Atwood machine mass accleration problem

[Benzoate]

Homework Statement

A light pulley can rotate freely about its axis of symmetry which is fixed in a horizontal position. A massless inextensible string passes over a pulley . At one end the string carries a mass 4m, while the other end supports a second massless pulley. A second string passes over the pulley and carries masses m and 4m at its ends. The whole system undergoes planar motion with masses moving vertically. find the acceleration of each of those masses.

Homework Equations

Newton's second Law of motion, F(net)=m*a

The Attempt at a Solution

The problem tells me I have to find the acceleration of 3 masses, two of which are attached to the second pulley.

There are Two physical systems I want to concentrate on containing four force equations I want to write outs: The first physical system will focus on the Atwood machine where the two ends of a string hold the 4m mass and the mass less atwood machine. The second physical system will include the massless pulley at the end of the string containing the first pulley. there will be force equations for the m and 4m masses, both of which are attached at the two ends of the string containing the massless pulley. Therefore, I should have a total of four force equations.

Atwood machine where there is a 4m mass and massless pulley attached to the ends of each string:

T-4*mg=4m*dv/dt; -T+m*g=m*dv/dt

since the pulley is massless, m= 0 and therefore T=0 and therefore dv/dt=0, which cannot be right since the problem states that the the whole systems undergoes planar motion and therefore the system must have some acceleration.

Atwood machine containing masses m and 4m.

4mg-T'=4*m*dv'/dt, T-mg=m*dv'/dt

Therefore, dv'/dt= g, which isn't right because if the acceleration of the all 3 masses were just g, the masses wouldn't have any tension



Atwood machine where the 4m and m

 

[edziura]

"Atwood machine where there is a 4m mass and massless pulley attached to the ends of each string:

T-4*mg=4m*dv/dt; -T+m*g=m*dv/dt

since the pulley is massless, m= 0 and therefore T=0 and therefore dv/dt=0, which cannot be right since the problem states that the the whole systems undergoes planar motion and therefore the system must have some acceleration."

If your 1st system (free body diagram) is as you describe, there are two forces you have omitted in your equation: the two tension forces applied to the 2nd massless pulley by the second string supporting the m and 4m masses at its end.