La? Hello, Jackson. So we're going to look at work, energy and power today. So we know the equation, work is force times, distance, power is work done over time taken, but you can also have work. Is force times distance. Or power, I should say. Power is force times distance. Over time. And that gives us an equation. Power is force times velocity. Okay, distance over time is velocity. So force times, velocity will also give us power. Okay, so that's a derived equation. Here's our equation for kinetic energy, a half mv squared gratiational tional potential energy. So power is the race at which work is done or the rate at which energy is converted. And then when we were talking about hooklaw elastic potential energy, a half fx or a half K X squared, so we can have two versions of that equation. And the important thing, they're all scalar quantities. So they're only magnitude. They have no direction. But sometimes we might have a force acting at an angle to the horizontal. So we have to take into account the angle at which the force is acting to work out the work done. So if the motion is in the horizontal direction, we use costs. So fs cothere, the force times the distance cothere. And the work done is the if we have a force like hook law, remember a spring obeying hook law, the work done is the area under the graph line. Okay. Conservation of energy. Energy can't be created or destroyed, but it can be transferred from one type to another. The energy is stored until it is transferred to another fall. So chemical energy in a battery, to electrical energy, to light or heat energy. When a car is moving steadily at 60 km an hour, its kinetic energy does not change, but there is work being done by the engine in overcoming air resistance and the transfer, this transfers chemical energy and fuel to internal energy of the car and the surroundings. So the internal energy is the sum of the kinetic energy and potential energy of the molecules vibrating in the car. Of the molecules. That's what heating is. So power measures how much work is done in a certain amount of time. It's a better method of comparison than just using energy transferred. If you wait long enough, you can transfer all the energy you want slowly, which means the system is not working hard. So the rate at which the work is done or the energy is transferred is probably a better calculation for efficiency. So power is force times distance. Over time, power can be used as force times velocity. You won't get that equation in the back of your book, but you know it's there. Efficiency measures how successfully energy is transferred to a useful form. So useful energy output over total energy input. It can be a ratio or it can be a percentage, but it generally efficiency doesn't have a unit unless you make it a percentage. So if we have an example before we look at our past paper type problems, I have a few multiple choice and a few longer type questions. Very often, this topic will accompany another topic. So we might come across it in a mechanics question, in an electricity question, how efficient are things? So a MaaS of four kilograms is moved horizontally with a speed of 2m per second. Calculate the work done on the MaaS in order to change its speed from 2m per second to 6m per second. So. So work done is changing kinetic energy. A half mv squared minus a half mu squared is equal to 2072 minus eight 64 joules is needed to increase the speed of the car. Calculate the constant force that would do this work in a distance of eight. Meahso work is force times distance, so we know the work, we know the distance, eight measures. So work divided by distance gives us a constant force of eight nutions. I think they forgot a half there. Power is worked, done. So calculate the power extended in order to change the speed in a time of 3s. So force, so work done over time taken, gives us 31 watts. Okay. So these are the equations that were given in the back of the book. Work change in work done is force times, change in distance, kinetic energy, gravitational potential, energy power is energy transferred per unit time or work done per unit time, efficiency, useful energy output over total energy input, or we can change that to power. So a few multiple choice questions. Jackson first, okay. Do you want to read the question? Okay, the question object of an object of MaaS is moved, the MaaS m is moved from the bottom to to the top of a slope. The vertical height of the slope is y, the horizontal distance between bottom and top of the slope is x. Which of the following gives the gain of gravitational potential energy of the project as it moves from the bottom to the top of the slope? What's the equation for gravitational energy? Mg H. So m is the MaaS, J is gravitational strength, so the H is a height. Y, so I choose be good. Which of the following is a vector quantity? Big momenton good. Okay, a website advertisers. An electric car with the following information, its efficiency is 195 watts. Water hours per kilometer, usable battery capacity is 22 kilowatt hours, battery charging power is 3.6 kilowatts, charging time seven hours, range 129 km. So that's not a very big range. Most journeys are more than 100 km an hour, or 100 km. State y for one mark, the efficiency given on the website cannot be a value of efficiency as defined in physics. What do you think that means? Whether efficiency defined, I don't know. Efficiency give on the website because efficiency in physics is a Percentage Yes. Percentage or no units because it's a ratio. Good. Explain why the kilowatt hour is a unit of energy. How is a kilowatt hour a unit of energy? You know, our unit, its of energy one ecule is a unit of energy kilowatts, our unity of energy. You advantage. W equal Yeah W equal to W P equal to W over t so W is equal to P T if the U the kw is the is a unit of power. So H is the unit of H. So k kw H is a unit of energy. Yeah good. Exactly. Calculate the efficiency of the battery, the efficiency of the battery using this information. A battery changing power 3.6 kilo. Changing time, seven hours charging, power charging, you see, you have to charge have you has your family an electric car or a petrol car? No, no, Yeah. The use petrol car, l car. So these electric cars are becoming very popular. So you have to charge your battery for seven hours. So you can do that overnight maybe. Okay. Use for battery capacity is 22 kio watts hour, so efficiency of the battery. Well, the efficiency 19 five, sorry, that is 195. I was divided by time. Cash tery charging power 3.6 kilowatts over time. So. So we put is divided by 3.6 kilowatts times seven ours. Gives us. 3.6 what that is three point 3.6 times Yeah kilowatts kilowatts. So time so we get this power input, but Yeah, the power times time gives us the amount of time to charge it. So. Our times, time is energy, and this is energy. This is energy input. So 3.6 times seven is 25.2. So we get no point. Eight, seven. Remember, we've just answered that kilowatt hours are energy and power times. Time to input to the battery is the energy we put into the battery. So the otherwise that is 25.2 because it's. Yeah seven hours. Yeah. So the power times the time gives us the energy input. Okay, Yeah. So a comparable petrol car has a petrol consumption of 21 kilkilometers meper liter, so that the electric car is cheaper to run. The cost of one liter of petrol is one pound 20. The cost of one kilowatt hour of electricity is 13p. So I'll just go back to the information we're given. Our electric car can travel 129 km before it needs to be recharged again. This is the energy it can store. So we could work out 129 km cost of a petrol car and 129 km for a journey in our electric car and compare them. Also, thank you. Okay. 21 the cost of is that so of petrol electricity one? So what's the total range? I mean, the distance. So the range of an electric 129, 129, 129 divided by. 21. 6.1. 呃。Yeah 6.1. Times 1.2. 7.4 pounds. So that is still 6.1, but that is times 1.13. 0.03. 0.79 hounds. So it's cheaper. Yeah. So. How did you work out the last bit? 22 kilowatt hours range 129. So if you show that the electric car. One blumiter is 13p. Yeah. Times 12, nine gives me. Three and 60. Yeah. Give one environmental advantage of an electric car. Why is it better for the environment that we all have an electric car? Wait. Less flosion. Can you specify the pollution? The what? Yeah, I think that is environmental pollution. E G C carbon dicode zero two. Hm. Nitrous oxides. So. No lead pollution. A lot of the petrol has a lead compound mixed with it, less carbon dioxide, fewer greenhouse gases, no pollution gases. Okay. The website provides the following additional information. The maximum engine power is 80 kilowatts. The maximum performance from zero to 28m per second in eleven point a half seconds, the MaaS of the car is 15 hundred kilograms. To duce whether the power of the engine is capable of producing this performance. So it's asking you to say whether it's is is they advertise it as to be. The power of engine producing this performance. Maximum engine power is 80 kilo. What what ts and maximum performance. Maximum performance. So the power, we can use the equation, power equal to the work down, divided by time, and the worked equation of work down is a half mv square. Oh. Point five times 15 hundred times 28 squared divided by 11.5. Sorry gofive. 51 kilowatts. So the power required is 51 kilowatts less than the engine power. So it does have enough power. Doesn't have enough power. It does. It does 51 kilowatts is capable of producing this performance. It's capable of producing this performance. It can go from north to 28m per second in this time. So it can. It can so this so we want this value doesn't doesn't exceed 80 kilowatts yes, if it was, Yeah. Okay. Which of the quantities is a base unit and a derived unit? So which of these is correct? Remember, we have our six space quantities, every other quantity and in physics is a derived quantity. Derived quantity in I based okay, basically derived units. A derived one comes from these, remember is a coulub, a base unit. No, it isn't is an apera base unit? Yes, that is a busy unit. Yes. So those are the wrong way around. So it's not a. What I choose to do. A car of MaaS 15, zero zero zero kilograms is traveling at a speed of 25m per second. The driver replies the brakes and the car comes to rest. Which of the following gives the decrease in kinetic energy in joules as the car is brought to rest? Is decreasing kinetic energy enduces 20 51.5 so. Not 25 times, 25 squared times, 1.5 times ten to the three. 1.5 to 1000 no. This one. A rope is used to apply a force to a box. The box has pulled a distance d along a horizontal surface. Which the following would you be used to determine the work done on the box? So when you have an angle, you have to take that into consideration. The force is working at an angle to the horizontal. Yeah. What? Down all the books? So walk down, walk down. That is. Distance, so cosign. Afcosin sitchemisty. This. Okay, a motor is used to lift an object. As shown, the object is raised through a vertical height of 75 cm at a constant speed of point 4m per second. Which of the following gives the rate of increase of potential energy of the object in watts? Okay, so this was not so that's so and height and this one not one, four. The potential energy. But it's the rate of in what's so it's a power. So the work done is gravitational potential energy, but it's a power. So power. Times, time. So the work done. Is lifting this MaaS through a height of 0.75m. At a constant speed. Remember this useful equation. Fucoute. So we know v. And we can work out the force using the information. So which of these is power equals force times velocity? So if that p equal to F V F equal to 0.25 kilograms times 9.881, Yeah newtrons per kilogram. So that is f and v is 0.4. So Yeah, that is this one. Good. Okay. So it's always worth remembering you have this equation you can use. This one, a power station, provides electrical power at a mean rate of 3500 megawatts, which the following gives the best estimate of the energy provided to consumers over a period of a year. If one year has this number of seconds. So that is capital m. So maybe that is ten to the six. So 8.5 times ten 29. Divided by. 7.2 times ten to the seven. Read the question again, Jackson. Over a period of air. So you're given the power, you're given the time. You want to time the out? Yeah. No, okay. This one. Correct. Okay. So as I said, this topic can be intertwined with mechanics, with electricity. So here we have an electric motor pulling a truck up pper slope at constant speed. The electric motor circuit includes a battery with no internal resistance, an ammeter, a volmeasure ter, a very high resistance digital volt meter now. When you think of the electrons, they don't what they need to go through. The Mothey don't want to be diverted this way if it's an easier route. Ot, so voltmeters usually have a high resistance to make most of the electrons flow through the motor that's doing the work. Okay? The truck moves through the vertical height of 0.2m in 15s. The current in the motor is 8.1 milliamps, and the potential difference across the motor is twelve volts. The MaaS of the truck is 550 grams. Calculate the efficiency of the motor. Efficiency motor motor efficiency. Okay, efficiency. So in this circuit, the current motor of 8.1Milap and the across the motor is twelve volts. So the power, the power equal to U T ui, sorry, ui, so 8.1 times. Times ten to the minus three. And then times twelve. Not one. Yeah no note point note 972Yeah so. And then it's a motor. The motor is vertical, not point 2m in 50 minute, 50s. Defense and the. So p equal to呃pay equal equal to W W over t。So walk down per unit time, walk down is a half a noa half mv square, but we don't know the velocity. So. Walk down, walk down is. No point two. 嗯。Work down, but maybe this work down equal to the gravitational potential energy. So that is zero 0.2 times zero 0.55. So the useful work done is mgh equals. Point 55 times 9.81. Times point two. Here, if we do hour times time down here, we can get the useful output energy. You're on the right lines. Good. Keep going. So that's equal to 1.07 91 joules. So that's the output energy useful outpush work. So if we do power times, time here, we get the use the work done. So the input work by the motor. So if we multiply this by 15s. We're comparing work input and work output. So we get zero. Point zero 972 times 15 is 1.458. 1.458 jwels. Okay, so the inpush. The output. So the efficiency will be. Is useful outpush. Divided by input 1.458. So that's. 1.2. 791 diviiby 1.458. 0.74. So our motor is 74% efficient. Do you understand? Yeah. So if youcarried on and worked, found the input work, done the useful work output by dragging the truck up the slope and then find the efficiency. The digital voltmeter is replaced by an analog voltmeter. Now an analog voltmeter is an old fashioned one with a pointer, which has a lower resistance to duce. How this will affect the efficiency of the motor circuit. Autommeter was not with much less resistance. Much less resistance. Well. So we're lowering the voltage. I think maybe that will Yeah that will increase the that will increase the pd and then decrease the current, then decrease the whole power and will infect the efficiency. I'll just go back. Look. So. So this folmeter is what we're talking about. So the resistance has been decreased. So if you think of it with two resistors in parallel, so this means the overall total resistance will decrease. So the current we would expect to increase. When you put resistors in parallel, the total resistance decreases, so the current will increase. What have we type two this? So a. Lower resistance lowers total resistance, so increases the current and affect the efficiency. You have to say how the efficiency is affected, okay? If you think of it, lower R of the lower total R, so increases the current and affeffso. I need to explain it. So if that if there is more current, if there more current and there's more power. More current flowing through the voltmeter and this small power. So this will decrease the efficiency and we can and we can get a less and we may get a less percentage. Yeah. So less efficient. If you think of it, you have a 5050 chance of being right if you're not sure. But essentially what's happening is more of the electrons can wander through this if it has a lower resistance, meaning there's less power delivered to your motor, making it less efficient. So that's the argument they're looking for. Current, greater current in the vote measure, energy power dissipated in the vote measure, power output from the battery increases, efficiency of motor decreases. Make sure you're answering the question. And then the last bit of this question was related to momentum. Remember momentum? Moments momare Yeah. Remember that. So velocity of truck b after the collision conversation of energy good. So momentum so they have the same momentum before collision and after collision. So momentum equal to the velocity times. An mv mv here mv equto momentum so so point 55. Times 5.4 equal to 3.0 point 35 times 2.1. Well, that's. 2.97. Kilograms meters per second plus. Zero before equals. 0.55. Times 2.1. After the collision. Plus we have to find the velocity of the truck b 0.35. Times vb. So we have enough information to solve that. Yeah. Yeah. So. We. No point 35 times vp but we are before collision that it is stationary Yeah so this is before. Okay. So 2.97 is equal to that times that plus that times that. So. Point 55 times 2.1. Which is 1.155. No point 35. Times Feb. So 2.97. Minus this. So that means 1.815. Is equal to 0.35. Times Phoebe. So vp is 1.815 divided by the MaaS, which is because it's a smaller MaaS. It has a bigger velocity, 5.18m per second. 5.18, 5.2. Okay, Jackson, how do you feel about that topic? Well, I think maybe I need to practice more explanation for why or how about that? Yes. So right, when are you back to school about Oh, I forget. Yeah tomorrow is the first January, so the fifth January. Okay, right Jackson? So enjoy tomorrow celebrating our calendar year. I don't know if you celebrate that with your family. It's definitely a holiday tomorrow. Okay, that well that is not Chinese New year. So with celebrties, is that in February? March? Yeah, February in February. Okay, okay, okay Jackson, I'll say goodbye then. Okay promise, miss.