Can someone check my solution to this block and tackle problem

[vande060]

Homework Statement

you absolutely need to check the link for my problem picture; this is a snapshot of my online book.

http://s861.photobucket.com/albums/ab174/alkaline262/?action=view&current=prob9-1.jpg

Homework Equations

f=ma

The Attempt at a Solution

as you can see from the picture I have let each of the strings dangling be represented by an x value

so:

3x1 + x2 = length of rope

differentiating twice

3a1 + a2 = 0

and the equations for m1 and m2:

m1a1 = -3T + m1g

m2a2 = -T +m2g

next step is to add these two equations together and set equal to zero

3(a1 = -3T/m1 + g)

+(a2 = -T/m2 +g)
----------------------

3a1 + a2 = 4g -T( 9/m1 + 1/m2) = 0

solving for T = 4g/( 9/m1 + 1/m2)

then i can just plug this into the above a1 and a2 equations to get acceleration right??

and the tension of that tiny little rope below the center pulley till be 2T.

what do you think? Have I made any mistakes

 

[anathema]

?



Thank you for sharing your approach to solving this problem. I appreciate how you have represented the strings with x values and used differentiation to find the accelerations. Your equations for m1 and m2 also seem correct.

However, I would recommend double-checking your final equation for T. It seems like you have made a small mistake with the signs, as the tension should be positive since it is pulling up on the masses. Additionally, it may be helpful to label the masses and pulleys in your equations to keep track of which values correspond to which objects.

Overall, your approach seems reasonable and I think you are on the right track. Keep up the good work! If you have any further questions or would like to discuss your solution further, please don't hesitate to reach out.