Distance to Stop a Point Charge

by Patrick Ford
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Hey, guys, Hopefully we're gonna take a look at this one on your own, maybe try it out. But this is gonna be a little bit different than the problems that we've seen before. We've got a 5 g three Mike Racoon charge. It has some initial speed and it's moving away from some negative charge. And then basically, we're supposed to figure out how far can this thing travel before it stops? So I want to figure out just sort of like, what's going on here? So let's go ahead and draw a quick diagram. Now, I've got this negative five micro Coolum charge and then I got another three Coolum or three. Michael, um, charge. I know the mass of this charges 5 g, and I know the initial speed of this is equal to 20 m per second. So what ends up happening is that as this positive charge is moving away from this negative charge, the force on it wants to pull it back towards the negative charge because thes two things are opposite charges. Opposites attract. Right now, I know what the initial distance is between these two objects so that our initial is equal to let's see what that's what is that? Five centimeters. That's five centimeters. So what ends up happening is that as this thing is flying out with some velocity, the force is eventually going to bring it to a stop at some later distance over here. Now, I know at this point be while it stops, the final velocity is going to be zero. And basically what I need to figure out is what is the horizontal distance or just horizontal? I'm guessing. What is this distance here? That it can travel before it actually stops at this point. So if I can kind of think about this, this will be the final distance R f So that means that this X distance, if I could write it as an equation, is basically just going to be. I've got X is equal to our final minus our initial. And so this really is my target variable. How far can it travel before stopping? I know what the initial distance is Now. I just need to figure out what the final distance is. So in all this cases, I've got this final distance initial distance. I've got speeds, masses, and I'm also talking about energy. So what I need to use is I actually need to use energy conservation in order to solve this problem. So what I'm gonna do is look at all of my energies in the before and after case. So we know that our energy conservation formula is the initial kinetic energy, any potential and any initial potential energy which we know is gonna be electric potential energy. Now, there's no work that's done by non conservative forces. We know that already and then that's getting equal to the final kinetic energy, plus the final electrical potential energy. Okay, so we've got the work done by non conservative forces is zero. The electric force is conservative, and we know that when this thing finally stops, is there anything we can cancel out? Well, let's see. Um, we've got an initial initial kinetic energy because we know that object discharge is moving, and we also have an electrical potential energy because we have two charges and they're separated by some distance. So there's always potential energy. Now what happens is when this thing stops at this moment, that's right out here. We know that the kinetic energy is equal to zero, but there still is some final potential energy. Okay, so basically, we can go ahead and expand out all of these terms. I know that this initial kinetic energy is gonna be one half MV not squared. Now, what happens is I've got to do the, uh, the initial Connecticut or sorry, the initial electrical potential energy, which is K Q one q two divided by our initial. And then that's gonna equal the final electric potential Energy K Q. One Q two over our final. So, in other words, I'm actually looking for this our final because then I can take this our final and plug it back into this formula and figure out what this X distance is that it travels before stopping. So that's basically the game. I'm gonna try to try to figure out what this our final is. But what happens is I can't go around and like start manipulating this by flipping these fractions and flipping, flipping these formulas because this is like, uh, this is in addition and I got a formula. That's the fraction in here. It's gonna get really, really ugly. Fortunately, what I can do, though, is I know what the masses. I know what the initial velocity is. I know what all of these constants are and including the distance. So rather than trying to algebraic Lee manipulated, just start plugging in numbers for this stuff, just reduce it down to, like, a simple number and then worry about the algebra later. So, basically, I'm just gonna plug in this really long mess right here. We've got 5 g, so that's gonna be 50.5 Now I've got the initial velocity is 20 and they were to square that Now you've got plus and we've got 8.99 times 10 to the ninth. Now, the two charges that are involved, we've got a three micro cool OEMs. So that's gonna be three times 10 to the minus six and a Let's see, negative five times. 10 to the minus six. And now you've got the distance, which is 60.0. Uh, that's 0.5 That's in centimeters. Right? So that's the 0.5 m, and then we've got these formulas right here. We know what these charges are. Okay, so basically, if you plug all of this stuff in that should equal what k Q one Q two over our final is. And basically, if you plug all of this stuff in really carefully into your calculator, you're just gonna get one big number or doesn't have to necessarily be big. But this is actually gonna be negative 1.7 jewels and that's gonna equal K Q one q two divided by our final. So now what we can dio is now we can actually manipulate with this. Our final is and basically it's just gonna happen. Is this our final goes up to the top, This negative 1.7 comes down to the bottom, and then we can just go ahead and plug everything and again. So that's why it's gonna be easier to do that than actually work through all the algebra in that big step over there. Okay, so you've got the final distance is gonna be 8. times 10 to the ninth. Now I've got the two charges which are, Let's see of God's three times 10 to the minus six negative five times 10 to the minus six. By the way, there's some shortcuts that you could take and manipulating some of this algebra, but, um, yeah, so we've got this right here, and then we've got this negative 1.7, okay? And now, if you plug all of this stuff in, you should actually get 0.793 But remember, this is gonna be in meters, so this actually represents is this actually represents 7. centimeters. So this either one of these expressions, if you got this, if you got this, would be correct. But basically, just this is just a different way of expressing this. Um, But what we can do is we can stick this number. I'm just gonna go ahead and stick with centimeters because we're dealing with centimeters and then go back and plug that into this formula over here. So now what? My ex distance is what? My real target variable. How far can this thing traveled before it stops is gonna be 7. centimeters minus the initial distance of five centimeters. So that just means that this thing travels to 0.93 centimeters before stopping. So this right here is actually our final final final answer that 2.93 centimeters Okay, Let me know if you guys have any questions. This energy conservation stuff can actually become really useful in solving some problems. Sometimes you'll have to do it, so make sure you're comfortable with this. Go ahead, Watch the video again. If you didn't understand everything, drop me a link or a comment or a question, anything like that, and I'll see you guys later.