Absolute independent motion

1. Mar 1, 2016

JustDerek

1. The problem statement, all variables and given/known data
I've been given a problem with pulleys which I have attached to this post. I've derived the equations shown in the post but I'll also write them below. What I'm struggling with is how to combine them.

2. Relevant equations
$l_1=S_a+2S_c$
$l_2=S_d+(S_d-S_c)$
$l_3=S_e+(S_e-S_c)$

In a similar example I've been given but with less pulleys it shows :
$l_1+l_2=S_a+4S_d$
This is the part I don't get. I don't get how the two equations combine to become that and I'm sure if I can understand that I can finish the rest.

3. The attempt at a solution

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2. Mar 1, 2016

Staff: Mentor

You can add the equations in any way you want. Something that gets rid of S_c and S_d is probably useful.

As an example, you have "+2 S_c" in the first equation and "-S_c" in the second one. You can multiply the second equation (both sides!) with two, then add the two equations.

3. Mar 1, 2016

Merlin3189

I'm not sure why you are trying to find $l_1, l_2\ and\ l_3$. There is no absolute value for them. Changing the length of any of them does not affect the velocity ratio nor the forces.
What I think you need to know are the velocity ratios and the force ratios, which you should be able to do by inspection in a simple example like this.
I would suggest the way to deal with the forces is to label one of them F or whatever, then write the others as multiples (or fractions.)

4. Mar 3, 2016

JustDerek

Managed to get there myself eventually but thanks for the intended help