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Car Colliding with Wall

Patrick Ford
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Hey guys, let's take a look at this problem here. So we have a 1200 kg car that's unfortunately gonna collide with a wall. So this is our 1200 kg car like this, it has an initial speed of 20. Unfortunately, it's going to hit a wall and over the course of the collision it actually crumples through a distance displacement. So basically the point of impact like this, it's gonna crumple over a distance delta X. Of one m. What I want to do in part A is I want to figure out how long the collision lasts. So that's a time. So how long the collision lasts is actually going to be a delta T. So I know the distance that that sort of deformed or crumples over, but I want to figure out what is the delta T here. So let's take a look which equation we're going to use. Well so far, we actually only one equation that deals with delta T. And that's the impulse equation. So let's go ahead and write this out. We have J equals F, times delta T, which equals the change in momentum, Mv final minus V initial. So let's take a look at all of our variables. What happens is we don't know the force, we don't know the time, that's actually what we're looking for here and we do have the velocity of the mass, We do have the final velocity initial velocity. So what happens is even if you could figure out the impulse by using this, M times V initial minus the final of the final days of the initial to figure out the impulse, you would still be stuck because you actually still have two unknowns in this problem. You have F and delta T. They're both unknown. So you wouldn't be able to solve for delta T. Using the impulse equation. So, what else can we use? Well, fortunately, what the problem tells us is that we can assume the acceleration during the collision is constant. What that means is we can actually go back and use our old motion or kidney. Matics equations to solve for delta T. Right? So that's really all we're gonna do. We're just gonna go ahead and solve for delta T. By using another set of equations we've seen before. So how do we figure out this delta T here? What we have to write three of us? We have to figure out three out of five variables. So I have my delta X, the initial, the final A and T. So this is what I'm looking for here. It's the whole reason that came over here is try to find delta T. So let's write out all I need is three out of five. I have my delta X. Is one. I have my initial speed is 20. Final speed zero. The A. Actually, I don't know. So I'm just going to use that as my ignored variable and that's perfectly fine. I have 3 to 5 and I can write an equation that deals with that souls for delta T. Now what happens is remember when you have the acceleration as your ignored variable, The equation that you're going to use is actually equation number four. Remember, some professors don't necessarily like you using this equation. I'm going to put an asterisk here. Just make sure your professor does allow you to use this equation. If they don't, you still can solve this Basically. You just have to solve using equation number two what the what the acceleration is. Then you can plug it into either one of equation number one or three to figure out the time. We're just gonna skip that and we're gonna go ahead and use the equation number four here. Sorry, let's do that. So equation number four says this is your delta X equals this is the initial velocity plus final velocity divided by two times the time. Just go ahead and plug plug in my numbers. This is one equals 20 plus two, divided by two. I'm sorry, 20 plus zero divided by two. Since that's and then we have times delta T. So basically I have 11 equals T. And so therefore your delta T is equal to 0.11 2nd. Alright, so that's actually how you figure out delta T. Here. Not by using impulse but actually by going back and using cinematics to solve these kinds of problems. Sometimes you'll have to do that. So now that we figure out delta Z is equal to 0.1 seconds. Now, let's take a look at the second part of our problem. The second part we want to figure out the magnitude of the average force that the wall exerts on the car during the collision. So basically, now if we go back to our impulse equation, we actually know what this delta T. Is the only equation. The early variable looking for now is F. And because we only have one variable now, we can go ahead and solve for this, right? So we only have one unknown variable. So J for part B is going to be F times delta T. And so this is gonna be, let's see delta P equals M. V final minus the initial. Just gonna write that out again. Now we're looking for the average force and we know what delta T. Is. We also know an M. V. Final and V. Initial are basically, I'm just gonna move everything over to the other side or this delta psi over to the other side and my f. Is just an equal. Let's see, I've got the mass, which is 1200 times the final velocity, which is zero. The initial velocity was 20. And then we're gonna divide that by the Delta T, which is 0.1 seconds. If you go ahead and work this out, what you're gonna get is 240,000 newtons. Because we were only looking for the magnitude of the forest, technically actually was supposed to be negative because of this negative sign. Right here, we can just leave it as positive because all we're looking for is the magnitude. So this is really our answer. 240,000 newtons. It's a massive force because it actually a very, very short period of time to stop a heavy car. It's moving at 20 m per second. You need a massive amount of force to do that. Alright guys, so let's look at this one. Let me know if you have any questions.