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A proton and an alpha particle are released from rest when they are 0.225 nm apart. The alpha particle (a helium nucleus) has essentially four times the mass and two times the charge of a proton. Find the maximum speed and maximum acceleration of each of these particles. When do these maxima occur, just following the release of the particles or after a very long time?

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Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 18

Electric Potential and Capacitanc

Kinetic Energy

Potential Energy

Energy Conservation

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Capacitance and Dielectrics

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Hope College

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So it's his question. We have two different particles. One is the O. R. For particle or it certainly is a helium atom. And went is proton. So the brought home has a charge of positive E, and it has an US the other particle, which is the hero. Nicolas has four times and mess and two times the church released from rest present. This started traveling in the opposite directions we wanted has a maximum speed in that small consideration for each of these, and we want to know where he's actually that is occur, so the easiest seem to find first is a maximum acceleration. Why? Because where a sister Parker's office released, they would have a force on each other, and it's this repulsive. Wasn't Makesem starting move? But this force equals cake. You want U to over her, our square. His force decreases the further apart from each other, So this force is the largest. When's the closest beating at the very beginning. So so they were also a cheap sir, maximum acceleration from this force because a rose ever equal over him. Keiko acuity over M R script. So because of force's largest and do it just wears what just released. Their exploration will be largest where they're just released. So the acceleration of the ARV a particle is on Carrie. Times is to Ko hee Square because it's e times two e over four times in our square where M is the mass of a single proton. So, uh, this's just to yeah, it's exactly so is to your times. It's a mass is one point 67 times sausages, actually, seven need a kilogram times our is 0.225 times 10 to the negative. My need. Er's on DH. So it is square. And so you were. Reader is eight types tent. Who's a nice future readers. Grouper, Coolum Square Time's on 1.6 times 10 to the negative 19 Colin can score, okay, And the acceleration is 1.36 times tend his 18 meter per second squared. So the acceleration for proton is again is to Katie. Scorer is also e times two e. But now we have a normal in bar screwed. So, uh, what's the new reader is the same as went absent to 90. Oh, don't forget to add the units T square of times too over. I'll put 67 times 10 to the objective to several terms. That opens 67 10 to 2 to 5 times 10 tz Let us fly squid. Okay, so this and a B five point for point for four times chanteuse e 18 beater person A square. So is this because he is four times larger on there's a previous one is that actually satisfies the conservation of momentum? Yeah. So it's a consideration for momentum We will see is yeah, what we get for funnies the speed like we already seared from suck celebration Because six moment, her has to add up to zero because it was initiated. West speed off. So am particle most before taps larger says this bead off some foreign particles because in times the of protocol a CE for M times V. Those are for particle. Is Cyril uh, so serious that another seaweed you too. We can this really rigid. I will actually changes to buy this because I know there will be obstetricians, so I don't want to do with this money aside. So we have the r equals on a force of reporter. Okay, so the next thing we need to do is we need to consider the conservation of energy because they're going away because serves under zit reporter Shin due to the electric field energy. So the electric potential energy is u equals. Okay, cute. You prime over our or in other words, is too k e square over our This's the initial energy and autopsies are changed into kinetic energy is a kinetic energy is well half off at the square but so envious. And for the proton is just em Times the pro tem square and there were have energy for other particle is full and times BP will see that the our father is one force of peopie Sophie are for Oscar. Chris, this also squared. So, um, Axis, if we simplified little bit, is where half plus two times 11 16. So it's one ace. Is this much okay for a vessel? From this, we will be able to fight the proton because we can re arrange it so that the home be brutal equals five 16. Okay, East Square over in, huh? Okay. And scratch it. So this is VP and we can't find it. I have a 60 times two twos externally. One my time's too less times 1.6 times too seductive, like too square over, uh, five times and is one point 67 times 10 to the 27 times are is zero point 2 to 5 times turned his back, too. What? Okay, No, just stare. Assis really quick to make sure it is. It's cracked. Whoa since. Okay, I think it looks good to me. Um, so I will keep calculated, and this turns out to be 4.43 times 10 to the force meters. A second isn't from here. We know that our father is went force of BP. So is one force times for when force three times changes. Of course, Leader per second. It's just one when we're one times 10 to Z force meter per second. Okay, so now we have also seized for Jennifer, So maximum speed was a maximum acceleration. We've already fudged hearsay. Occur right immediately. Uh, just follow. The released is a maximal speed Is here is this actually will happen after a very long time, actually, infinitely long time. Because why? Because the total energy is the energy is a kinetic attitude, plus potential entry and if we wanted to be reaches a maximum speed. We want off the energy to be kinetic energy. So we want the potential energy to zero because the protection energy has this form. So the potential energy is only zero where art is an infinity. So we need to be, if infinitely far away from each other, for them to have the highest speed.

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