[MUSIC] Power is defined as the rate of doing work or the rate of converting energy. In this non-calculus course we'll look at the average power, P = delta W over delta t. The unit one joule per second is called a watt, symbol W. No, there's that letter W again. Be really careful. Capital W might mean weight, a force or work, a scalar quantity or it could be watts, a unit. Here, my speed and kinetic energy are pretty constant so, if we neglect air resistance, I'm converting my internal energy into gravitational potential energy. Here in my height H is increasing at about one meter per second. So my mechanical power output is about 700 joules per second, or 700 watts. This gives a human scale to the unit. A fit person can output roughly a kilowatt, briefly, and perhaps 100 to a few hundred watts, for longer periods. Using the definition of work and the definition of velocity, we see that power is force times the velocity times the cause of the angle between them. If you're fit and healthy, you might like to use this technique to measure your power output on a long staircase but be careful. So, here's a problem that combines power and friction. [SOUND] You drag a mass in at constant velocity on the surface with coefficient of kinetic friction mu sub k. What is the rate of doing work by each of the two forces? See how you go. Remember air resistance. Let's get quantitative about it. Suppose you have a not very streamlined object like this plate. And you push it through the air at constant speed v. Suppose our object with cross sectional area A, travels a distance D equals vt. Then suppose that all of air in front of it is accelerated from rest up to speed v. So we have to do work on that air, the work is a half MV squared. Using the density, rho = mass over volume, and the volume AD, we have mass = rho AD = rho AVT. Substitute that for mass and we have work equals half rho AT v cubed. Divide both sides by time to get the power. We see the power goes as v cubed. That's an important reason why it's hard to go fast. Twice as fast eight times the power. We're not finished yet, because sometimes this picture underestimates the amount of air accelerated. And in most cases, it overestimates it, especially if the object is streamlined, in which case it pushes much of the air out of the way, rather than accelerating it. So, we include a factor called the drag coefficient, C sub D. That's, yet, another empirical constant. We usually have to measure it experimentally. Happily, C sub D turns out to be almost independent of the speed, v Here are some approximate values. Well, you can guess what's coming, yes, a question about power and air resistance. We define power as the work done or the energy converted per unit time. We can do the reverse and write energy or work equals power times time. Consider an electrical appliance that uses a kilowatt say a toaster or a hair dryer. Good question, what would I know about hair dryers? [LAUGH] The appliance runs for an hour. How much electrical energy does it convert? Well, we multiply 1 kw by 3600 s, this gives us 3.6 MJ, which is known as a kW.hr. A kilowatt hour, power times time gives energy. The kilowatt hour is a unit of energy that the electricity companies often use. Depending on where you live and the time of day, they will sell a kilowatt hour of energy for between very roughly $0.10 and a dollar. If this looks like a bargain, that's because it is. Let's put it in context. A unit for power used in the USA is the horsepower which is 746 watts. This may not seem much for a horse given that I was producing 700 watts here. The difference is that a horse can provide this power all day. For a human over a whole day, even 100 watts is a pretty large value. Long before electricity, only rich people had horses. Most hard labor was done by humans. So let's imagine that I'm a laborer. Tote that barge, shift that bale, and that I produce 100 watts. I work a 10 hour a day. [LAUGH] Back then there were no unions. So I produce 1 kilowatt-hour in a day, [LAUGH] and I collapse at the end, exhausted. So let's have a look at an electricity bill and replace kilowatt-hours with laborer days. Viewed that way, it's a bargain. As to why energy is so cheap, that's a difficult political question. Well, now that we can analyze and quantify forces, work, energy, and power, there are many important practical questions that we can investigate. We'll do some of those in the quiz and in the test, but I'm hoping your curiosity will drive you to look at a lot more. Next week, momentum, collisions and yet another way of presenting Newton's second law. [SOUND] We'll also have some fun [LAUGH]. See you then. [MUSIC]
