Video transcript
Newton's First Law tellsus that an object at rest will stay at rest, and objectwith a constant velocity will keep having thatconstant velocity unless it's affected bysome type of net force. Or you actually could say anobject with constant velocity will stay having aconstant velocity unless it's affectedby net force. Because really, thistakes into consideration the situation wherean object is at rest. You could just havea situation where the constant velocity is zero. So Newton's FirstLaw, you're going to have your constant velocity. It could be zero. It's going to stay beingthat constant velocity unless it's affected,unless there's some net force that acts on it. So that leads to thenatural question, how does a net force affectthe constant velocity? Or how does it affect ofthe state of an object? And that's what Newton'sSecond Law gives us. So Newton's SecondLaw of Motion. And this one is maybethe most famous. They're all kind offamous, actually. I won't pick favorites here. But this one gives usthe famous formula force is equal to masstimes acceleration. And acceleration isa vector quantity, and force is a vector quantity. And what it tells us--because we're saying, OK, if you applya force it might change that constant velocity. But how does it changethat constant velocity? Well, let's say I havea brick right here, and it is floating in space. And it's pretty nice for usthat the laws of the universe-- or at least in the classicalsense, before Einstein showed up-- the laws ofthe universe actually dealt with pretty simple mathematics. What it tells us is ifyou apply a net force, let's say, on thisside of the object-- and we talk about net force,because if you apply two forces that cancel out and thathave zero net force, then the object won't changeits constant velocity. But if you have anet force applied to one side of thisobject, then you're going to have a net accelerationgoing in the same direction. So you're going to havea net acceleration going in that same direction. And what Newton'sSecond Law of Motion tells us is that accelerationis proportional to the force applied, or the forceapplied is proportional to that acceleration. And the constantof proportionality, or to figure out what you haveto multiply the acceleration by to get the force, or what youhave to divide the force by to get the acceleration,is called mass. That is an object's mass. And I'll make awhole video on this. You should not confusemass with weight. And I'll make a wholevideo on the difference between mass and weight. Mass is a measure ofhow much stuff there is. Now, that we'llsee in the future. There are other thingsthat we don't normally consider stuff thatdoes start to have mass. But for our classical, or atleast a first year physics course, you couldreally just imagine how much stuff there is. Weight, as we'll seein a future video, is how much that stuffis being pulled down by the force of gravity. So weight is a force. Mass is telling you howmuch stuff there is. And this is really neat thatthis formula is so simple, because maybe we could havelived in a universe where force is equal to mass squaredtimes acceleration times the square root of acceleration,which would've made all of our math muchmore complicated. But it's nice. It's just this constantof proportionality right over here. It's just this nicesimple expression. And just to get our feet weta little bit with computations involving force, mass,and acceleration, let's say that I have a force. And the unit of forceis appropriately called the newton. So let's say I have aforce of 10 newtons. And just to be clear, anewton is the same thing as 10 kilogram metersper second squared. And that's good that a newtonis the same thing as kilogram meters per second squared,because that's exactly what you get on this side of the formula. So let's say I have aforce of 10 newtons, and it is acting on a mass. Let's say that themass is 2 kilograms. And I want to knowthe acceleration. And once again, in this video,these are vector quantities. If I have a positivevalue here, we're going to make the assumptionthat it's going to the right. If I had a negative value, thenit would be going to the left. So implicitly I'mgiving you not only the magnitude of theforce, but I'm also giving you the direction. I'm saying it is to theright, because it is positive. So what would be acceleration? Well we just use f equals ma. You have, on theleft hand side, 10. I could write 10newtons here, or I could write 10 kilogrammeters per second squared. And that is going to beequal to the mass, which is 2 kilograms timesthe acceleration. And then to solvefor the acceleration, you just divide bothsides by 2 kilograms. So let's divide theleft by 2 kilograms. Let me do it this way. Let's divide theright by 2 kilograms. That cancels out. The 10 and the 2, 10divided by 2 is 5. And then you have kilogramscanceling with kilograms. Your left hand side, you get5 meters per second squared. And then that's equalto your acceleration. Now just for fun, what happensif I double that force? Well then I have 20 newtons. Well, I'll actually work it out. Then I have 20 kilogrammeters per second squared is equal to-- I'llhave to color code-- 2 kilograms timesthe acceleration. Divide both sides by 2kilograms, and what do we get? Cancels out. 20 divided by 2 is 10. Kilograms cancel kilograms. And so we have theacceleration, in this situation, is equal to 10 metersper second squared is equal to the acceleration. So when we doubled the force--we went from 10 newtons to 20 newtons-- theacceleration doubled. We went from 5 metersper second squared to 10 meters per second squared. So we see that they aredirectly proportional, and the mass is that howproportional they are. And so you could imagine whathappens if we double the mass. If we double the mass in thissituation with 20 newtons, then we won't be dividingby 2 kilograms anymore. We'll be dividingby 4 kilograms. And so then we'll have 20divided by 4, which would be 5 and would be metersper second squared. So if you make the masslarger, if you double it, then your accelerationwould be half as much. So the larger the massyou have, the more force you need to accelerate it. Or for a given force, the lessthat it will accelerate it, the harder it is to changeits constant velocity.
I'm an enthusiast with a deep understanding of classical mechanics, particularly Newtonian physics. My knowledge extends to the principles of motion, forces, and their mathematical representations. In this context, let's delve into the concepts presented in the provided video transcript.
The video begins by discussing Newton's First Law, which states that an object at rest will stay at rest, and an object with constant velocity will maintain that constant velocity unless acted upon by a net force. This underscores the idea that forces are required to alter the state of motion of an object. The concept of net force is crucial here, as it considers the overall effect of multiple forces acting on an object.
Moving on to Newton's Second Law, it introduces the famous formula: force equals mass times acceleration (F = ma). Here, force and acceleration are vector quantities, and the relationship between them is defined by the object's mass. This law emphasizes that the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass.
The distinction between mass and weight is also highlighted. Mass is a measure of the amount of substance in an object, while weight is the force with which it is pulled by gravity. The formula F = ma simplifies complex scenarios by providing a straightforward relationship between force, mass, and acceleration.
The video concludes with a numerical example illustrating the application of Newton's Second Law. By using the formula F = ma, the video calculates acceleration when a force of 10 newtons is applied to a 2-kilogram mass. It demonstrates that acceleration is directly proportional to force and inversely proportional to mass. Doubling the force results in a proportional doubling of acceleration, while doubling the mass leads to halving the acceleration.
In summary, Newton's laws of motion provide a fundamental framework for understanding the relationship between forces, mass, and motion, offering a concise and powerful tool for analyzing physical phenomena.
