Power

check out these weightlifters the one on the rights lifting his weight faster but they're both doing the same amount of work the reason I can say that is because work is the amount of energy that's transferred or to put it a simpler way this is the way I like to think about it work is equal to the amount of energy you give something or take away from something both weight lifters are giving their weights the same amount of gravitational potential energy they both lift them two meters and the masses or 100 kilograms each plug those into the formula for gravitational potential energy and you find that the work done by each weight lifter is 1960 joules 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 weight lifters doing we can distinguish their actions in physics by talking about power power measures the rate at which someone like these weight lifters or something like an automobile engine does work to be specific powers defined as the work done divided by the time that it took to do that work we already said that both weight lifters are doing 1960 joules of work the weightlifter on the right takes one second to lift his weights and the weightlifter on the Left takes three seconds to lift his weights if we plug those tines into the definition of power we'll find that the power output of the weightlifter on the right during his lift is 1960 joules per second and the power output of the weightlifter on the left during his lift is 653 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 thousand kilogram car starts from rest and takes two seconds to reach a speed of five 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 that the engine had a power output of six thousand two hundred and fifty 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 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 infinitesimal x' 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 six thousand two hundred and fifty watts at every given moment since the instantaneous power never changes the average power just equals the instantaneous power which equals 6250 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 then how would you find the instantaneous power well we know that power is just the work per time so something we can try is to plug in the formula for work which looks like FD cosine theta and then divide by the time something that you might notice is that now we have distance per time in this formula so let's isolate the distance per time distance per time is just the speed so I can replace D over T with V in this formula and if you plug in the instantaneous speed of the car at a given moment in time you'll be finding the instantaneous power output by the force on the car at that particular moment in time so to find the instantaneous power output by a force plug in the force on the object at a particular moment in time multiplied by the speed of the object at that same moment in time then multiplied by cosine theta but be careful here theta isn't any old angle it's the angle between the force on the object and the velocity of the object but in many cases the force is in the same direction as the velocity which means the angle between the force and the velocity is zero and since cosine of zero is one you don't really need the cosine in the formula at all and you find that the instantaneous power is just the force times the speed all right so what does power mean power is the rate at which work is done what does average power mean average power is the work done divided by the time interval that it took to do that work what does instantaneous power mean instantaneous power is the power output of a force at a particular moment in time