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2 masses connected by a string wrapped around a massless pulley, F applied to pulley. 
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#1
Feb412, 12:28 PM

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1. The problem statement, all variables and given/known data
m_{1} and m_{2} are connected by a massless string wrapped around a massless pulley. An external force F is applied to the pulley. m_{1} does not equal m_{2} find the acceleration of each mass, the tension in the string, and the acceleration of the pulley. F external and m_{1} and m_{2} are known. there is no gravity or friction in the problem. 2. Relevant equations F=ma 3. The attempt at a solution What i've worked out so far is that we must consider two reference frames to determine the accelerations. If we can calculate the acceleration of the pulley and the acceleration of one of the masses, the acceleration of the other mass should be determined. If we consider the pulley's reference frame, one of the masses will be accelerating toward the pulley and the other mass will be accelerating with an equal and opposite acceleration. If we consider m_{1}, we see the pulley accelerating toward m_{1} and m_{2} accelerating with an equal acceleration. how can we combine these two reference frames to determine the accelerations in the lab frame? is the acceleration of the center of mass of the system relevant? 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 


#2
Feb412, 12:53 PM

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hi tonicandgin! welcome to pf!
call the position of the pulley x, call the length of string between the pulley and m_{1} and m_{2}, respectively, L_{1} and L_{2} … and use the fact that L_{1} + L_{2} must be constant … what do you get? 


#3
Feb412, 08:18 PM

P: 3

thanks for the response.
to clarify: what do you mean by "call the position of the pulley x"? is that its position before the force is applied and everything starts moving? or does x change as the system moves? what i have so far is: call position of the pulley x. call the length between pulley and the 2 masses L_{1} and L_{2}, respectively then position of m_{1} = x  L_{1} + 1/2 a_{m1}t^{2} and position of m_{2} = x  L_{2} + 1/2 a_{m2}t^{2} i've done a bunch of algebra trying to make use of L_{1} + L_{2} = L but nothing seems useful. I think what i should do is write position equations for each mass and then take two time derivatives to get acceleration, but the only position equations i can write include the accelerations I'm looking for in the first place. 


#4
Feb512, 04:40 AM

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2 masses connected by a string wrapped around a massless pulley, F applied to pulley.
hi tonicandgin!
(just got up …) then you get … position of m_{1} = x  L_{1} position of m_{2} = x  L_{2} then call the tension T, and do F = ma for each mass separately … what do you get? 


#5
Feb612, 05:48 PM

P: 3

thanks for the help. so far I have:
a_{1}  a_{r} = a_{p} a_{2} + a_{r} = a_{p} where a_{r} is the relative acceleration of each mass with the pulley. ( m_{1}x_{1} + m_{2}x_{2} ) / ( m_{1} + m_{2} ) is the center of mass of the system. if we take two time derivatives we get ( m_{1}a_{1} + m_{2}a_{2} ) / ( m_{1} + m_{2} ) which must equal the only external force, F. F must = 2T this is as much as i could get out of my professor today, he seemed to think it was solvable from here, but i still feel like there are too many unknowns and not enough equations. 


#6
Feb712, 04:38 AM

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hi tonicandgin!
(just got up …) yes, there are two ways doing it your can either start with F = ma for the centre of mass, as your professor suggests, or you can just do F = ma for each of the three bodies separately 


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