This first equation, what is this equation used for? Which one? First one? A hooks through the spring constant force and extension excellent, the second equation ep is a half fx, which is equal elastic possenergy very good number three sigma. His four server area Yes No No. Good. And epsilon curly e stray. And number five, modulus Young, modulus good. And then we have the fluids equations. So fd, what does fd stand for? When we have a boll or a marbled falling through a viscous liquid, what type of force is produced? This Yeah a drag force, a resistor force, yes, a draank force, like the resistance of the fluid. So six pi ewhat does eto stand for. Viscoste good what does little R stand for? Radius good. And then this this equation. Is that the volume of subsphere? Volume of sphere capital v times density times g. Is equal to the weight, which is equal to the thrust. The upthrust is equal to the weight of the water displaced, which is equivalent to the volume times the density times g. If you think of volume times density, we know MaaS is density times volume. Volume times density is MaaS. So MaaS times g is weight, which is the acting in the opposite direction to upthrust. If you have a ball bearing falling through a fluid. The weight acts downwards, the upthrust acts upwards, and the drag force also acts upwards. So that's the drag force on a ball falling through a fluid. This is the uttruforce, and this is the weight. So those two forces, if our object is falling at a constant speed, fd plus U should equal to W. Okay. What about this one, number eight? Audifair good, and this one. Can be used to find the terminal velocity of our sphere. So when it's moving, so it speed up initially, then itmove at a terminal velocity. And that's the equivalent to the volume times the density of the steel minus the density of the glycerol over the viscosity equation. And then. Nine and then ten density. Okay. So let's look at these questions and remember, we can refer to these equations because you're given them in the back of your. So to drag force f on a sphere of radius are moving through a bscous liquid eta at the speed fee is given by this equation, show that Pascal seconds is the unit for viscosity. So they've rearranged the equation for us. Eta viscosity is equal to force over six pi rv. So you do the rest, prove that these are the units for eta viscosity. Visguste so the units of visguste are. Our scseconds we have to prove those seconds. Oh Yeah so the F R and v. So six pi can be ignored. So we can ignore these because divide and because that is f divided by R and V. V is the velocity and is that I think I think ophilosopy meters per second and times R is the radius, and that is meters and and that is meter square for a second. So that is Pascal second. Now watch it by force. Newons newtons divided by area is the, is the pressure and the pressure, and the pressure is unit is Pascal, that's go. Excellent. Good, very good. The formula for stokelaw applies to laminar flow only. The ball in the thicker below is moving downwards through a fluid exhibiting laminar flow. Add streamlines to indicate the motion of the fluid relative to the ball. So let's break this down. What does laminar mean? Jackson, I don't know. That means this. I didn't hear that means this a favor. I still don't understand laminar. No, very thin. Yeah in layers. So if our ball is moving through a fluid. And if we know there's a drag frictional force, so if the ball is moving in this direction, the fluid will act to oppose that motion. So and laminar means in layers, I think that's what you were trying to say. So laminar means in layers. Layers now will the arrows on these lines, these blue lines, be down or up? Will the fluid move with the ball or against the ball? Opposing the motion. So will the layers go down or will they go up? Bearing in mind we know that this is a drag force. Because there's three Marks for drawing this diagram. So what do you think? Are the layers going up or are the layers moving down? 5050. Think of a parachute. If we think of a parachute falling through the air. So the air exerts a drag frictional force on the parachute, doesn't it? So the arrows will show the fluid is trying to move in the opposite direction to oppose the ball bearing falling, okay? The force dropout. Is in that arrow. So this represents the drag force exerted by the fluid. If you drop a ball bearing into honey, it will move very slowly, won't it? So this drag force. We St the full. This resists the motion. Of the whole. The fluid. So the ball is trying to move down, the resistive forces act up, okay? The motion of the fluid. Do you have questions about this? No, but I won't. Know about what's the purpose of this question? Okay, it's a motion. Yeah, I say the motion. Okay. Yeah, God is if you think of oil companies, they send oil through pipes long distances. So oil is a fluid. Gas is sent through pipes. Water is sent through pipes. So anything that flows through a tube will have laminar flow. You hope it's not turbulent flow. So laminar. Versus turbulent. So turbulent flow is when the lines start getting very. Confused. So turbulent flow is when your layers start to cross over, so you get turbulent flow. So if you have if you own an oil company and you want the oil to get from the store to the factory, you have to make sure fluids can flow, okay? And again, ability to flow depends on viscosity. Two. Oil tends to be more viscous than water. Okay, let's try and do the next question. The density of cooking oil is measured using the falling ball method. A 1 mm diameter steel ball is dropped down a column of oil, and the time it takes to fall 60 cm is measured. This is repeated five times. It is assumed that the ball quickly achieves terminal velocity. The times recorded were this plus this five times. Determine the average term minal velocity of the ball in meters per second meters per second as a terminal velocity. Terminal average terminal. So what's the first think this one, 10.3, 10.3 plus 10.22, plus 10.25, plus 10.38, plus 10.36, and then divided by five. 1010, 10.3, Oh God, so 10.3 and then 60, 60 cm, that is not 26m. And then divided by this answer, and then then the answer is not point 28, not 58. Another. Yeah but Yeah so terminal velocity is not point zero 58. Units for velocity. Meters per second, meters per second. It's very important in physics to push units. Jackson, Yeah, I know. I but always Yeah, but I always forget is when I says question, son, not in writing. Remember writing in Yeah, I always remember writing. It helps you to keep track of what your numbers are as well. Okay. And there's the point is you can lose Marks if you don't put units sometimes. I know in most exams they have the units for you. Sometimes they don't, and it stops you getting lost in your calculating. Okay, draw a free, a labeled free body force diagram to show all the forces acting on the ball ll, which is when it is falling with a terminal velocity. What will these forces be? The force. The formula. And so we only know about the force. Well, first of all, we know it's falling. So what force causes everything to fall? What forces acting on you to keep you stuck to the earth? So okay, there are two there are two questions. Okay? Yeah, so you know that is which I see. And that's not all. So where it's falling slowly through the oil, cooking oil. So what force or forces will act to oppose the weight, otherwise it would just accelerate. We know it travels with a terminal velocity. So it means there's balced forces. So if that is if there balance of force, maybe there's another force in the opposite direction. Yeah Ruof the. But that's still not balanced. Okay, washes the utter force air resistors. Yeah. So drag force. The drag due to the fluid resistance and that's upthrust. So that plus that should equal that. So it tends to be drawn like that. This plus this should equal that to show terminal velocity. So the ball is having its equivalent wadisplaced, giving an upward force upthrust. And then we have a drag force due to the viscosity of the oil. The viscosity of oil can be found using the formula eta is to the density of the ball minus the density of the oil times g, times R squared over nine v. Determine the viscosity of the oil. If we know the density of the ball, the density of the oil and we know. The diameter of the steel ball. So do you want to write this? Do you have paper pen, or do you want to just plug all your values into a calculator? So I have the pen. So the row be the density of the bothe density of the oil anyway, know that. And v is terminal velocity and R is the radius. So we've already, I think we've worked out the terminal velocity. Yeah, Yeah, not one, zero, five, eight. Yeah. So we know that whoops, diameter is 1 mm. So equal, could you one times ten to the minus three? No, no, no. Note point five. Meters and so the Yeah that the radius so viscosity. Beta equal to. Two times no no not. Maybe I should change the equation because then it grams per centimeter be. So we should change it to the meter. Meter cube. Yes. So we get. Two times. 785 north. Kilograms per Meare cute. Minus. 9:20. Times 9.81. Times. 0.5 by ten to the minus. Minus three squamiss one that is 7850 and that is 920. So density is. Yeah density, but that is centimeter cube. That is centimeter cube. Okay, so times ten choose a six. Equals 7.8. I tend I converted to the kilograms to ten to the three over. One I ten. Minus two cubed. Right let's work that out 7.85. Minus two. If you work this out, Jackson, I've converted the grams to kilograms by saying 7.85 by ten to the minus three and then 1 cm, you grams. Yeah. So I've converted. So that becomes seven, eight, five, zero. Kilograms. Her Meare cute. If you work this out, okay. And the same with this 0.92, I tend to the minus three. Over one by ten to the minus two cute. So that gives us 920 920. So is space. So my equation is over nine v so all of this divided by nine times are terminal velocity 0.058. So if you work all of this out. 785 north -920 equals times two equals times 9.81. Times point five x minus three. Squared. Divided by nine times point zero eight. 58. So when you do that, you get 0.065 pascalals. Seconds. Okay, Yeah. So we've converted that to kilograms per meter cubed. We've converted that 2m per second. We've converted diameter to radius. Okay. So we've revised what we mean by laminar flow in layers. We know that the drag force resists the flow of the object through it. And remember, these equations only apply stoke slot only applies when we have laminar flow. When the flow is going through fluid that can travel in layers. Okay, let's try this one hook law. So we have all these equations which we can use. Ich folks kslow? F equal to K X. If you write a word equation, you'll get the Marks. If you write symbols, you won't get the Marks in a level Jackson, so f equals kx. Let's write that as a word equation. Force equal to spring constant times extension. The word equation. This is up to a point. Can you see there's two Marks here, Jackson? So this is one mark. What happens when you keep adding forces to this spring? Do you still get an extension is proportional to the force? We need to add one more point here. As long as what happens at this point. The limit of proportion. Good, so as long as the elastic limits is not okay, so the force is proportional to the extension, as long as the elastic limit is not exceeded. That's where you get your two Marks. The graph shows the behavior of a spring under increasing loads. Determine the load and extension when the spring reaches its limit of proportionality. At what load will the spring reach its limit of proportionality? So you use the graph to find a load. What would you say? Load extension, the sprbrushes its limit of proportionality. Limit of proportionality is the beginning of the curve. But the beginning of curve Yeah, maybe I find that. 28 mm. Seven newtons. Determine the force constant of the spring. Constant of the spring. So the constant of spring, f equal to K X, so k equal to f divided by X R. Okay, it gives me the equation. So seven divided by 20. No, seven divided by 28 times ten to the minus three, 250. What are the units for your spring constant? The spring constant Newton per meter. It's a shame when you've done the hardware, not ticket. So units are important. Determine the elastic potential energy stored in the spring when it is extended by 20 mm. Well, the elastic potential energy equal to a half F X, so if x equal to two, 28 times ten to the minus three. Read the question again carefully, Jackson. It's not 28. When the spring extends, 20 is 20 mm, so it's two times ten to the minus two. And what is the force? The force. Well, the force is the. Five good times I have yes 0.05 chows good. The graph shows the behavior of a ductile material under increasing tensile force. The material deforms plastically for extensions above 20 millihow. Much work is done in increasing the extension from 20 to 100 mm. So let's look at this question. What do we mean by ductile. Soft. Soft I think ductiequal to soft. Yes, can. Oops. The drone. Into a, so it can be drawn out. You know, when you heat last, you can draw it out into a long wire. So ductile in physics does mean soft, but it means can be drawn into a wire. So you would say copper is a ductile material. Okay ducle. So the copper wire will get longer up to a point, and then itextend massively, and then itbreak, okay, material deforms plastically. Do you remember the difference between elastic and plastic? A difference. Yeah a difference. So. A spring is elastic up to a point because when you release the force, it goes back to its original shape. Yeah I give a force to elastic and it all goes back to the original. But the plastic didn't take Yeah plastic state minutes d forward. If force is removed. So an elastic material is like rubber, but if you keep stretching rubber, it will eventually become plastic. It won't be able to extend anymore itstay permanently deformed. Okay, so this is a ductile material. The material deforms plastically after 20 mm extension. How much work is done in increasing the extension from 20 to 100 mm? Need you 100. How much work is done? Well, the equation of work done is that fs. First times distance. So if distance same as extension, that is 18 mm, that is eight times or not point zero eight. And. 24 to 30 to 28 four newtons, not 25 times. Yeah, not point five times four newtons times note eight 0.04 times four 0.16 just use. It's actually Yeah, not a half. So you were right sh it's 26. Times. 8 mm. So that gives me. Two, one choose. Yeah 2.08, 2.1 juice while extending from 20 mm to 100 mm. Very little of the work then goes to additional stored elastic potential energy. What happens to the remaining energy? What tends to happen to energy that seems to disappear? It tends to be the energy tends to be transferred to a different form. Some of it goes to permanently changing the atoms in your ductile material. There are. Some misconversion two. Very. What is the main way that energy is wasted in a system? Given that for the weight. So work is done on your wire in stretching it. And then some of the energy, the work is done to permanently deform the wire, and some of the other energy is converted to a wasted form of energy, which is given out to the surroundings. What does that type of energy usually occur as? What is that energy? Most machines are only about 30% efficient. Some of the rest of the energy is wasted as. Yes. And the reason why very little of the work done goes to additional story elastic potential energy is that some energy is waste. As what type of energy which isn't very useful thermal energy? Yeah where is it? Stanparmal energy? Good. Okay, Young modulus. We're doing well today, so we have stress, strain, Young modulus. So define tensile stress and explain why its units are the same as those of pressure. Measure the truth. Remember, you have the equations. What is the equation for stress? Well, suggest equal to the. So just equal to the extension extension stress divided by initial stress. No, that's the strain. This is stress force divided by area. Good. Explain why its units are the same as those of pressure. So we've done an equation like this. So that's force. So the units for force are nutions and the units of area are measures to the meter squared squared. So and the equation of pressure is force divided by area, same as Yeah, same as Pasca. So so same as pressure near. Define tensiles strain and explain why strain does not have units, have any units. So stress is force over area. Strain is change in length over length. The tense strings are a strstring equal to a the ded, the extended strength divided by initial strength. Length length length length Yeah length Yeah okay so the string is the ratio between the length so Yeah same equsame units same so Yeah there they have the same units so it's it's a ratio so it has it does not have have any units good they cancel they cancel each out so a ratio. Hence, explain why Young modulus has the same units as stress. So the Young modulus. Four more minutes, Jackson. We're doing very well today. What's the Young noutilus? Yes, mosolus is stress divided by the drawing? So equal could choose a pascar divided by no units, because string has no units. Yeah, that is one. So this Pascal, this Pascal, so the same as stress. Yeah. So the Young modulus of copper is 120 giga pascals. A 3m length of copper wire of this diameter is subject to a tensile force of ten usions. Determine the tensile stress in the wire. So we know the force. We know the diameter, we don't know the area. So we have to work out. For silver area. Diameter, so no point 25. I tend to the minus three. Squared. Times pi. So force over area, so pi times no. Latwo five x minus three squared. So ten not come one, so let copate that. Let me use e and G5 point one times ten to the seven yes, your favorite one. Good. Determine the resultant extension of the wire. We have one minute to do this. So. Seconds. So the copper and and that's the result of extension on. And so forth. So we know the stress 51 or 5.1 by ten to the seven. We know the length times three. Over the Young modulus so 120 gigaso 120 by ten to the. Nine, 120 giga pascals. What do we get? 1.2, 1.3, 1.3 times ten to the minus three. -3m, 1.3 mm. Good work today, Jackson. We did very well today. We're getting a good handle on all these equations. Okay, enjoy the rest of your day. We're meeting at 1130 tomorrow, aren't we? 1130? Okay, maybe. Yeah. Okay. Bye bye, promise, miss.