Two protons are released from rest when they are 0.750 nm apart. (b) What is the maximum acceleration they will achieve and when does this acceleration occur?

Video transcript

Hey everyone. So this problem has to do with Colin slaw. Let's see what they are asking us. We know there are two electrons, they have a separation of 1.2 nm, they are released and allowed to move freely. And we are asked to determine the greatest acceleration that the electrons experience and specify when that acceleration is observed. So first, let's um recall that they are talking about acceleration. Um and so we can remember Newton's second law, which is just the force equals mass times acceleration. So that's how we're gonna get our acceleration term in there that we're gonna solve for. And then cool. Um law, we're dealing with um you know, charged particles. So we can use columns law, which we recall is the force equals K Q one, Q two over R squared. So looking at these um all these terms, let's recall K is columns constant and that's 8.99 times 10 to the ninth. Newton meter squared squared, um Q one and Q two are the same and they are constant because they are electrons. So it's called the charge of an electron is negative 1.6 times 10 to the negative 19 columns. Um R is the distance between two particles. And so, um at the initial separation that is 1.2 nanometers, which I'm going to rewrite as 1.2 times 10 to the minus nine m. The mass of an electron is also constant. So Let's recall that is 9.11 times 10 to the -31 kg. So we're just going to set these forces equal to each other. Um, and solve for the acceleration here. So we'll rewrite that equation as a equals K. I'm just gonna say Q squared because Q one and Q two are the same over M r square. So we're actually going to take a look at this equation here and we'll see that the acceleration is inversely proportional two, the distance squared. So that means that the acceleration will go down as the electrons repel each other. So the highest acceleration is at the moment of release when r equals 1.2 nanometers. So that actually answers our second part of the question um first and then but that actually allows us then to set to solve for acceleration because we know the distance that we need to use is this 1.2 times 10 to the -9 m. And so from here, it's just a plug and chug. We will right out all of the values that we know is constant. The charge of the electron squared over the mass of the electron times the distance between the two particles Squared plug that in. And we get 1.7 six, sometimes 10 to the 20 m/s squared. And so that is the answer to the first part what our actual acceleration is. And we already to determine the acceleration was going to the highest when we had a separation of 1.2 nm. And so looking at our potential answers, that is answer D. All right. That's all we have for this problem. We'll see you in the next video.