Mechanics- Connected Particles
Two particles P and Q of masses 20kg and m kg are connected by a light inextensible rod. The particles lie on a smooth horizontal plane. A horizontal force of 60N is applied to Q in a direction towards P, causing the particles to move with acceleration 2 m s^2.
Could anyone help me with this?
Could anyone help me with this?
Original post by Illidan2
Two particles P and Q of masses 20kg and m kg are connected by a light inextensible rod. The particles lie on a smooth horizontal plane. A horizontal force of 60N is applied to Q in a direction towards P, causing the particles to move with acceleration 2 m s^2.
Could anyone help me with this?
Could anyone help me with this?
Sure, but what's the question, and what's making you stuck?
Oh wow. I forgot to post the question! Sorry. So, i've given you the relevant information, but the question is:
Find the mass, m, of Q.
Now, I drew a diagram (you know by now how poor my presentation is, so I haven't included it), but it isn't exactly like the diagram in the solution. The solution appears to have a force of 60N leading AWAY from P, rather than towards it (i'll show you what I mean in a screenshot).
In every other regard, for practical purposes, my diagram is the same as the one in the solution, except that I have the 60N arrow drawn the opposite way to the diagram in the solution(and the direction of acceleration to match it). This in itself is something I am "stuck" on, as I am confused as to why this is the case.
Naturally, I used F=ma, but ended up with m=30, when I know m should really be 10(as I checked my answer in the solution afterwards)
Also, why is T not factored into the equation F=ma? Or is this just because F would be 60+T-T, and therefore the two Ts in opposite directions cancel each other out?
Find the mass, m, of Q.
Now, I drew a diagram (you know by now how poor my presentation is, so I haven't included it), but it isn't exactly like the diagram in the solution. The solution appears to have a force of 60N leading AWAY from P, rather than towards it (i'll show you what I mean in a screenshot).
In every other regard, for practical purposes, my diagram is the same as the one in the solution, except that I have the 60N arrow drawn the opposite way to the diagram in the solution(and the direction of acceleration to match it). This in itself is something I am "stuck" on, as I am confused as to why this is the case.
Naturally, I used F=ma, but ended up with m=30, when I know m should really be 10(as I checked my answer in the solution afterwards)
Also, why is T not factored into the equation F=ma? Or is this just because F would be 60+T-T, and therefore the two Ts in opposite directions cancel each other out?
(edited 6 years ago)
Original post by Illidan2
...
Firstly, note that the two particles are connected by an inextensible rod therefore if you push P in the direction of Q, then you're pushing the entire system in the direction of Q (from P). Easier to think about it as a physical object in front of you, an inextensible rod would be something like a metal bar connecting the two particles - hence pushing Q in the direction of P pushes the whole system as I've mentioned.
As for why T isn't included, it's because Newton's Third Law tells us that internal forces cancel each other out (which in this case is the tension inside the rod) hence having no effect on the overall motion
Original post by RDKGames
Firstly, note that the two particles are connected by an inextensible rod therefore if you push P in the direction of Q, then you're pushing the entire system in the direction of Q (from P). Easier to think about it as a physical object in front of you, an inextensible rod would be something like a metal bar connecting the two particles - hence pushing Q in the direction of P pushes the whole system as I've mentioned.
As for why T isn't included, it's because Newton's Third Law tells us that internal forces cancel each other out (which in this case is the tension inside the rod) hence having no effect on the overall motion
As for why T isn't included, it's because Newton's Third Law tells us that internal forces cancel each other out (which in this case is the tension inside the rod) hence having no effect on the overall motion
I see! This makes perfect sense. Does this then apply to strings, too? When two particles are connected by anything inextensible, I should always treat them as a single system? Does this work for any number of connected particles too, or is this only in the specific case of two joined by a single inextensible rod/string?
Original post by Illidan2
I see! This makes perfect sense. Does this then apply to strings, too?
Not really, a string can be inextensible but it can also be slack which is what would happen when the distance between P and Q would be less than the natural length of the string.
When two particles are connected by anything inextensible, I should always treat them as a single system?
No, this depends on context.
Does this work for any number of connected particles too, or is this only in the specific case of two joined by a single inextensible rod/string?
If you want to extend your question to an arbitrary amount of particles joined up by an inextensible rod, then yeah the principle remains the same.
Thank you!Original post by RDKGames
Firstly, note that the two particles are connected by an inextensible rod therefore if you push P in the direction of Q, then you're pushing the entire system in the direction of Q (from P). Easier to think about it as a physical object in front of you, an inextensible rod would be something like a metal bar connecting the two particles - hence pushing Q in the direction of P pushes the whole system as I've mentioned.
As for why T isn't included, it's because Newton's Third Law tells us that internal forces cancel each other out (which in this case is the tension inside the rod) hence having no effect on the overall motion
As for why T isn't included, it's because Newton's Third Law tells us that internal forces cancel each other out (which in this case is the tension inside the rod) hence having no effect on the overall motion
It says it applies a force to Q in the direction of P, in your response you said if you push P in the direction of Q. Using your logic stated pushing Q in the direction of P should cause an acceleration in the direction of P, however in the diagram in the answers it shows the acceleration going away from from P. I may be silly and missing something but I really cant wrap my head around this, any help would be great.
(edited 1 month ago)
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