Tension downward acceleration problems

[dkgojackets]

Im supposed to find T1 and T2 using m1, m2, and g. The whole system is accelerating downwards with magnitude g/2.

Maybe if I get this I can figure out the more complex ones. Thanks.

 

[OlderDan]

Im supposed to find T1 and T2 using m1, m2, and g. The whole system is accelerating downwards with magnitude g/2.

Maybe if I get this I can figure out the more complex ones. Thanks.

Draw free body diagrams for both the masses and see if you can work it out. We will help you if you show us your attempt.

 

[dkgojackets]

Its tough to put in paint, but for m1 I have T1 going up, T2 going down, and .5(m1)g going down. On m2 I have T2 up and .5(m2)g down.

Looking at m2, I have the sum of forces being T2 - .5(m2)g

I'm not used to having the system accelerate, but right now I can only think of making T2 = .5(m2)g. T1 would be .5(m1 + m2)g then. I just don't think that is correct.

 

[dkgojackets]

Nevermind, it is :)

 

[dkgojackets]

OK here's the one I am really stuck on. I am just not completely sure what's going on. I'm looking for T. The units are kg for mass of the blocks, and I am assuming massless/frictionless pulleys.

I drew the FBD for each mass, I am just not sure how to connect it all.

 

[dkgojackets]

So far I am thinking about trying to balance the force on each side of that middle pulley. I have the total mass on the right side that its carrying as 7+2.5? (since half of that 5 is attached the the "floor".) For the left side, I am thinking the mass there now is .5 (half of the 1 is attached to the "ceiling", so I need to get another 9 kgs (and 9 x 9.8 = 88.2 N as T).

Is this completely wrong thinking?

 

[OlderDan]

OK here's the one I am really stuck on. I am just not completely sure what's going on. I'm looking for T. The units are kg for mass of the blocks, and I am assuming massless/frictionless pulleys.

You have two strings and therefore two tensions. You need to know how far each mass moves in relation to the other masses. With that information, your FBDs should get you a solvable system of equations.

 

[dkgojackets]

Still stuck. I think I am missing the effect that the masses have when they are attached to the pulley, not the actual string.

 

[OlderDan]

Still stuck. I think I am missing the effect that the masses have when they are attached to the pulley, not the actual string.

I think I misinterpreted the problem. Nothing is moving here? Is that correct?

It is so frustrating when this system freezes up like this. I’ve been frozen out for a long time.
In case I cannot get back in, here is what I have assuming nothing is moving.

TL is the tension in the upper left string
TR is the tension in the lower right string.

T + 1kg*g = 2TL
TL = 7kg*g + 2TR
TR = 5kg*g

 

[dkgojackets]

Thank you. That makes sense now.