Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

(II) A neutron collides elastically with a helium nucleus (at rest initially) whose mass is four times that of the neutron. The helium nucleus is observed to move off at an angle $\theta_{\mathrm{Hc}}^{\prime}=45^{\circ} .$ Determine the angle of the neutron, $\theta_{\mathrm{n}}^{\prime},$ and the speeds of the two particles, $v_{\mathrm{n}}^{\prime}$ and $v_{\mathrm{He}}^{\prime}$ , after the collision. The neutron's initial speed is $6.2 \times 10^{5} \mathrm{m} / \mathrm{s}$ .

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$v_{1}^{\prime}=5.1 \times 10^{5} \mathrm{m} / \mathrm{s}$$v_{m_{c}}^{\prime}=1.8 \times 10^{5} \mathrm{m} / \mathrm{s}$$\theta_{m}^{\prime}=76^{\circ}$

Physics 101 Mechanics

Chapter 9

Linear Momentum

Motion Along a Straight Line

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Cornell University

University of Washington

Simon Fraser University

Hope College

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.

03:47

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.

19:15

(II) A neutron collides el…

03:02

A neutron traveling at $2.…

01:19

A neutron of mass $m$ and …

12:07

A neutron initially at res…

17:55

In a nuclear reactor, a ne…

07:04

A neutron moving with velo…

08:22

(II) An atomic nucleus of …

02:48

A fast moving neutron is s…

01:48

01:17

Neutron Scattering Show th…

08:15

(III) An atomic nucleus of…

12:19

A neutron with mass $m$ ma…

of fairly involved complex other algebraic lee complex problems. So let's get to it initially. So this is what it looks like. Initially you have neutron moving. It spewed visa boo, um, and Torrance, the helium nucleus, which is at rest after the collision. Neutron moves, which you'd be prime at an angle. Data be prime from the horizontal and ah, the helium nucleus also moves on with lost lee D h e prime at a at an angle fate R h e prime from horizontal in the opposite direction. So, uh, three equations to use here, uh, first will be, uh, momentum conservation in the ex direction. So, uh, in the ex direction, you initially just have the neutrons mass calling that and somebody here Liam's math of m h e re. Which, by the way, it's four times and said be very helpful fact for this problem. So anywhere initially, you have m b redo momentum in the ex direction. Finally, you have m B V b prime co sign data be prime. So, uh, the V b prime in the extraction The extraction plus M h p v h b prime um uh co sign data 82 Prime, uh, so horizontal component of VH. You prime note that M h e is four times and be massive neutrons and this just becomes four m b and cancel out all the embassies And you What you get is V b equals V B Prime Co sign Theda, be prime. Uh, plus four VH be prime co side data H e prime. And this we will call. Uh, well, let's actually write things down in terms of you be prime VD Prime Co sign data to your pride will be equal. Two V B minus four times Do H b Prime Co sign Veda h e prime and that is our equation. One no kept equation to is momentum conservation in the wind direction. So initially there's nothing in the UAE direction turns of momentum and the after collision you have m b B B prime sign data be prime. So momentum of be in the UAE direction plus M h E V A g prime sign data each e prime. So again, uh, why component of momentum looks looks make that cleaner Why component of momentum of ah, momentum of momentum after collision off the helium nucleus and again this is for me. She is four times and BBC two and four times and be so them bees cancel and writing this down in terms of you be prime your TV prime Signed data be prime. Is it cool to those looks? This will be a negative. I've got to mention this will be a negative because, uh, the healing requests is traveling in the opposite. Why direction? Right. So, Vehbi pride aside, data be prime is equal to four times aviation prime this forum be times sine theta scientist Ada h you prime. And that is equation too. All right. And finally, the question to you is the conservation of kinetic energy. Initially, you have 1/2 em do V b squared plus 1/2 m h b are looks That is the initial momentum. Initially, there's no momentum from the ah, hell, Um, if it's finally you have 1/2 mhp times v h e Pride Square, just magnitude here plus 1/2 and b v b Prime squared because this is four times of M b. The NBC's cancelling. Of course, the 1/2 has cancel. And what you end up with your is that, uh, be prime writing in terms of Phoebe Prime is Vehbi Props squared is V B squared minus four times GHB private squared. This is our equation. Tweet. Okay, so, um, go ahead and solve this This mess of, ah, algebraic problem. The 1st 1st step is to add up equations to square equations one and two and add them up. Okay, so squaring equation one on the left hand side, you got V B Prime squared times co sign squared data. Uh, prime, Um and, uh, that's it on the left hand side. Ah, it's that we have. Yes. And so that is equal. Okay, so that's Vera. The 1st 1 plus Vehbi prime squared times. Sign squared from squaring the left hand side of the equation two times sine squared. Pardon my mess. Um, I'm sides squared. Uh, data be prime. And, um, so bad. Okay, so that is the left hand side. So let's just Let's just concentrate on that for a second, okay? S Oh, well, you have here is baby prime squared times sine squared data be prime plus co sign squared. Uh, data be prime, which is equal to B be prime squared. This is because co sign squared X plus side square. Lex is always one. And so this whole thing becomes one. And data be primary don't know is eliminated from our equations. Excellent. So this is the left hand side. Um, the right hand side becomes Ah, let's see. You have Vehbi squared minus two times V b uh, times four times. VH deprives the two times four is eight, but it's two times eight months a times B times. Ah, whoopsie daisies Times the h p prime prime. That's it. Uh, plus four v a g prime the coast out late. There's a concert Was a data terminal. Extremely sorry. It is a very how'd you break Lee? Intensive problem. As I mentioned before. Uh, tons co sign stayed up. Uh, h e primes plus 16 via YouTube prime squared co sign square Seda H e prime. Um, And then from the second equation, you have in addition to that plus 16 th e prime squared sine squared data h you prime. And so again, you noticed that there's ah, uh, co sign squared, plus sign square terms. So this whole thing So the data a CI prime from these last two terms. Cancel, uh, are, um, the sides squared in the co sign squared turns to one, and you get, um whoops. Wanna stand ran? Here s O you get on the right hand side. V b squared. Um, minus eight V b v H e prime, uh, co sign Seita a ci prime plus just 16. The ah h e prime. Quick. That's it. Therefore, this because therefore, we have physical following equation. Um, Vehbi prime squared is equal. Two the B squared minus eight BB VH be prime. Co sign data H E prime the 16 th e prime square. Okay, um, what's this? Is b b squared. All right, Okay. And so from equation. And now we invoke Equation three from Equation three. We have the V B prime squares, B B squared minus four. She's prime square. And so this is equal to V B squared minus four. V h p Pride squared, So the vbs cancel. Excellent. Now we're left V B square terms canceled. Um, this is from equation three. Okay, So, uh, what what do we have left? We have v b. Prime squared is equal or rather, BB prime square does not come in quite yet. You have, Um, You have eight V b v H E. Prime times co sign Theda. Aged. Prime ah is equal 2 20 times. V h e. Prime square. Right. And, uh, that okay, Therefore, we divide both sides by views you price by eight times views you prime. Uh, and what we get is ah, VH be prime is equal to point for eight over 20. Um, quick, four tons. Uh, co sign data h q prime tons view be. And so you get 0.4 times V b, which is the initial velocity of neutron, which is, uh, 6.2 times 10 to the five meters per second times co sign, uh, 45 as we're given. And this comes out to be 1.75 times 10 to the five meters per second. And that is the velocity of human nucleus after the collision. All right, so we've got that big thing out of the way. And so now we're gonna use our equation, um, three again on from equation three. You can get Phoebe Prince of Eby Prime Square. Therefore, will be, um ah v b squared which is 6.2 times 10 5 meters per second. Quality squared minus four times V H G prime square, which we just found just 1.75 times 10 to the five minutes per second. Quiet. He's quick. So therefore of you be prime is just a square root of that 5.1 times 10 to the five meters per second. And finally from ah, equation. Um, equation, too. You have that, um, you have that signed they Toby Prime is equal to is equal to four times the h e prime signed data H e prime over the be prime their fourth day to be prime this arc sine off this stuff. So that's four times 1.75 times 10 to the five, uh, times sign 45 over Vehbi Prime, which is, uh, 5.1 times 10 to the five. And what you get is data because, um, for 76 when zero degrees, they to be front, and that's it.

View More Answers From This Book

Find Another Textbook