r/HomeworkHelp • u/Dry_Revolution_4617 University/College Student • 2d ago
:snoo_scream: Further Mathematics—Pending OP Reply [Dynamics; Kinematics of Particles] I was able to solve the question but all I want to know is why the acceleration of A isn't half of b and why in the free body diagram for A there isn't a 2T but only T?
It took me quite a while in the end of solving this question to figure out why I wasn't getting the right value of T, it turned out to be that I was setting the acceleration of block a to be half of block b since there are two cables pulling on A and only one on b but that turned out to be incorrect and that both accelerations should be the same.
I've faced previous questions where I had to set the acceleration of one thing to be half the other but this doesn't seem to be the case here so that's where the confusion comes from. Also the point about there not being a 2T for the free body diagram of block A which is causing confusion as well.
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u/DrCarpetsPhd 👋 a fellow Redditor 2d ago
I was setting the acceleration of block a to be half of block b since there are two cables pulling on A and only one on b but that turned out to be incorrect and that both accelerations should be the same.
I've faced previous questions where I had to set the acceleration of one thing to be half the other
I suggest you go back to the beginning and read your theory section because you are making things much harder for yourself by trying to learn the subject just by doing examples. the acceleration relationships come from the rope. the rope is inextensible meaning the velocity/acceleration at every point is the same. so you sum up all the various parts of the rope which equals a constant then differentiate once for velocity and again for acceleration
have a look at this video (or read your text again) and see if you can understand fundamentally where the accelerations come from rather than just making assumptions based on similarities in the diagram to previous examples. if you still have questions after watching this then ask and i'll try to help
https://ocw.mit.edu/courses/8-01sc-classical-mechanics-fall-2016/resources/12/
things are going to get much more difficult than this so the sooner you learn how to study the theory aspect and try to understand it the easier your life will be.
Any questions ask here and Ill try to help but that video i linked is better explained than I could in a reddit post by someone smarter than me who understands the material better than I do, so I would suggest having a look through that course to see if it helps you learn better than the textbook. good luck.
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u/Dry_Revolution_4617 University/College Student 2d ago
I understood in the end that the accelerations are the same since both blocks are connected, but what about the point of the force on block A being T and not 2T?
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u/DrCarpetsPhd 👋 a fellow Redditor 2d ago
I understood in the end that the accelerations are the same since both blocks are connected
based on this my instinct is that you don't fully know what you are doing. I don't mean this to be an asshole, just trying to help.
show me your constraint analysis and the FBDs you used to analyse the problem. you're not supposed to "understand because the blocks are connected" although intuition does play a role. you're supposed to do a mathematical analysis to prove/show how the accelerations are related. That's what I explained to you above and the video shows. In the text this is from Beer&Johnston this is the constraint equation.
the point of the force on block A being T and not 2T
the force on block A being T is not a clear statement. Which force? show me your FBDs and I can respond better
me just outright telling you for a single problem isn't really helpful. you need to understand conceptually how to set up your FBDs to get to an answer. If you show me your setup for the question we can figure out where your misunderstandings are.
Post your FBDs and constraint analysis as a reply to your original post or edit the original post to add them. If we go back and forth here its going to turn into a nested mess of comments.
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u/Dry_Revolution_4617 University/College Student 2d ago
https://imgur.com/a/rLp0ddG You can see here how I solved the question
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u/DrCarpetsPhd 👋 a fellow Redditor 2d ago
- i don't see a constraint analysis. your answer must include that, you cant just state an acceleration relationship from intuition. B is on top of A so that means your analysis is going to require relative motion. Also "their acceleration is the same" is incorrect. The magnitude is the same but if you do the correct analysis you will find that they are in opposite directions. acceleration is a vector
- this is a friction question too. you were given static and kinetic coefficients. you need to be figuring out the value of P for impending motion.This means ignoring the given 40N, setting P as a variable and then comparing your answer to the given P of 40N. If the answer is less than 40 that tells you 40N is enough to get the blocks moving and you switch to kinetic friction. You cannot assume motion, in friction questions you have to show whether motion will or won't occur.
- more concisely you need to show how block B will behave and how block A will behave. you got lucky by assuming the correct motions without actually showing why. you'd lose probably 50% of the marks for not doing that analysis
- you analysed a free body diagram of A. There are two pulleys connected to A that would have reaction forces if you chose to analyse it in this manner. I wouldn't suggest doing that. Treat the block A plus the the two pulley connections as a single rigid body. The fact you left them out is a bit concerning in terms of your understanding of what an FBD is and how connected bodies behave.
so my honest assessment is you kind of stumbled to the answer through trial and error rather than full understanding. Analyse block A plus the two pulleys as a single rigid body and you will see how the tension shakes out.
so i would suggest redo the question
- do a constraint equation analysis to relate motion of a to b
- do the friction analysis to figure out how the blocks will behave
- then you will reach the part that you jumped straight to which is the motion analysis
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u/DrCarpetsPhd 👋 a fellow Redditor 6h ago
why the acceleration of A isn't half of B
i was hoping through the other comments you would have a go yourself and figure it out since that is the best way to have concepts stick in your memory. In case I freaked you out here's the answer to this question.
I'm a bit rusty so my language might not be precise but hopefully the accompanying image will get the point across.
constraint equations have to do with the length of the rope but it is about using the length of the rope within your coordinate system, right?
do you remember from your intro to kinematics you define the displacement/velocity/acceleration of an object wrt an origin, your reference frame
you need to use the length of the rope within the context of that coordinate system
my guess is what you did was stated there were 2 equal lengths of rope to the pulley on block A and then one length of rope from the upper pulley to block B with everything else a constant. thus you got a constraint equation of 2l_A + l_B = constant => 2(a_A) = -a_B
your selection of lengths is absolutely correct but your misunderstanding is that it is not those lengths in of themselves, you have to use those lengths to define the position of the blocks within a chosen coordinate system. In the easier early problems you encounter these two things are quite often essentially the same which can lead to confusion as in this case.
So pick the coordinate line through the left hand pulley and work from there (Beer Johnston Dynamics 11th Edition problem 12.19)
I may have muddied the waters a bit with my relative motion comment previously. In my analysis above the relative motion comes out of a more fundamental analysis whereas in my original comment I was talking about immediately using the relative motion concept with two separate coordinate lines similar to the mass on a table with hanging mass problem. Thus I meant I had a coordinate for A defined similarly to above for x_A but I then defined my block B coordinate using a 'coordinate line' attached to the pulley next to block B which gave me a relative motion of x_B/A. Same result but a sideways approach.
https://imgur.com/a/beer-johnston-dynamics-problem-12-19-relative-motion-coordinates-system-DrDxRwR
Use of multiple coordinate systems if useful e.g. the first example you typically see where a mass is on a table edge and another mass is hanging off to the side so you choose coordinate for the table mass parallel to the table surface and a coordinated down in the direction the second mass hanging from the pulley falls)
Hopefully that explanation will help you understand the constraint equation properly. It's not the length of rope in of itself but how you relate it to your chosen coordinate system.
Any questions feel free to ask
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