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Two 4.80 kg balls are attached to the ends of a thin rod of length 36.0 cm and negligible mass. The rod is free to rotate in a vertical plane without friction about...

Question

Two 4.80 kg balls are attached to the ends of a thin rod of length 36.0 cm and negligible mass. The rod is free to rotate in a vertical plane without friction about a horizontal axis through its center With the rod initially horizontal (the figure) , 94.0 g wad of wet putty drops onto one of the balls, hitting it with a speed of 4.71 m/s and then sticking to it: (a) What is the angular speed of the system just after the putty wad hits? (b) What is the ratio of the kinetic energy of the system af

Two 4.80 kg balls are attached to the ends of a thin rod of length 36.0 cm and negligible mass. The rod is free to rotate in a vertical plane without friction about a horizontal axis through its center With the rod initially horizontal (the figure) , 94.0 g wad of wet putty drops onto one of the balls, hitting it with a speed of 4.71 m/s and then sticking to it: (a) What is the angular speed of the system just after the putty wad hits? (b) What is the ratio of the kinetic energy of the system after the collision to that of the putty wad just before? (c) Through what angle (deg) will the system rotate before it momentarily stops? Punty Wad Rot Aicn ais (a) Number Units (b) Number Units (c) Number Units



Answers

Two $2.00 \mathrm{~kg}$ balls are attached to the ends of a thin rod of negligible mass, $50.0 \mathrm{~cm}$ long. The rod is free to rotate in a vertical plane without friction about a horizontal axis through its. center. With the rod initially horizontal (Fig. $12-31$ ), a $50.0 \mathrm{~g}$ wad of wet putty drops onto one of the balls, hitting it with a speed of $3.00 \mathrm{~m} / \mathrm{s}$ and then sticking to it. (a) What is the rotational speed of the system just after the putty wad hits? (b) What is the ratio of the kinetic energy of the entire system after the collision to that of the putty wad just before? (c) Through what angle will the system rotate until it momentarily stops?

In the institution, it is told that two balls are attached to the end of a thin road and this road can be rotated in a vertical plant. Now it is told that A party of weight that is given to us, 50 g drops onto the one ball and hitting it with a speed of three m per second. And after that it is stick to it. Now we have to find the angular the spirit of the system just after the party red hit. So first of all um during the diagram for this given fusion. So let this is the thin road and two balls are attached so let this is first of all and this is second ball and these are attached at the end and that this is the center of this road. No, this distance is Day by two and this distance is also day by two. And let this is the part Which strikes to this. And we have given the velocity of this beauty that is 3m/s. Let mass of these parties M2 and most of these balls are and one and this point is like this is all. So first of all I'm writing the given data. So we have given the mass and one that is two kg. And we have given the mass M2 that is 50 g or I can say 15 to 10 to the power minus three kg. We have given the distance that is the easy cost too 57 But I can say 0.5 m. And we heard you want to do Spirit. That is physicals to three m/s. Now in this problem there is no external force. So where momentum is conserved. So we can say that initial angular momentum is given by That is 11 physicals to this is I am doing to this is we in today by two and we consider it final angular momentum is That is L two is the momentum of this 40 plus momentum of the ball. So this is everyone into the final velocity into this is D by two plus, this is everyone into the final into D by two. This is the momentum of the was less Momentum of the port and this is M2 into the final into day by two because all the three balls have same velocity. So we can say that your momentum is conserved. So conservation of momentum Which says that and 111 is equals two Aalto. So from here we get the value of now put this two equals so you can say that this can be written as I'm doing to this is we In today by two days equals to this is anyone. This is two times of M one VF into this is D by two plus M two into VF into day by two. No, we can see that we have his bitterness, that is Omega into day by two. So finally we get omega F from here and this is two times of M two and two V upon two times of and one plus M two into the. Now put all the data in this equation and we get the angular speed. So this is to into 15 to 10 to the power minus three into this is three upon This is two into 2 plus This is 0.05 And so this is 0.5. So from here we get this is 0.148, radian per second. So this is the aspect of our first part of the problem. Now in the second part we have to find the ratio of the kinetic energy of the system after the collision to that of the Okay, just before so we can see that initial kinetic energy is given by that is half of em too into we square and final kinetic energy is given by the kinetic energy of the balls. It is plus kinetic energy of potus. The kinetic energy of duties. This plus kinetic energy of the ball is two times of half of And when we finally square so we have to find this ratio. So we can say that given the initial upon here, Finalist given by that is I am too upon this is too time self and one plus M two. Now put all the data on the situation and video. This is your point. Do you know 123. So this is the answer of our second part of the problem. Now, in the 3rd part we have to hold that we have to find the angle that the system rotate before it moment release drops. So we have to find the angle so we can see that initial potential energy is beyond by the M two into three in two day by two. And final potential energy is beyond by that is I am doing to disease The into this is day by two of 1- Course Tita and initial kinetic energies that is half of this is two times of and one plus M two And today by two Holy Square into disease omega finally square. And finally the system stops. The final kinetic energy is zero. So we can say that form energy conservation that initial kinetic energy and initial potential energy equals two. Final kinetic energy plus final potential energy. Now put all the data in this situation and we get close to it as opposed to this is minus of one by two, two times of and one plus M two upon this is I am choosing to B x two Whole Square, Sorry, this is D by two into omega final Holy square. So from here we get the value of tita and this data will comes out to be- of 91.3° or I can say five will be 1 81.3 degrees. So this is the author of our third part of the problem. I can show it diagram also, so this is our ball system and this is here ball and this is the party which is attached to A. And let we can show that. Let this is the angle is twitter, so this angle is our angle file, so this is a lie, and this is our answer for this demonstration. Thank you.

In this kitchen part a in part a the appropriate model to treat the projectile and the road isn't I sold a tiered system ideology, a system what, Experiencing no net, external tore or fourth while in part B we have total angular momentum. Total is it was to aloft particles and particle plus l Road we get between was toe m V. I often divided by two plus zero. As we get the total Andrea, I'll be divided by to no. Now they have cases in guest. See, we have in parts even have total angular momentum. I totally is. It was toe I particle plus I rode which is equals toe one upon 12 on d squared plus Mowlam the upon to hold square because the values I total is equals to peace. We're more deeply m plus three m divided by 12 now in bar B. After the it could express the anger momentum as Al Total in Part D v couldn't aloft Total is it was too. I total multiply maker I total multiply makeover. Chizik was too. The square multiply with M plus three m divided way 12 window maker now in party dick Organizing the at angular Momenta Misconduct LF physicals to L A We get the square, multiply with this square Multiply with M plus three m divided by 12. Multiply with omega bigot Um, off the i d divided by two. From here we get the value for Mega, which is 6 a.m. off via a divided by B six animals were diverted by DeMARE d play and plus three Now in part if we have k is was 21 by two and most the ice quit Now in part G, we have total kind of take energy Kato politicals to one by do I total Martin play with Maiga's quit No. One by two i total is the square into M plus three and divided by two murder blood. This is Multiply Omega Square with your six MP I divided by d off on capital M plus three and the whole square We get the total kind of chicken allergic. A total is opposed to three m squared in tow. We I square divided by two into capital and plus three now in part after G. We have part etch the change in mechanical energies There ducky changing mechanical energy, which is half off half MV I square didn't minus negative. Open at minus three and square, we ask where divided by on blustery and which is It was too animals and the squares Mowlam's on the square, divided by two in tow, em plus three. Then the fractional change in mechanical energy is directional changes on Abu I am blessed three.

So initially as the 1400 kilogram object is moving with the velocity off Sierra 14000.250 meters and it hits a stationary object off massive 1600 kilograms. Nor that all numbers have three significant digits. From here on, I just right on one significant. I'll write it down without any significant digits, but they all have three significant digits after the collision because you don't want four kilogram mask is moving at an angle of 36.9 degrees with a velocity 012 meters per second. Let's say the other object does it want six kilogram is moving toninety kita below the X axis with our lost three. Now we want to find out the magnitude of this velocity and the angle it makes with the X axis for fighting. Now we simply used conservation of momentum in both directions. Let's say our hearts under large insects on vertical direction is white, so let's go with first white direction. Initially, the object was moving horizontally and this object was not moving, which means initial moment. And why was Cyril? But finally, let's call this object Alice, call its object object has Wyman Wyndham, Mass. Which is 014 As velocity it is you want to. I'm scientist. Just sign 36.9 degrees. And for object B, the wife wanted would be mass 016 kilogram. I'm the last to leave time scientist, but not that white component is in downward direction and hands. We have a minus sign. Using this equation, we can see recent data, which is the white 0.40 point two signed, 36.9 divided by 0.6, which turns out to be refined. Is it a Wade meter per second? Nor that I left the minus sign here because this is negative now for we ex. We simply use themoment on conservation in extraction. Initially, the moment of the next direction was just going on Object. Just mask 0.4 and velocity they want to fight. It is equal to the final moment, which is the excellent off object. There would be mass times Velocity and Scott's Tita less They want time off. Optic B would be mass Little 16 and velocity times past Tita. Now we can write. Write this instead, as we X Now from this figure, we X do we 0.25 and syrup on for minus 014 and 0.2 cost 36.9 divided by 016 which transported the 0.6%. Hence the magnitude ofthe loss TV the square root ofthe big X squared plus y squared just 0.1, Mr President. And the angle Tita is simply down in words. Off the vibe I re X It's chance out to be 53 on 13 degrees in the fourth quarter and, oh, between cities clockwise 53.13 degrees from X axis. Now for Barbie, we want to find out the initial and find finally kind of energies. The initial kinda country was simply the kind of candy off object it, which is half mask 014 and velocity squared, which is the 014 1 to 5 squared. Which is it you want? They don't want five jewels and for the final indignity is simply adding final kind of anti off Auntie's off object and after B, which are I'm smart times. Velocity squared this half and a mask and velocity is weird. I'm sorry. In the last part. Yeah, that's it. This dance or do we want? You don't want one, Jules. As you can see, there is a drop in energy changing kinda country. Initial mine is final. Would be 0.1 feel 015 Jules, this is the amount of energy last during the collision, and this usually turns into heat or something like that.

Hi everyone. This is a problem based on collision of a particle with the rigid body which is three to rotate about the given access. This problem can be solved by conservation off angular momentum and energy. Here it is given a rod off mus m, having led to deal by abated and vote mid Quite old our projectile having the mask Mhm Moving with speed v I collides toe the rod and stick with it as soaring their figure. We have to find first part appropriate model mhm to describe the motion off Partick it and Rod In the second part we have toe fight the moment off energy off the system about all entire part. We have to fight angular Momenta before prison. Deeper we're toe find angular momentum after police If and Guler Velocity omega is and globalism to your profession In part we have to fight the angular better city off rotation in F Kyra technology before religion, the heretic energy After collision and fractional change in kinda technology, let us start solving it first part. Yeah, it can be solved by conservation off angular momentum. Uh huh. As external talk on the road and particle zero No second but angular momentum before religion. Angular momentum off the particle is M V I. Dave, I too and that often order zero because it is addressed. So it will be M v I de upon to and she part we have to calculate moment off inertia. So moment off inertia will be moment off. Inertia off the particle plus moment off energy off rod moment off in a single particle is m divide to his square and that off the road is and de square by 12. So it can be It is m plus three times off a small m de square by 20 Uh huh the after religion angular momentum It will be I into Omega that is m plus three m the Square omega upon 12. By applying the conservation off Anguilla because external talk is zero, we can find the angular velocity off rotation. So M v I de upon toe will be equal toe. I am plus three m d squared omega upon 12. So it is to be six am I upon Deep Empress three years no kind of technology before the religion half and via is wet after collision half I When you guys square? Yeah, Moment of inertia is and plus three the D squared by 12 in tow Or May guys square 36 a m e squared We I swear de square m pless three m square So final kinda technology you will get three by two I am a square we a square upon m polis 3 a.m. No fractional changing kind of technology Her final kind of take energy on initial That is kind of technology after collision and before the operation. So we can like three y two m squared Create is sweating m plus three m divided by half mv I sweat So it is doing three AM upon AM pill Astrium. That's not Thanks for watching it.


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