The motor at C pulls in the cable with an acceleration (solved)

The motor at C pulls in the cable with an acceleration...
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Book used: R. C. Hibbeler and K. B. Yap, Mechanics for engineers - dynamics. Singapore: Pearson Education, 2014.

[@nayrahalhelo6323]

Actually this was short and straight to the point 👏🏻thank you...

[@QuestionSolutions]

Glad to hear! You're welcome and good luck with your studies!

[@syabongajele6431]

lately your channel is my habitat Sir

[@QuestionSolutions]

❤ Glad you enjoy it :)

[@ahmadaloufi4067]

Are you Sadio Mane?

[@user-gu8pe3ol7g]

The acceleration of B is actually going to the left so why we didn’t consider it as a negative?? Ba=-5t So S = -2.5t^2 So 0.125t^4-2.5t^2=3

[@QuestionSolutions]

Once you draw your position coordinates, that direction, (regardless of the movement of blocks), will be considered positive. At the end, if you end up with a negative answer, then it's opposite to the direction of your position coordinates.

[@darrylcarter3691]

The way I would see left as being positive and right being negative is looking at the rope attached to Block A. Notice how the length is decreasing.

[@QuestionSolutions]

👍

[@darrylcarter3691]

@@QuestionSolutions thank you man. you’re the best.

[@QuestionSolutions]

@@darrylcarter3691 Thank you :)

[@sarahkamal2585]

This was very useful. thank you!

[@QuestionSolutions]

I am really glad to hear that. Best of luck with your studies!

[@Aurora-pp3cs]

Why Sa+Sb= 3m? Wouldn't it be 6m since the position of both blocks was displaced from 3m to 0m, which means each of the blocks was displaced by 3m, and that will make a total of ( Sa+Sb)=3+3= 6m I am confused about this part. Please clarify. Thank you!!

[@QuestionSolutions]

The question is only asking us to calculate the time needed for the blocks to be apart 3 m from each other. Another way to think is that they start from d = 3 m, and we need to find when d = 0 m. Hope that helps.

[@simeonserafimov4823]

@@QuestionSolutions can you clarify a bit more please? How do I think about this? Is it the fact that the sum of the two that needs to equal three which means that B will make a displacement to the right and A to the left SIMULTANEOUSLY until B will be at the end of A (from the left) so that d=0? Thanks in Advance!

[@QuestionSolutions]

@@simeonserafimov4823 That is correct. It's a weirdly worded question, but it is simultaneous movement. So the movement of both blocks (3 m in total), gives us the d = 0 we are looking for. I think students get confused thinking its 6 m, but the datums are opposing, so it becomes simultaneous movement. I think a good way of seeing this is to use a ruler and 2 erasers and push with your fingers to get an intuition for what this question is asking. :)

[@NAYAN-t3e]

​@@QuestionSolutionsFollowing from sign convention of C side, As B moves to the Left, simultaneously A moves to right, both are starts from rest at t = 0. From given, d = 3 m at t = 0. Then, for d = 0 then, B should move by that distance d = 3 on left side, relative to A at that particular instant. Hence, relative displacement of B with respect to A, S_B/A = S_B - S_A in vector form, + d = + S_B - (-S_A ) As from C side (i.e. convention) Displacement of A at any instant is in right (i.e. - ve) while, displacement of B is in left direction ( i.e. + ve) as the motor D draws in B in left direct. So from C side convention it is in left & correspondingly d is displacement of B w.r.t. A at any instant, Means it covers d = 3 m from right to left in +ve direction, As the language of problem says when d becomes zero means it should move from d = 3 (on right side) to d = 0 towards left. So, + d = + S_B - (-S_A) becomes, + d = S_B + S_A As you given the step. Is my approach correct ? Or else any mistake in my approach, please suggest it asap. I will be thankful.

[@williamrotty5691]

Hi, what is the point C for which u gave the distance Sc? is it an just an arbitrary point between the motor and block A?

[@QuestionSolutions]

Yes, that's right. We need that to show the movement of the cable.

[@yveskourieh]

thanks!!!😊

[@QuestionSolutions]

You're welcome :)

[@enrikvantichelen8243]

So you just drop the constant after integration?

[@QuestionSolutions]

Please take 8 minutes to watch this video: kzbin.info/www/bejne/f6bHgYN9frtoh68 I think it'll help a lot and clear up a lot of questions.

[@rastonick5891]

im confused to why its 2Aa+Ac

[@QuestionSolutions]

Sorry, where are you referring to?

[@Kimi-vn7jz]

Why must we take the aA as positive value before integrate?

[@QuestionSolutions]

You don't have to really do that, but I just find it a lot easier to work with positive values, that way, you don't have to keep writing arrows to the left. At the end, you will still have to make it positive to get the displacement. So why not just do it at the start and then you don't have to worry about it. At least that's what I do when I solve questions. I hope that makes sense, but you can do it the way you mentioned too and then switch signs at the end. Entirely up to you.

[@Kimi-vn7jz]

Question Solutions but still why do I have to change it to positive value? What if I plug in - 0.125t^4+2.5t^2=3. Would it be wrong?

[@QuestionSolutions]

@@Kimi-vn7jz Good question. Yes, that is wrong. You are now using two different references to find the answer. If you use that reference (sa = -0.125t) as negative, then from that reference, you will get -2.5t for sb, and -3 m as the distance between them. I am not 100% sure how to explain this clearly, I think when you do a lot of questions, it will probably click in your mind. Change it to positive, and all should be good. I think the text book states the values need to be written so that it "has a positive sense."

[@Kimi-vn7jz]

Question Solutions okay thanks a lot! This is only applies for pulley right?

[@QuestionSolutions]

@@Kimi-vn7jz You're very welcome. And yes, for pulleys, a positive sense is used.

[@lucasvanhove5032]

thx

[@QuestionSolutions]

You're welcome.

[@ElCrankoPunko]

can you pls explain how Sa + Sb = 3 ?

[@QuestionSolutions]

Please watch this video first: kzbin.info/www/bejne/f6bHgYN9frtoh68

[@ElCrankoPunko]

@@QuestionSolutions saw that still have doubt

[@QuestionSolutions]

@@ElCrankoPunko So what we're trying to do is calculate the time needed for the blocks to be apart 3 m from each other. Another way to think is that they start from d = 3 m, and we need to find when d = 0 m. So we can say the length SA plus the length SB has to be 3 m. This 3 m is the difference. I hope that makes sense.

[@ElCrankoPunko]

@@QuestionSolutions Is it like Sa-(-Sb) = 3

[@QuestionSolutions]

@@ElCrankoPunko It's the difference between the lengths, so you can think of it the way you're thinking.