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(III) A neon atom $(m=20.0 \mathrm{u})$ makes a perfectly elastic collision with another atom at rest. After the impact, the neon atom travels away at a $55.6^{\circ}$ angle from its original direction and the unknown atom travels away at a $-50.0^{\circ}$ angle. What is the mass $($ in u ) of the unknown atom?[Hint: You could use the law of sines.]

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39.9 $\mathrm{u}$

Physics 101 Mechanics

Chapter 9

Linear Momentum

Motion Along a Straight Line

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

University of Winnipeg

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

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In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

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Okay, so we're in chapter nine. Problem 59 here. So it says a neon adam of in vehicles, 20 Tomicki tips. Makes a perfectly You lost that collision with another arrest. After the impact that neon Adam channels way scattered by 55.6 degrees in the unknown, Adam travels at negative 50 degrees scattered away. So what is the mass of the unknown? Adam? What? Okay, so we have this drone out here, and first we know that we're gonna use limited conservation. And that tells us that in the one is a factor pickles and anymore be one Brian Waas into you too, right? Okay. So from this equation, we know that we can write this whole situation out as a trying. So what that looks like is we have initial B then one view one our initial woman horizontally, um, in this needs to equal to that has added together. So one of the first Spector we add is this one then one b one crime added with the second vector into the two. Crime equals this perspective. So that's just in Vector Edition equation Written jeon er graphically geometry. That's where I was looking So now the angle between the one prime the one we give is here. The angle between the one and the two prime here was given as five. So we know we can write this last one called out for So now we have this triangle. So how do we right this? Well, we know triangle That Alfa must be 1 80 minus data my net spy so we can figure out what outfit is from that. Okay, You figure that 74.4 degrees. That's what our output it is. So it gives us a hint that we could use the signs. So what is the law of signs? Tell us with a lot of signs. Tell us that m one V one prime over the one next to it which was And one the one is given by sign of by over sign of Alfa. We can also right Another one here as into the too proud over and one people. This is a sign of data open sign about. So how can How does this help us? What we can, right? The one prime and be too proud in terms of the other. So this is V one signed five over signing in this equals V one sign theater of signed up for. Okay, so we're getting there, so we use momentum conservation to get this. Now we need to use energy conservation. Well, we already said it's perfectly elastic, so we know that Connecticut he's are conserved. So we have this equation here Starting close someone half into the two prime square. Okay, one has canceled, and now we can plug in what we have for velocities. So we get em. One B one square equals in one. The one sign Phi over. Sign Alfa squared plus into notices. Be one. Oh, well, look at me for getting things. Let's go back over here for a second. These in one's cancelled outright. But these didn't. That's why I left something out here. This should have been in one over and to Adam. Okay, back over here. So when we plugged that in, that means this is signed Data one, over. Sign Alfa into look, not square. Well, we should see immediately. All these view ones are canceled. That means we can just write this now in terms of the masses. So let me see if I have enough room here. So if you rearrange this equation right year into, we should see that in two equals in one science. Where to? Data over. Sine squared of Alfa minus. Sorry, we're here. Five. Cool. So we can put this in there. So 20 atomic units times sign of 55.6 degrees squared all over. Sign of 74.4 degrees square minus sign of 50 degrees square. Awesome. Replogle in a calculator. This comes up to me. 39.9 atomic units is into awesome. That was what we wanted. So, yes, you got it.

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