Isaac physics - moments and collisions
Been trying this question for weeks , my teacher cant even do it. If anyone could supply a solution and answers I would be very grateful
Three particles A, B, and C lie at rest in that order in a straight line on a smooth horizontal table (completely elastic ) The particle A is then projected directly towards B with velocity u . Particle A collides with B which then collides with C , the masses of A, B, and C are m , 2m and 3m . the velocity v1 of A immediately after the collision with B is -u/3.
(a) Find the velocity w2 of B immediately after the collision with C, in terms of u and m .
(b) Find the velocity w3 of C immediately after the collision with B, in terms of u and m .
(c) What is the speed vf of the composite particle after the second impact, if the balls, of mass m , 2m and 3m , collided completely inelastically instead?
Many thanks.
Three particles A, B, and C lie at rest in that order in a straight line on a smooth horizontal table (completely elastic ) The particle A is then projected directly towards B with velocity u . Particle A collides with B which then collides with C , the masses of A, B, and C are m , 2m and 3m . the velocity v1 of A immediately after the collision with B is -u/3.
(a) Find the velocity w2 of B immediately after the collision with C, in terms of u and m .
(b) Find the velocity w3 of C immediately after the collision with B, in terms of u and m .
(c) What is the speed vf of the composite particle after the second impact, if the balls, of mass m , 2m and 3m , collided completely inelastically instead?
Many thanks.
Original post by Halleline
Been trying this question for weeks , my teacher cant even do it. If anyone could supply a solution and answers I would be very grateful
Three particles A, B, and C lie at rest in that order in a straight line on a smooth horizontal table (completely elastic ) The particle A is then projected directly towards B with velocity u . Particle A collides with B which then collides with C , the masses of A, B, and C are m , 2m and 3m . the velocity v1 of A immediately after the collision with B is -u/3.
(a) Find the velocity w2 of B immediately after the collision with C, in terms of u and m .
(b) Find the velocity w3 of C immediately after the collision with B, in terms of u and m .
(c) What is the speed vf of the composite particle after the second impact, if the balls, of mass m , 2m and 3m , collided completely inelastically instead?
Many thanks.
Three particles A, B, and C lie at rest in that order in a straight line on a smooth horizontal table (completely elastic ) The particle A is then projected directly towards B with velocity u . Particle A collides with B which then collides with C , the masses of A, B, and C are m , 2m and 3m . the velocity v1 of A immediately after the collision with B is -u/3.
(a) Find the velocity w2 of B immediately after the collision with C, in terms of u and m .
(b) Find the velocity w3 of C immediately after the collision with B, in terms of u and m .
(c) What is the speed vf of the composite particle after the second impact, if the balls, of mass m , 2m and 3m , collided completely inelastically instead?
Many thanks.
Can you post what you tried / what are you (your teacher) having problems with?
Presume is parts E..G in
https://isaacphysics.org/questions/three_collisions
(edited 4 weeks ago)
I'm not sure how to post pictures of my working ( and I don't have my notebook on me right now ) however we have mostly been trying to deprive the equation using KE= 0.5 x m x v^2 and p=mv and then solving for the velocity by substitution. I've also tried simultaneous equations but I keep getting the answer for Part D rather then Part E so I'm not sure what we are missing. My teacher was also trying to simplify it with fractions , he thought C would take a 1/6 of the 2/3 of the 1/2 from A's velocity but that wasn't right either.
Sorry if that's too brief ill post more of our working once I have my notebook.
Sorry if that's too brief ill post more of our working once I have my notebook.
Original post by Halleline
I'm not sure how to post pictures of my working ( and I don't have my notebook on me right now ) however we have mostly been trying to deprive the equation using KE= 0.5 x m x v^2 and p=mv and then solving for the velocity by substitution. I've also tried simultaneous equations but I keep getting the answer for Part D rather then Part E so I'm not sure what we are missing. My teacher was also trying to simplify it with fractions , he thought C would take a 1/6 of the 2/3 of the 1/2 from A's velocity but that wasn't right either.
Sorry if that's too brief ill post more of our working once I have my notebook.
Sorry if that's too brief ill post more of our working once I have my notebook.
It would be good to see what you tried and you can either post pictures here using the camera icon "upload image" in the (top) toolbar of the reply box or upload them to something like imgur and link them or just type the main points/equations.
Rather than using ke directly which gives quadratic-linear simultaneous equations to solve, restitution (a "simpler form of ke"), which uses the approach and seperation velocities, gives linear-linear equations (with momentum).
So really its just two linear simultaneous equations (linear restitution and linear momentum) in 2 unknowns to solve and it gives the correct ans, so fairly basic gcse maths. Using ke directly will also give the correct ans, but its just more work than necessary. It really helps to see what youre trying to do though/how youve set up the problem etc.
(edited 4 weeks ago)
Both of these got incorrect answers , there was more but can’t find them right now.
Me and my teacher went through your last reply but got it wrong again and we also tried using kinetic energy directly but again wrong (didn't get a picture of the working ) , I’ll try it again on my own now and I’ll post what I get. My teacher is also trying to use a more fractional route ( that B with have 2/5 of A’s velocity and C will have 3/5 due to the masses if I can remember what he said) once he sends me his working I’ll post it as well. Thank you so much for your help.
Original post by Halleline
Just completed part E! 
I used the 2/5 from the total mass of B+C and A’s velocity , -u/3. I also tried the same method for Part F but it must be something different , if you have any suggestions they would be greatly appreciated. Thank you!
Ok, thats (obv) the right answer, but Im confused about the working which is probably more important. So forget about the ans to E) and start again. Obv E and F are related, so
E and F represent the collision between B (2m, 2u/3, w) and C (3m, 0, v) and a sketch with that info marked on is important. So momentum conservation gives
(2m)(2u/3) = 2m*w + 3m*v
and restitution (or KE) gives
2u/3 - 0 = v - w
Solving those two equations should be easy for v and w? It shouldnt be more than about 5 relatively simple lines. There is some simple reasoning you can do such as C is at rest and B is lighter than C, then the direction of motion of B will be reversed (w negative) etc.
When you get it right, try it with KE and ask about what you dont understand. Im a bit surprised about the "writing fractions down" which your teacher seems to be saying rather than writing down the basic equations and solving them (properly).
(edited 4 weeks ago)
Original post by Halleline
Complete Part F also!
It’s so much simpler once I’ve done it , thank you again , I’ve very grateful for all your help!
I’ll try and attempt the last part but i don't really understand the question so I’ll try my best. I’ll keep ya updated!
It’s so much simpler once I’ve done it , thank you again , I’ve very grateful for all your help!
I’ll try and attempt the last part but i don't really understand the question so I’ll try my best. I’ll keep ya updated!
wbf, Id really try and get these parts "right" first and write them out clearly. If you assume you know w, then v is a "write down" as its simply
v - w = 2u/3
v = 2u/3 - 2u/15 = 8u/15
Youre doing a page of working when its 2 lines. Good you get the ans, but in an exam its too much work / mistakes are too likely.
Original post by Halleline
Complete Part F also!
It’s so much simpler once I’ve done it , thank you again , I’ve very grateful for all your help!
I’ll try and attempt the last part but i don't really understand the question so I’ll try my best. I’ll keep ya updated!
It’s so much simpler once I’ve done it , thank you again , I’ve very grateful for all your help!
I’ll try and attempt the last part but i don't really understand the question so I’ll try my best. I’ll keep ya updated!
If youre going onto G, completely inelastic means that the balls will coalesce in a collision. Again, restitution with a coefficient of 0 is simpler than KE (but equivalent).
I understand the importance of time management in an exam don’t worry , but for just a piece of homework I’d much rather take my time and make sure I understand the solutions before I focus on exam technique where I will eventually cut down the working out.
I tried your suggestion for v and w and it’s pretty much the same amount of working for me at least but as long as I understand where the answer was deprived from , even if it’s a lot of work , it makes no difference to me. Plus even if it’s a page of work it only took 5 minutes , the picture I sent was re-written to not cause any confusion as the original was really scribbly , so 15 mins total.
I’ll attempt G now I’ll let you know how for I get.
I tried your suggestion for v and w and it’s pretty much the same amount of working for me at least but as long as I understand where the answer was deprived from , even if it’s a lot of work , it makes no difference to me. Plus even if it’s a page of work it only took 5 minutes , the picture I sent was re-written to not cause any confusion as the original was really scribbly , so 15 mins total.
I’ll attempt G now I’ll let you know how for I get.
(edited 4 weeks ago)
Original post by Halleline
Thanks for the help!
Let me know if you would’ve done it a different way .
thats all you need, as long as youre happy that there are still two collisions etc.
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