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Question 516 pointssave AnswerTwo blocks are on frictionless horizontal table: block of mass m,"1.26k8 travelling with speed Va"1Zm/s toward another block...

Question

Question 516 pointssave AnswerTwo blocks are on frictionless horizontal table: block of mass m,"1.26k8 travelling with speed Va"1Zm/s toward another block of mass mz-4.67kg which IS initially at rest coil spring; which has spring constant k-37Nim; attached t0 the second block In such way that it will be compressed when struck by the first block 0s shown in the figure below: Determine the maximum compression Of the spring: Express your answer using two decimal places:Mmz

Question 5 16 points save Answer Two blocks are on frictionless horizontal table: block of mass m,"1.26k8 travelling with speed Va"1Zm/s toward another block of mass mz-4.67kg which IS initially at rest coil spring; which has spring constant k-37Nim; attached t0 the second block In such way that it will be compressed when struck by the first block 0s shown in the figure below: Determine the maximum compression Of the spring: Express your answer using two decimal places: Mmz



Answers

In Fig. $9-63,$ block 1$($ mass 2.0 $\mathrm{kg}$ ) is moving rightward at 10 $\mathrm{m} / \mathrm{s}$ and block 2 (mass 5.0 $\mathrm{kg} )$ is moving rightward at 3.0 $\mathrm{m} / \mathrm{s}$ . The surface is frictionless, and a spring with a spring constant of 1120 $\mathrm{N} / \mathrm{m}$ is fixed to block $2 .$ When the blocks collide, the compression of the spring is maximum at the instant the blocks have the
same velocity. Find the maximum compression.

Good day in this question we will be solving for the maximum compression of the spring. So from the problem the velocity of the system as a whole. When the spare reaches the maximum compression eggs satisfies the momentum conservation of and one the one plus M two V. Two. It was M1M 2 and the velocity of the system. So solving from the velocity of the system we have M. One. We want less em to be divided by M one plus M two substituting. We are given that M one yes two kg. And the The one is 2 kg and the speed one is then meters per second. The M two yes five kg. And It has the speed of three m/s. If I did buy two kg plus five kg we will give us the speed of this. Are the velocity of the system. 05 m/s. No solving for the change. We need to solve for the change in kinetic energy of the system. So Change in kinetic energy of the system is 1/2 M one plus M 23 squared miners one have and when we one squared my nurse and one half and to veto squared. That is genetic energy final minus initial. So Solving we have 1/2 times two plus five I was five m/s squared minus one half of two. I understand meters per second squared -1/2 on five. Hello Promise Times 3m/s grade. Well give us the change in kinetic energy Is equal to negative 35 jewels. So there are a lot of the conservation of energy requires the one half gay X. M squared, which is the maximum compression is equal to the negative of the change in kinetic energy. The solving for X. M. We have two Times -2 Delta K divided by K square root. So substituting negative two squared of negative two. There's negative 35 jewels. If I did buy 11 20 utan perimeter. Well give us a maximum compression of 0.25 meters. Thank you.

Hello. So for this problem we've got this mass A. Which is two kg. Running into mass B. Which is five kg. S. A. Is moving at 10 m per second B. Is moving at three m per second. We know the K the spring constant of the spring and we need to figure out how far it will compress. We're told in the problem to note that the maximum compression at the point of maximum compression, they'll move as one unit or so we can treat this as a inelastic collision. So momentum will be conserved. So the total momentum before the collision is massive blockade times V. One blockade plus massive black B times V. One of Black B. And that is going to equal the combined mass as a black A. Plus massive black beat times their new speed as they move off together. We'll just call that be too. So if we solve this for me too, we're going to get the right side of this equation all over the combined mass And we'll get a V two five meters per second. So if you plug all this in all these numbers in um you should get five m per second, provided we used our parentheses correctly. So this is the final speed. Now that we know the final speed, we can we can start using conservation of energy. So we have uh an initial kinetic energy from each of these two things. We're going to have a final kinetic energy. And the difference between these two kinetic energies is how much energy gets stored in the spring. And so we're going to have um kinetic energy from black A plus kinetic energy from black B equals kinetic energy of block A. B. System plus the amount of energy lost to the spring. Mhm. So this Right side it's just 1/2 mm Eva one squared. So one half times two times 10 squared plus one half MBBB one Squared Arby's. So 1/2 times five times 3 square. And on this side if you plug in those numbers, you'll get 122.5 jules on the left side on the right side, we can figure this since we know all that stuff plus and be B two squared. So one half times seven is their combined mass times five squared For that, you'll get 87.5 jewels plus us or us. So plus us. So this you this potential energy here in the spring is going to be this minus that. Which ends up being 35 jules is the potential energy stored in the spring. And we were given the case so we can actually solve this as well. So this it's going to be one half K. X squared is the amount of energy stored in the spring where X. Is the compression of the spring. So this is what we're looking for right there. That X on this shift colors here for this part. So if we solve this for X, we're going to get X equals you times two divided by K, and then square root of the whole thing. So to you overcame Where you is 35 jules. Kay is 1120 newtons per meter. So we plug all that in. We're going to get any compression of 0.25 person.

Okay, so we're in Chapter nine. Problem 41. So we have this three kilogram block sliding, fractious Lee friction. Honestly, Tong, it's table top eight meters per second and it hits this second block. That's at rest with a massive 4.5 kilograms. But it had this spring on it with a scream constant of 850 newtons per meter. Part ay says what is the maximum compression of spring? Okay, so we know that at the maximum compression of Miss bringing the blocks will not be moving relative to each other. There would be exactly the same then all of the interaction between the blocks this internal to the mass spring system. So that means the momentum conservation can be used to find this common speed. So what we mean by that is P initial p final meaning that in one B one equals and one plus into comes this V prime. She's a common speed of moving together at five Max living compression. Okay, so we also know that the mechanical energy is conserved so we can find the energy stored in the spring and then the compression of the spring. So what That means energy conservation initial equals the final. This means the initial energy, which is just the kinetic, equals our final Connecticut G, the prime squared plus be met Mount stored and our spring, the potential energy stored in the spring. Awesome. So now we can just solve this. For what? Accidents? So we rearranged us for X. We get this large equation of one over K times and one into over, then one of us and two time's the one square Listen. So this was just solving both of their solving this for X with both of these equations. Okay, so we know all these things now so we can just plug this in. So we get scared of one over a 50 per meter. Then we have three kilograms times 4.5 kilograms over 7.5 kilograms. Times eight squared meters squared per second squared. We plug up. Listen, we get an answer of explain 037 meters. That is our maximum compression. Awesome move on a part B. So now we just want to find the final velocities. Well, we should already know that this is an elastic collision. So that's the answer. Two part see actually books Trump ahead and said, Is this collision in plastic? Well, we know it's going to be because all the forces are conservative because there's no friction if there was friction and that's a non conservative force. But since all the forces here are conservative, we know that it is elastic. Okay, so moving back to part B since it's elastic weakens, use simple equations. Find the final velocities so we can look back at example 98 or problem 40 and we consult please. So for a stationary target and you elastic collision, we have the one prime is the one times em one minus two over in one plus and two. So it's playing that out since is eight meters per cent times negative 1.5 kilograms over 75 kilograms. So we get a final velocity for you. One prime of negative 1.6 meters per cent go. We could do the same thing for you to crime and this becomes be one times to 10 1 over em. One plus tempted cool. So this is eight meters per second times seven kilograms over 7.5 kilograms. Sorry, that's not something that's 63 times two is six simple math. Okay, six kilograms of 7.5 on this coming up to 6.4 meters per second. Cool. We got all the answers there.

In this fusion given that it is that is there is a figure you want. So first, I will draw this figure. So in this difficult, there is a hard surface given and on this hard surface there are two block is given. So first block having mass that is Given in the occasion, that is two KK. And uh, similarly 2nd block is Having same us, that is two KK. And there is a spring is attached to second block. And now in the question is saying that initially they both are left, but after some time, this first block is going in this direction with the velocity that is given one m per second. So in the cushion, it is asking that we have to find the maximum compression of the spring. And in the confusion, the spring constant is given that is equal to 100 newton per meter. So this data is given. Now let's start answering this fusion. So in the answer, I will say that the mass of block is first. For first block I considered must be relatedness. That is M. A. Is equal to two Kg. And for a month of second block that is MB will recognize that is two kg. Now initial velocity five first block will be written as that is the A. Is equal to There is one m/s, an initial velocity. Yeah, for second block will be recognized that is zero because the second block is A. I consider that is maybe is equal to zero because the second block is you can see that it is at rest position. So here I had written the value that is equal to zero. Now in the collection is being constantly is given that is K. Is equal to 100 newton per meter. So no next to peace. As you see in the figure. This first blog is trying to move with one m per second in this direction and taking a coalition with second block which is initially attached position. So after coalition, the first block, the four first block, the velocity is going to decrease continuously. And at the instant of time the wall system that is first block and this spring and the second block most together with calm university that is I considered that is considered capital. We So I can see that here. I will write that is after the collision wall system. Mhm. That is block West block. Yeah, let's spring plus second block. Yeah. Move together. Mhm. With a common well city, which I said that capital we here, I had assumed this. So now next to bees here, I am using the law of energy conservation of energy. So apply the law of conservation of energy. That we say that total kinetic energy before collision will be equal to total kinetic energy after collision plus spring energy. So the left side were written as that is total kinetic energy before poisoned. It is files. M A. Yeah plus sorry, M V A square plus half N B B B square is equal to have M. A. We squared plus half M A V square for the MVV square. Yeah. Plus the spring energy that is Have KX two. Yeah. So now simplified. So your ex is it compression? You can understand that here. Excuse you compression of his being When the first block is trying to collide with the 2nd block. So no next to these years have to read the data. Then it will be returning after substituting. I can say that the left side will be written as that is half multiplied by MTV A square will be that is two multiplied by one is square plus half M B b b square. That will witness series two multiplied by zero square is equal to half M. E will be there is two multiplied by ear in both terms on the right side, on the first boat term I will take the square common so and decide. Well written. I said this half M A plus half empty. So after putting the value, I can sit at a half, multiplied by two plus half, multiplied by two. Yeah. And outside we wait and I said yes, we square plus half now case given that it's been constant value is that is 100 multiplied by X square. Simplify it. Then I will get the equation that is after stalling one minus two. Z squared is equal to 50 k 50 x square. So this is a question number one. No. As you see in the figure, there is no action force is acting in order gentle direction. That miss. I can say that here momentum is conservative. So apply the second law that is law of conservation of momentum. So according to this law, the next step will be written is that is initial momentum will be equal to final momentum. So it means initial momentum. That is M. A. Plus we A sorry mm. Multiplied by V. A. Plus MB. Multiplied by B. B is equal to pantages of M plus M. B. Multiplied by capital. We no simplify it by capturing the data. Then it will be tennis after south shooting the value. No next step will be that is and maybe a means to multiply it by one. Plus MB will be that will be two multiplied by zero is equal to advantages of mm plus MB. That means two plus two multiplied by capital. We not simplify it. Then I will get the value of capital weed that is equal to After installing value said his half meter per second. So no I can see that. This is a question # one and This is a equation number two. So by using this equation number one and equation number two the next stable brightness That is here. What I'm doing is putting the value of the from a question number two two. in equation number one Then it will be written is it is 1 -2. We square. It means yeah from equation number yeah yeah two put the value of the yes yes in equation number one. So it will be written. That is a result is one month two weeks square means one minutes two multiplied by half. His square is equal to X 50 X square. So now simplify it. Then I will get the compression of a spring that is X. Is equal to okay after stalling, I will get that is X. Is equal to then Sorry, 1/10 meter. Or I can see that in centimeter. It will witness that is X is equal to X. Is equal to hunt. Sorry, 10 centimeter. So this is the answer of given question. That is maximum compression of a spring will be Yeah, that is X will be equal to or I can see that actually equal to there is 1/10 meter or I can see that 100. Sorry, 10 centimeter. So I had sold the fusion completely. Thank you.


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