6. Intro to Forces (Dynamics)

Forces & Kinematics

# Liftoff!

Patrick Ford

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All right, guys, let's check out this next one. Here we have a 1000 kg rocket that is accelerating upwards due to some thrust. So I got this rocket like this. I know the mass is 1000, and I got a couple of forces on it during the 1st 20 seconds of its motion. We know the Weight force or the force of gravity downwards. This is my W is going to equal 10,000. We also have a couple of other forces, like the force of thrust that's basically like an applied force. So what I'm gonna do is I'm gonna call this F T for thrust. I also have a force of air resistance that's acting downwards because this rocket is going to start accelerating. We're going to start moving upwards like this. So what happens is the air resistance I'm gonna call this F air is gonna point downwards. And I know this is 5000. I also know this thrust is 25,000. Alright, So I've got all these forces. There's no normals or frictions or anything like that. What I want to do is figure out the rocket's velocity after 20 seconds we know that the initial velocity is going to be zero because it's gonna start from rest. But then later on, it's gonna have some final velocity. So this final velocity is actually what I'm looking for here. So if I want to figure out the final, I'm gonna have to list out all of my other telematics variables, right? Like my initial velocity I want also want the Delta y. And then I had the acceleration end times I'll need all of these things. So the Delta y I don't know what that is. I know that Vienna zero starts from rest. The acceleration. I don't know either. And I also I know the time is 20 seconds. Right, So this is gonna be my 20 seconds here. So we have here that the two out of five variables, right? We have two out of five, which means we can't actually use an equation to solve for the final Yet we're gonna need another one of our variables, just like we have have done before. When we get stuck, we're gonna try to use this. Uh, we're gonna try to figure out this A by using f equals M a. So we're gonna use f equals m A to figure out acceleration. And we're now we're just going to add all of our forces in the vertical direction, right? All of our forces act only along the y axis. So what happens is this rocket is traveling upwards, so I'm just gonna choose the upwards direction to be positive. And so that means that our f t is positive and we expanded our some F and then our f air is gonna be downward, so it gets a negative, and then our weight forces also gonna be negative as well. So this equals mass times acceleration. Remember, I want to figure out this a here so I can plug it back into this, um, into my kinetics variables and then pick an equation. All right, so now I just replace all the values that I know. This is 25,000, then I've got this F air is 5000, and then I've got minus this 10,000 from the weight, and this equals mass, which is 1000 times acceleration. All right, so if you work, all this out you're gonna get is 10,000, you're gonna get 10,000 over here is equal to 1000 times a So that just means that our acceleration is 10 m per second squared. Alright, so our acceleration is 10, which means we now have enough information to figure out economics equation. Right? So now we have 3 to 5, and now we're gonna go ahead and just pick out one of the arrow equations. So I'm gonna go over here if I want to find out the final velocity. The final velocity is basically going to be the equation that ignores my Delta X right. So I'm gonna I'm gonna ignore my Delta X or my delta y over here, And that's just gonna be equation number one. So I got an equation number one, which is the final equals V initial plus 80. So I don't want the final. This is just gonna be zero plus now I've got an acceleration of 10, and then I got in a time of 20 so this is basically just going to be 200 m per second. All right? So look to your answer choices and it's answer choice A. That's it for this one, guys

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