Diagram & Calculations for Pulley System with Masses 8kg, 2kg, and 4kg

[mcintyre_ie]

I’d appreciate some help with the following question:

The diagram shows a light inextensible string
having one end fixed at O , passing under
a movable pulley A of mass 8 kg and
then over a fixed light pulley B.
The other end of the string is attached to
a light pulley C, of negligible mass.
Over pulley C , a second light inextensible
string is passed having particles of mass 2 and
4 kg respectively, attached. All pulleys are smooth.
(i) Show in a diagram the forces acting on each pulley when the system is released from rest.
(ii) Find the acceleration of
pulley A
pulley C
each particle.

Heres a link to the work I've done so far which i think i have correct (Ive spent about an hour working on my equations, but theyre not making much sense).

Work So Far

The correct answers are:
(ii)
Pulley A - g/11
Pulley C - 2g/11
Particles - g/11 and 5g/11

Im unsure if my accelerations are correct - would i be right in saying that for every 1m Pulley A falls, pulley C rises two metres, along with both particles? So that would mean pulley C has twice the acceleration of Pulley A? And both particles move with the acceleration f +/- 2a?

Thanks in advance for any help.

 

[Doc Al]

Originally posted by mcintyre_ie
Im unsure if my accelerations are correct - would i be right in saying that for every 1m Pulley A falls, pulley C rises two metres, along with both particles? So that would mean pulley C has twice the acceleration of Pulley A? And both particles move with the acceleration f +/- 2a?

Almost, but not exactly. Yes, pulley C has twice the acceleration of pulley A (in magnitude). If you call the acceleration of pulley A "a" (down), then the acceleration of pulley C is "2a" (up). When you write out your equations, be sure to use a consistent sign convention. For example, the way I would look at it, your first equation should read 2S - 8g = -8a (since you've chosen up as positive).

Also, if "f" is the magnitude of the acceleration of the particles with respect to pulley C, then the full acceleration of the particles would be: 2a +/- f. Once again, use a consistent sign convention when writing the equations.

 

[mcintyre_ie]

Thanks for your reply, I am constantly mixing up signs. Thanks again for your help.