box. And now we're going to lift it up with a certain amount of force and it's going to have a certain amount of displacement. Now when we're doing work against a gravitational force, we're lifting it up, it's helpful to use the symbol H because the displacement is basically the height. And starting with our basic work equation, Fd cosine theta. The... Force that you need to lift an object up at constant speed is mg, it's just the weight of the object. And then d, instead of d, we're going to go ahead and use h. We're not going to worry about cosine theta because the force and displacement are in the same direction. And we have a name for mgh, and we call this gravitational potential energy. And really it's the change in the gravitational. potential energy that matters and so we're going to write delta p e equals to m g and this h is really the change in position so rather than writing delta h oftentimes we'll just write it as as h one of the nice things about calculating the change in potential energy is that it's path independent so whether i lift the box straight up or if i were to use stairs and carry it all the way to the top the box has the same mass g is the same 9.8 And H, the height here, is going to be the same. So they would have the same change in potential energy. So gravitational force is an example of what we call a conservative force. And a conservative force is one for which the work done by or against it depends only on the starting and ending points of a motion and not on the path taken. Another conservative force example would be a spring force. So going back to our work energy theorem, which tells us that the net work. equals to the change in kinetic energy. If in our problem only conservative forces are acting on our system, we can say that the conservative work is equal to the change in kinetic energy. Now, is there non-conservative work, non-conservative forces that can do work on the system? And yes, they can, and we'll talk about that in a moment. But for right now, if there's only conservative forces acting on our system, then there's only... conservative work that's occurring in our problem. When there's work done by a conservative force, that's going to cause a decrease in the potential energy. So you can see that in the situation on the left here. So we have a box, gravity is pulling the box down, and so as it goes down, there's going to be a decrease in potential energy. Substituting negative delta PE into Wc, we get negative delta PE equals Wc. delta ke delta just means the change in and it's going to be the final minus the initial so we can rewrite it as final potential energy minus initial potential energy and with the negative around the whole thing and then equals to the final kinetic energy minus the initial kinetic energy and if we move all the initial to one side to the left here and all the final to the right we get ke initial plus p initial equals to Ke final minus Ke initial and this is called the conservation of mechanical energy. When only conservative forces are involved such as gravitational forces and that there are no non conservative forces like friction, the total mechanical energy is constant. When we say mechanical energy that refers to potential and kinetic energy and so for example this box is falling to the ground the total amount of Mechanical energy is going to stay the same, but the potential and kinetic energy are changing. We can use pie charts to illustrate this idea that the total amount stays the same, so the circles are the same size. However, the potential energy is changing as it's falling. The potential energy is decreasing and it's getting less and less. However, the kinetic energy is increasing. We can also illustrate this idea of conservation mechanical energy, of the mechanical energy with this pendulum. So starting off on the left here we have All the energy is stored in the gravitational fields, which is potential energy. And as it swings down, now its energies transform into the energy of motion, which we call kinetic energy. And then it swings back up. At some point, some of the energy will be potential energy, and some of the energy will be kinetic energy. Now we'll take a look at non-conservative forces. So a non-conservative force... is one for which work depends on the path taken, for example, friction. Also, a non-conservative force adds or removes mechanical energy from a system. An example would be thermal energy dissipating from the system. So now let's compare two different systems, one with non-conservative forces and one without non-conservative forces. So we'll start with the one that does not have any Non conservative forces so we'll start on the left here in our system here is a spring and our box so this box is high above the ground so it only has gravitational potential energy. And as it falls it compresses the spring and now it has spring potential energy or elastic potential energy and then, when it bounces back up it's got both gravitational potential energy not as much as before so put a little. Prime there and plus K E. So it also has some kinetic energy. Now the potential energy at the beginning is equal to the spring potential energy in the middle, which is equal to the potential energy plus the kinetic energy at the last situation here. Now we'll take a look at a situation where there is a non-conservative force. So now the box on the right here falls and hits the ground. And the force of the ground on the box is a non-conservative force, and it's not easily recoverable. We can't get that energy back. But the question is, where did that energy go? Because we start off with gravitational potential energy. It hits the ground, and it's got zero gravitational potential energy. So where did that energy go? And so it's transformed into heat or sound or deformation of the ground. So what I'd like to do now is to derive an equation for energy that takes into account non-conservative forces. So net work includes both non-conservative forces, work done by a non-conservative force, and work done by a conservative force. Combining that with the... work energy theorem W equals delta Ke we get WNC plus WC equals the change in kinetic energy. Next we're going to substitute for the work done by conservative force we know that WC equals negative delta Pe and then plugging that into our previous equation we get that the WNC equals the change in kinetic energy plus the change in potential energy. Since delta just means the change in, delta Ke just means final kinetic energy minus initial kinetic energy, we can go ahead and replace the delta with the final minus initial. And then lastly, we can rewrite the equation as follows, that the initial kinetic energy plus the initial potential energy plus the work done by non-conservative force is equal to the final kinetic energy plus the final potential energy. Work done by non conservative force can be positive, negative or zero. If the work done by a non conservative force is positive, then the mechanical energy will increase. So down here we have an example of this box here that we're pushing it to the right. We have an applied force, which is a non conservative force. We have friction, also a non conservative force. We're pushing it to the right, a displacement of D. And so in this situation, the Work done by non conservative force is positive and so this system right here is going to have a mechanical energy that increases so even though the gravitational potential energy is going to stay the same because not going higher the kinetic energy will increase as it goes faster and faster. Now we'll take a look at a box that is sliding to the right and the only horizontal force acting on it is friction. Friction is a non-conservative force. The work done by this non-conservative force is negative because it's in the negative direction. We're making right positive. In this situation, the mechanical energy is going to decrease. Even though the gravitational potential energy is zero because it's not moving up or down, however, it's slowing down so the kinetic energy is decreasing. Therefore, the total mechanical energy is also decreasing in this system. Now we'll take a look at a situation where we're pushing the box to the right and we're pushing at constant velocity. So the work done by the non-conservative force, applied force and friction, is going to be zero because the applied force and the friction are equal to each other. So the net force is zero. So the work is zero. And mechanical energy is conserved, which means that the potential plus the kinetic energy is zero. In this case, it's not moving up or down, so the potential energy is zero. and it's not speeding up or slowing down, so the kinetic energy also doesn't change. All right, now we'll take a look at power. So power is the rate at which work is done. How quickly is work done? And the equation for power is work divided by time. And since work is equal to the change in energy, we can also write it this way, delta E divided by T. So let's say we have an elevator that is getting that's being lifted up. And let's say that's taking 42 seconds for it to go up 28 meters. So the displacement is 28 meters and that this elevator has a mass of 2000 kilograms. So the power is going to be W over T and the W is the force times. The displacement divided by T. We're assuming that the force and displacement are in the same direction. The force is 2,000 kilograms of MG. So I'm going to use MG here. So 2,000 kilograms times G, 9.8. And D is 28 meters divided by the time of 42 seconds. And we get 1.3 times 10 to the fourth. Watts now let's say that we have an object that is moving to the right and we've had we were pulling it with 12 newtons and it's moving with a speed of 3 meters per second. Now there's another way to calculate power and which is work divided by time we know work is force times displacement divided by time. If you look at displacement over time, we remember from kinematics that that's equal to velocity. So power can also be calculated from the force times the velocity. And here we're assuming that the force and the velocity are in the same direction. So to calculate this problem, we just take 12 times 3 and we get 36. So 36 watts. And so the unit of power is watts.

In this video, we'll be reviewing how to calculate work, energy, and power. We're going to start with this box. And let's say we pull it at an angle, F here, with a certain amount of force.

And it moves across the ground with a certain amount of displacement. In physics, we have a term called work. And work can be very useful in analyzing problems like this.

And it's equal to the component of the force times the displacement. component of the force in the direction of the displacement. And if it's not in the direction of displacement, then we're going to multiply by cosine theta.

And this will give us, f cosine theta will give us a component of the force in the direction of the displacement. So let's say that this force is 20 newtons. And let's say that the displacement is 3 meters.

And our angle, angle theta, is going to be 30 degrees. So to calculate the work, It's just going to be 20 times 3 times cosine 30 degrees. Get rounded 52 joules. Now work can be positive, zero, or negative. So let me start with a situation where the work is positive.

So work is positive if the force and the displacement are in the same direction. So using our previous example where we have a box. But this time it's getting pulled in the same direction as its displacement.

The work is going to just be the force times the force 20 newtons times the displacement of 3 meters and we get 60 joules. Work can also be 0. If you exert a force on an object, let's say the box we... Or we're just holding it up.

There's a force that we're pushing it up on and the displacement is zero. Let's say the displacement here is zero. It's not it's not moving up. We're just holding on to it.

Maybe it's on our palm and we're just holding up. The work would be zero because there's no displacement. Or let's say that we are holding it up, but our displacement is sideways.

We're just going across the room. So it's just this sideways in this case. Work would also be zero work can also be negative if The force is in the opposite direction of the displacement so example of that would be friction So let's say here we have friction and let's say friction Was 10 newtons and this box was going to the right has a displacement of going to the right of? 1.5 meters And let's say we're making right positive.

So right is positive. So in this case, our work is negative 10 force times the displacement 1.5 and we get negative 15 joules. So work can be positive, zero or negative. We'll see the significance of this in just a little bit. Work can also be represented graphically on a force-verse position graph.

So on the left here, we have an object that's being pulled at a constant 3 newton amount of force from position 2 to 4. And the area under the curve right here, this represents the work that was done by this force. So we have work is going to be equal to, I'm going to calculate the area under the curve, which is going to be 3 times 2. And we get 6 joules. On the right here, we could do the same method as well.

So except this time, the force is not constant. It's going from 3 to 5 newtons over the same amount of displacement here. And so once again, I'm going to find the area under the curve here.

Now, I'm going to break this up into two parts, into a triangle, and then also break it up into a rectangle. So this... is going to be 1 half area of a triangle, 1 half base times height, so 1 half 2 times 2, I get 2 joules. And then down here I get, it's a rectangle, so base times height, 2 times 3, and I get 6 joules.

And if I combine the two, if I combine these two, I get 6 plus 2, I get a total of 8 joules of work done by this force. Sometimes there are more than one force acting on our system. Each of those forces can be doing work on the system.

The sum of those work is our net work. Here in our example we have an applied force to the right and a friction to the left. This box has a displacement of 3 meters to the right. To calculate the net, We can calculate the work for each of the individual forces in atom up or what we could do is to use the net force times the displacement cosine theta.

In this case, our applied force is 20 newtons and we have a friction of 10 newtons. And so our net. force is 20 minus 10 would be 10 newtons the displacement is 3 and the cosine we don't have to worry about that because the net force is parallel is in the same direction as its displacement so we're just going to leave that alone so 10 times 3 we get 30 joules so now that we've defined what work is we're going to combine it with One of our kinematic equations to derive what's called the energy, the work energy theorem, and this is the big payoff. And this is the reason why we define work the way we do, because then it gives a relationship between work and kinetic energy, which we'll see in a moment. So we're going to start with our definition of work, which is work is equal to force.

And we're talking about the net work. It's going to be equal to the net force. times displacement.

We're going to assume the net force here is parallel or in the same direction as displacement, so I'm not going to worry about the cosine at this moment. So using F equals ma Newton's second law, I can substitute ma for the net force is equal to d. Next, I'm going to substitute one of our kinematic equations, which is VF squared equals VI squared.

plus 2a times the displacement. And I'm going to divide 2d on both sides, so I get vf squared minus vi squared divided by 2d is equal to the acceleration. I'm going to substitute the acceleration in here. So I have m times vf squared minus vi squared divided by 2d.

And there's going to be another D and you'll notice that the D's will cancel out and that leaves me with 1 over 2 mv final squared minus 1 over 2 mv initial squared. And all of that is equal to the net network and we have a special name for 1 over 2. mv squared and we call that kinetic energy so 1 over 2 mv squared and so we can also rewrite this as the net work the net work is equal to the final kinetic energy minus the initial kinetic energy and this is what we call the work energy theorem so the work energy theorem tells us. that the net work on a system is equal to the change in the system's kinetic energy. So let's apply this equation to our problem that we just solved in our previous example. So we have this box that's moving to the right, has a displacement of 3 meters, and the net work done on it, which we calculated, was 30 joules.

And this is work done from the applied minus the work done by friction. And let's say that the initial velocity was 0. And now we want to find out what is the final velocity. So to calculate that, we can use our equation. And we can substitute 30 joules for the work that was done, which is equal to the final kinetic energy, which is going to be 1 over 2 m v final squared minus. And the initial is going to be 0 starting from rest, so 0. And we want to find VF.

So let's say that the mass was 10 kilograms. The box was 10 kilograms. OK.

So to find, to calculate this, we can just take 30 is equal to 1 over 2 times 10. And we're looking for VF squared. So we have 30 equals to 5. VF squared, 30 divided by 5 is 6. Equals VF squared we're going to square root both sides and we get that the VF is about 2.4 meters per second so this is telling us that after pushing the box 3 meters with a net work of 30 Joules that the box will end up with a final velocity of 2.4 meters per second so now we'll look at a special case of doing work against gravitational force so taking our same box. And now we're going to lift it up with a certain amount of force and it's going to have a certain amount of displacement.

Now when we're doing work against a gravitational force, we're lifting it up, it's helpful to use the symbol H because the displacement is basically the height. And starting with our basic work equation, Fd cosine theta. The...

Force that you need to lift an object up at constant speed is mg, it's just the weight of the object. And then d, instead of d, we're going to go ahead and use h. We're not going to worry about cosine theta because the force and displacement are in the same direction. And we have a name for mgh, and we call this gravitational potential energy. And really it's the change in the gravitational.

potential energy that matters and so we're going to write delta p e equals to m g and this h is really the change in position so rather than writing delta h oftentimes we'll just write it as as h one of the nice things about calculating the change in potential energy is that it's path independent so whether i lift the box straight up or if i were to use stairs and carry it all the way to the top the box has the same mass g is the same 9.8 And H, the height here, is going to be the same. So they would have the same change in potential energy. So gravitational force is an example of what we call a conservative force.

And a conservative force is one for which the work done by or against it depends only on the starting and ending points of a motion and not on the path taken. Another conservative force example would be a spring force. So going back to our work energy theorem, which tells us that the net work.

equals to the change in kinetic energy. If in our problem only conservative forces are acting on our system, we can say that the conservative work is equal to the change in kinetic energy. Now, is there non-conservative work, non-conservative forces that can do work on the system? And yes, they can, and we'll talk about that in a moment. But for right now, if there's only conservative forces acting on our system, then there's only...

conservative work that's occurring in our problem. When there's work done by a conservative force, that's going to cause a decrease in the potential energy. So you can see that in the situation on the left here.

So we have a box, gravity is pulling the box down, and so as it goes down, there's going to be a decrease in potential energy. Substituting negative delta PE into Wc, we get negative delta PE equals Wc. delta ke delta just means the change in and it's going to be the final minus the initial so we can rewrite it as final potential energy minus initial potential energy and with the negative around the whole thing and then equals to the final kinetic energy minus the initial kinetic energy and if we move all the initial to one side to the left here and all the final to the right we get ke initial plus p initial equals to Ke final minus Ke initial and this is called the conservation of mechanical energy.

When only conservative forces are involved such as gravitational forces and that there are no non conservative forces like friction, the total mechanical energy is constant. When we say mechanical energy that refers to potential and kinetic energy and so for example this box is falling to the ground the total amount of Mechanical energy is going to stay the same, but the potential and kinetic energy are changing. We can use pie charts to illustrate this idea that the total amount stays the same, so the circles are the same size.

However, the potential energy is changing as it's falling. The potential energy is decreasing and it's getting less and less. However, the kinetic energy is increasing. We can also illustrate this idea of conservation mechanical energy, of the mechanical energy with this pendulum. So starting off on the left here we have All the energy is stored in the gravitational fields, which is potential energy.

And as it swings down, now its energies transform into the energy of motion, which we call kinetic energy. And then it swings back up. At some point, some of the energy will be potential energy, and some of the energy will be kinetic energy.

Now we'll take a look at non-conservative forces. So a non-conservative force... is one for which work depends on the path taken, for example, friction.

Also, a non-conservative force adds or removes mechanical energy from a system. An example would be thermal energy dissipating from the system. So now let's compare two different systems, one with non-conservative forces and one without non-conservative forces. So we'll start with the one that does not have any Non conservative forces so we'll start on the left here in our system here is a spring and our box so this box is high above the ground so it only has gravitational potential energy. And as it falls it compresses the spring and now it has spring potential energy or elastic potential energy and then, when it bounces back up it's got both gravitational potential energy not as much as before so put a little.

Prime there and plus K E. So it also has some kinetic energy. Now the potential energy at the beginning is equal to the spring potential energy in the middle, which is equal to the potential energy plus the kinetic energy at the last situation here. Now we'll take a look at a situation where there is a non-conservative force.

So now the box on the right here falls and hits the ground. And the force of the ground on the box is a non-conservative force, and it's not easily recoverable. We can't get that energy back.

But the question is, where did that energy go? Because we start off with gravitational potential energy. It hits the ground, and it's got zero gravitational potential energy.

So where did that energy go? And so it's transformed into heat or sound or deformation of the ground. So what I'd like to do now is to derive an equation for energy that takes into account non-conservative forces. So net work includes both non-conservative forces, work done by a non-conservative force, and work done by a conservative force. Combining that with the...

work energy theorem W equals delta Ke we get WNC plus WC equals the change in kinetic energy. Next we're going to substitute for the work done by conservative force we know that WC equals negative delta Pe and then plugging that into our previous equation we get that the WNC equals the change in kinetic energy plus the change in potential energy. Since delta just means the change in, delta Ke just means final kinetic energy minus initial kinetic energy, we can go ahead and replace the delta with the final minus initial.

And then lastly, we can rewrite the equation as follows, that the initial kinetic energy plus the initial potential energy plus the work done by non-conservative force is equal to the final kinetic energy plus the final potential energy. Work done by non conservative force can be positive, negative or zero. If the work done by a non conservative force is positive, then the mechanical energy will increase.

So down here we have an example of this box here that we're pushing it to the right. We have an applied force, which is a non conservative force. We have friction, also a non conservative force. We're pushing it to the right, a displacement of D.

And so in this situation, the Work done by non conservative force is positive and so this system right here is going to have a mechanical energy that increases so even though the gravitational potential energy is going to stay the same because not going higher the kinetic energy will increase as it goes faster and faster. Now we'll take a look at a box that is sliding to the right and the only horizontal force acting on it is friction. Friction is a non-conservative force. The work done by this non-conservative force is negative because it's in the negative direction.

We're making right positive. In this situation, the mechanical energy is going to decrease. Even though the gravitational potential energy is zero because it's not moving up or down, however, it's slowing down so the kinetic energy is decreasing. Therefore, the total mechanical energy is also decreasing in this system.

Now we'll take a look at a situation where we're pushing the box to the right and we're pushing at constant velocity. So the work done by the non-conservative force, applied force and friction, is going to be zero because the applied force and the friction are equal to each other. So the net force is zero. So the work is zero. And mechanical energy is conserved, which means that the potential plus the kinetic energy is zero.

In this case, it's not moving up or down, so the potential energy is zero. and it's not speeding up or slowing down, so the kinetic energy also doesn't change. All right, now we'll take a look at power. So power is the rate at which work is done. How quickly is work done?

And the equation for power is work divided by time. And since work is equal to the change in energy, we can also write it this way, delta E divided by T. So let's say we have an elevator that is getting that's being lifted up.

And let's say that's taking 42 seconds for it to go up 28 meters. So the displacement is 28 meters and that this elevator has a mass of 2000 kilograms. So the power is going to be W over T and the W is the force times.

The displacement divided by T. We're assuming that the force and displacement are in the same direction. The force is 2,000 kilograms of MG. So I'm going to use MG here. So 2,000 kilograms times G, 9.8.

And D is 28 meters divided by the time of 42 seconds. And we get 1.3 times 10 to the fourth. Watts now let's say that we have an object that is moving to the right and we've had we were pulling it with 12 newtons and it's moving with a speed of 3 meters per second. Now there's another way to calculate power and which is work divided by time we know work is force times displacement divided by time.

If you look at displacement over time, we remember from kinematics that that's equal to velocity. So power can also be calculated from the force times the velocity. And here we're assuming that the force and the velocity are in the same direction.

So to calculate this problem, we just take 12 times 3 and we get 36. So 36 watts. And so the unit of power is watts.

Transcript for:Key Concepts of Work, Energy, Power

Transcript for:
Key Concepts of Work, Energy, Power