Finding force - Newton's second law (Solved example)

- [Instructor] Let's solve two problems on Newton's Second Law. Here's the first one. A heavy couch of 60 kilogram was accelerated from rest to 20 meters per second in five seconds on a frictionless surface. Find the force acting on it. Okay, let's see what we're dealing with. We have a couch which is accelerated from rest. That means initially that couch was at rest. Let's say this is our couch which is at rest and it's accelerated to 20 meters per second in five seconds. So a little bit later, the couch is in motion. So let's say it's accelerated to the right. And a little bit later, that is five seconds later, it is found that it's moving 20 meters per second, let's say to the right, on a frictionless surface. So let's imagine it's on some kind of an ice or something. So there is no friction over here. And we are asked to calculate the force acting on it. Why should there be a force? Well, because we are speeding up this couch, it's going from rest to motion and to do that, somebody must push on it, right? And so somebody should be pushing on it to the right. I'm pretty sure you can visualize this, right? And that's what we need to calculate. We need to calculate with what force someone is pushing this couch. All right. So let's talk about what's given to us. What is given? It's given that initially the coach was at rest. And so its initial velocity is zero and usually we choose u as a letter for initial velocity. So u is zero. We also know after five seconds, it has a final velocity of 20 meters per second. So time is also given to us. Time is five seconds. What else are we given? Well, we are given the mass of that couch. So m is 60 kilograms and we need to calculate what the forces. Okay. So what do we do? How do we calculate the force? Well, the important thing to notice is we are asked to calculate the force and we are given the details of motion, which means we need to connect force and motion. Which equation connects force and motion? Well, Newton's Second law. The famous equation F equals ma is a connection between force and motion, right? So let's go ahead and use that equation. Let's see if we can use it. So what is net force? Net force means the total force acting on our object. Since there's only one force acting on that object, that is F that itself is our net force. So that itself is what we need to calculate. Okay? M is given to us. Okay. That's good news. A, oh, that's not given to us. A is acceleration. That's not you into it. So how do we calculate the force? Well, acceleration is not directly given but we are given the initial velocity. We're given the final velocity and we're also given the time. So using this, maybe we can calculate what the acceleration is. And once we do that, we can plug in over here and we can calculate what the net force is. So the first thing we need to do is calculate the acceleration. How do we do that? Well, acceleration is a rate at which velocity is changing. Change in velocity divided by time. So it is v minus u, that is a change in velocity divided by time. And since everything is given to us, we can first calculate the acceleration and then we can plug in and then we'll calculate what the net force is. So you wanna give it a try first? Go ahead, give it a shot, pause the video and see if you can first try this all by yourself. Okay, let's do this. So acceleration, a, is gonna be the v, that is 20 meters per second minus u, which is zero divided by t, which is five seconds. And so that gives us 20 minus zero is zero. So 20 divided by five is four and the units are meters per second per second. So that is meters per second squared. So that is our acceleration. And now that we have our acceleration, well, we can just plug it in over here and we can calculate the net force. So again, if you didn't try this before, great idea to pause and continue this yourself. Okay, let's do it. So the net force is just F because that's the only force acting. If there are two or more forces acting, then we need to add them or subtract them depending on the directions. But there's only one force acting. We don't have to worry too much about it. There's no friction. That's good. Okay, so F is gonna be equal to m, which is 60 kilograms times the acceleration, which we just calculated, four meters per second squared. And we can now figure out what that force is. We just have to multiply. Six times four is 24 and there's a zero. And the units become kilogram meters per second squared. And that's our answer. And by the way, since this is the SI unit, this is the standard, we have chosen all standard units, the SI unit of force, this is often called newtons. And so we can say the force acting on our couch is 240 newtons. That's the answer. Okay. Let's solve another one. The driver of a jeep cruising at 30 meters per second hits bricks. The jeep comes to a skidding stop in 75 meters. If the mass of the jeep, including the driver is 1,000 kilogram, find the force between the jeep and the ground. Okay. Again, let's draw what's given. We are given that there is a jeep that is cruising at 30 meters per second. So let's say this is our jeep. Let's imagine it's going to the left at 30 meters per second, the driver hits the brakes. And so the jeep comes to a skidding stop in 75 meters. So maybe the jeep goes a little forward and slows down, and then eventually it stops. So finally it stops and comes to a rest. We were given the mass of the jeep and everything. We're asked to calculate the force between the jeep and the ground. So what does that mean? Well, you see, again, over here, the jeep is slowing down and whenever objects are speeding up or slowing down, in other words, accelerating, there must be a force acting on that object, right? So similarly, over here, if it's slowing down, some force must slow down that jeep. Which force do you think that is? Well, you could guess that's the force of friction. That's the force between the ground and the jeep that's pushing and slowing it down. And basically that's what we need to calculate. Now, just another small question before we go ahead. Which direction do you think frictional force is acting? Do you think it's acting in the forward direction? Our backward direction? Think about it, it's slowing down. Well, if friction was acting in the forward direction to the left over here, then that jeep would accelerate. It would go faster, right? When you push something in the direction of motion, it goes faster. But since it's slowing down, that means the friction is pushing that jeep. So the frictional force must be this way. So let's do it that over here. The frictional force must be in this direction. It's actually near the wheels and the ground but I'm just gonna show it over here. It's in this direction. And that's the force that we need to calculate. Again, let's write down what's given. This time, the initial velocity is 30 meters per second. The final velocity, that is zero because it comes to a rest. What else is given. This time time is not given. Instead, they have given us the stopping distance. So the distance traveled by the jeep. So let's say the distance from the back wheel to the back wheel. You can calculate distance from anywhere. Let's do it over here. Anyways, that thing, that distance is 75 meters. So the displacement is given to us as 75 meters. And the mass is given, 1,000 kilograms. And again, and we're asked to calculate this force. So that is a force of friction. That force is what we need to calculate. So again, you can see the problem is we can use F equals ma but a is not given. So the first step is again to calculate what acceleration is and then figure out what the force is. So again, how do you calculate the acceleration this time? Time is not given. This time, the displacement is given. Oh, maybe we can use equations of motion to do that? We have studied three equations of motion. So again, pause the video and see if you can crack this. First, calculate the acceleration and then let's see you can, if you can calculate the force Okay, go ahead. Give it a try. Okay, hopefully you've tried. Since we are given u, v, s, and we need to first calculate the acceleration, the equation that we can use is v square minus use square equals 2as. And this equation is derived in other videos, in previous videos. So if you need more clarity on where this equation comes from and some more practice on that, you can go back and watch that videos. Anyways, over here, if you plug in, v is given as zero, final velocity. U is 30. So that's 30 squared, 30 meters per second squared. And that equals 2a, which we need to calculate, times 75 meters. Now from this, I'm pretty sure you can go ahead and calculate a. You just have to do the algebra. You just have to divide but I'm pretty sure you can do that, right? I'm gonna leave that to you. If you do that, if you do the algebra, then just to save some time, I'm going to tell you directly what that a turns out to be. A turns out to be negative six meters per second squared. And you can check this. You can just pause the video and you can just check that. And the negative sign comes because there's a negative sign over here. And now that we found what acceleration is, you can just go ahead and plug it in in our F equals ma equation. Again, there's only one force acting on our jeep and that's the force of friction. And so if we plug in, we will get F, that's the net force, equals mass, which is 1,000 kilograms times the acceleration, which is -6 meters per second squared. And if you multiply that, 1,000 times six is 6,000. So you get -6,000 kilogram meters per second is squared is newtons. And so that's our answer. So the frictional force, so the force between the jeep and the ground is 6,000 newtons. And what is that minus sign saying? Well, that minus sign is actually telling us that the force is in the opposite direction of motion, but we already knew that. So basically, even if you didn't know this, just by looking at the final answer, looking at that minus sign, we can tell, oh, the force is in the opposite directions. And so in general, if we have problems where force is asked and we're given details of motion, then first we'll calculate what the acceleration is, if it's not mentioned, and then we can plug that in and in our F equals ma formula and calculate the required force.