Power

by Patrick Ford
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Hey guys. So up until now, all of our problems have been involving work and energy. And in some problems you'll have to calculate or find how quickly that energy gets transport or is done to another object and that's exactly what power is. So in this video, I'm just going to quickly introduce you to the equation for power. We're going to see what it is and we're going to check out some problems. So the whole equation for power is that the average power is equal to the amount of work that is done or gets done by an object, divided by the change in time, is how quickly that work it's transferred to something else. So the reason this is often called an average power is because we're calculating between two points in time. Now, another way we can write this is by using the relationship between work and energy. Work is just a transfer of energy. So sometimes you might actually see this equation written as E over tea. The unit that will use for power is called the watts, which is written by the symbol W. Which is kind of confusing. So don't confuse this. W. Here with the work that's done. Unfortunately, they both use the same letter but the want is really just a jewel per second, its energy divided by time. So we've actually seen this diagram before up here. This is really just a diagram that relates all of the important variables that we've seen so far in the chapter. Like forces and works and energies and all we're doing here now is we're just adding another branch. We're just adding another connection between work and power. Power. As we said as we said before, is just how quickly we are doing work. So this is just W. Over delta T. That's really all there is to it. Let's go and check out some examples here. So we're going to calculate how many energies or how many jewels of energy is done by a 100 watt light bulb. So this is actually just giving us the power, this is peak was 100 we want to find out how much energy uses in an hour. So this is actually a time. So this is an hours and we want it in seconds. So this is just gonna be 60 minutes Times 60 seconds per minute. So just in case you didn't know this, this is actually 3600, that's how many seconds are in an hour. And so basically what happens is we have our p average equation which is equal to the work that's done over time. But it's also related to the amount of energy that something consumes per time as well. So between these two equations work and energy, we're trying to figure out how many jewels of energy is done. So we're actually going to use this relationship right here, we're trying to solve for this e. So we can do is we can just solve for this. E. is really just going to be the average power times the time. So this is going to be 100 watts Times 3600 seconds, and you get a energy of 360,000 jewels. So, a lot of your problems are gonna actually gonna be solved using this pretty straightforward equation. Um So that's how you do this. All right, so let's go ahead and move on to the second one. Now, we're gonna have objects that are moving uh and and exerting forces and changing velocities. Right? So here we have a 1300 kg sports car. So, I've got this flat ground like this. We know that the mass of this car is 1300 and it starts from rest, which means that the initial velocity is equal to zero. And what happens is it's accelerating from rest because of the engine of the car. So it's being pushed by some force here. I'm going to call this f engine like this. And eventually at some later time, we know that the velocity of the car is not zero anymore. It's actually equal to 40m/s. So we have the time frame that this happens in this delta T. Is equal to seven. And we want to figure out how what is the average power that's delivered by the engine? So, think about it like this, right? This is our p average like this, that's ultimately what we want to find. And this is really just because the force that the engine produces is going to move this car or through some distance. This force acts through some distance like this, this X. Which I actually don't know what it's doing. Some work as it's pushing it through that distance. That's really that's the whole reason that this car accelerates from zero, which has has no kinetic energy and then it finally has an energy velocity of 40. So we've had a transfer of kinetic energy and therefore some work is done. So how do we calculate this power? So RP average is really just going to be the work that's done divided by the change in time or it's the energy divided by time. So we're not going to use this equation because we know that some work has been done and we also know that the change in time is seven seconds. So all we really have to do here to figure this out is figure out how much work is done by the force of the engine. So how do we do this? How do we calculate work? Well, according to our diagram here, we can always calculate works if we have forces and displacements by using F. D. Cosign Theta and then if there's multiple works, you can just add up all of the works done. So if you don't have a force and you actually can't use either one of these equations to calculate work. So then we're kind of stuck here. How do we actually figure out the work? Well, remember that the all the other way you can solve for the work is by using the kinetic energy theorem. The network that's done an object is equal to the change in kinetic energy. And remember that this change in kinetic energy is actually related to the change in velocity. So here we have a velocity of zero and at 40. So now we can actually calculate what that change in kinetic energy is. This is delta K. E. And this is really just one half M. The final squared minus one half M. The initial squared. So all we do here is we have actually have the mass and we have the velocities at both the beginning and end. So we can calculate this. We know that this right term here is going to go to zero because the initial velocity is equal to zero. And so basically we're just gonna plug in this expression in for our work. So we can actually just go ahead and calculate this and use in one fell swoop. We can say that the average power is going to be one half M. V squared like this divided by the change in time. So we just plug in all of our numbers. This is gonna be one half of 1300 the final velocity is 40 squared and they're gonna have divided by seven seconds. And what you're gonna get is you're going to get um and then when you plug this in you're going to get 1.4 times 10 to the sixth watts. That's the total amount of power output by the engine in order to accelerate this car and give it some kinetic energy. So that's it for this one. Guys, let me know if you have any questions.