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Object $A$ has $27 \mathrm{~J}$ of kinetic energy. Object $B$ has one-quarter the mass of object $A$. (a) If object $B$ also has $27 \mathrm{~J}$ of kinetic energy, is it moving faster or slower than object $A$ ? By what factor? (b) By what factor does the speed of each object change if total work $-18 \mathrm{~J}$ is done on each?

In this question, it is given if probe in it moving with kind of dignity, kind of dignity off. And to give it 3.2, you know what happened? Word. So this has to be converted into your so kind of technology. Opera phone bill me Work one suits in tow. Rental depart minus 90. Join, We have to fight with party speed. Proton is moving. Do you know that kind of dignity? It's goingto happen. Be square from this equation. Well, a city off 41 would be so I saw kind of dignity upon must. Now we have toe substitute the value in it. Kind of dignity on Proponent has given take 200 and 1.6 10 to the power minus 19 year old and mass of the proton is 1.6 of it and 10 to the power off my desk. 27 Katie. So when you solve it, you will get 7.8 in tow. Tend to give our fight me te per second. So this is on support. This problem. Thank you for

Hi all here we have a number of modes of C 84 then is equal to eight by 16 people. 2.5 miles road means coil. See our must be sequel to wrote off three RT by M. Okay here, Musical 16 R is equal to 8.31 400 to 7. Then she becomes three in 28.31 400 raise to seven in 2 300 divided by 60. This one becomes 46.76 in Dubai and rest too for crm is can be also your mama's Okay. Say about speed, there is a limited for a second and it will be called to 6.83 18 to try and raise to four centimeter for a second. So then here asked about kinetic energy, K E. Okay, the kind of cannot the question can be written us three way too and Artie we all know all the values. Okay Then it becomes a three way to indu .5 indu 8.314 in do 300. Okay, That is 1870.65 June Thank you. Okay, the desert can technology. Thank you

All right, This problem has to do with kinetic energy and rest message. So the only equation we need to know for this is twenty six dash by B, which says that kinetic energy is equal to gamma minus one times M c squared. Okay, M C squared is actually the rest mass energy. Okay, so when we want kinetic energy to be equal to percent, thirty three percent of the rest mass energy, all that saying is that you set you set this equal two thirty three percent of best mass energy, so M c squared and so writing it down properly, you have gamma minus one times m C squared equals thirty two percent, meaning point three three times. I don't C square. Thanks. You see here that the M C Square's cancel really nicely and you're left with gamma equals one point three teams. All right, And gamma, as we know, is this one over square of one minus V squared over C squared factor. And so you can square both sides of this and and eventually what you end up with is it v equals point six five nine three see are about sixty six percent the speed of light is when is where kinetic energy equals a third of rest mass energy, and that's a

Um you know atomic gas at a temperature mono atomic gas at temperature t equals to 25 C. Which is equal to 2 98 Calvin. Okay so for the party of the question we have to determine the average Uh kinetic energy per molecules. So which is given by U. equals to three x 2 KB. Multiplied by T. Where K. V. Sportsman constants of substituting values. We get three by two. Multiplied by 1.38 multiplied by 10 to the power minus 23. Multiplied by 2 98 Calvin. Okay so from here after solving we get energy uh mono atomic guests per molecule equals to 6.17 but 10 to the power minus 21. You okay? Now for the part of the of the question in which we have to determine the RMS spiel so rMS speed we RMS is equals two three K. B. D. Day whereby small empty. Okay so now substituting values and here we get under root of three, multiplied by KB is 1.38 Multiplier weight into the power minus 23 multiplied by temperature is 2 98 Calvin. and divide by of the mass of a single atom is given as 6.65 manipulate they tend to the power minus 27 kg. Okay, So from here after solving we get we RMS equals to 1.36 manipulated by 10 to the power three m per second. Okay, so this is the answer for the but B of the questions. So this is the answer for the party and this is the answer for the part B. Okay.