Pulley System equilibrium problem

[Dcarroll]

Homework Statement

If the system below is in equilibrium, show that tan(Theta) = 1 + (2M/m)

View attachment Doc1.doc

Homework Equations

F=ma

The Attempt at a Solution

I was pretty confused with this problem. All I think I know is that the force being pulled downward on M is F=mg/2. Can someone explain to me how to solve the next part?

 

[berkeman]

Homework Statement

If the system below is in equilibrium, show that tan(Theta) = 1 + (2M/m)

View attachment 29838

Homework Equations

F=ma

The Attempt at a Solution

I was pretty confused with this problem. All I think I know is that the force being pulled downward on M is F=mg/2. Can someone explain to me how to solve the next part?

Can you post your Free Body Diagram (FBD) sketches of the two masses for this problem? That's usually a good first step in this type of problem.

 

[Dcarroll]

Ok I tried drawing the free body diagrams for the masses-

View attachment Doc1.doc

 

[berkeman]

Ok I tried drawing the free body diagrams for the masses-

View attachment 29854

That's a start. I don't think you can write the upper right vector on M just yet, though. Now, for each FBD, what equations do you write, and how do you use them to solve for the tensions?

 

[Dcarroll]

Well don't I have the equations in my FBD? For example the tension force caused by "m" is F=mg, and the two tensions for the strings holding "m" up are F=mg/2? I am just confused on what to do next. We have never done any problems like this

 

[berkeman]

Well don't I have the equations in my FBD? For example the tension force caused by "m" is F=mg, and the two tensions for the strings holding "m" up are F=mg/2? I am just confused on what to do next. We have never done any problems like this

I was thinking of the component-wise sums of forces. The Fx and Fy sums need to each sum to zero, right? That should be how you can work out the final tensions, especially for mass M.