How to Calculate the Mass for Static Equilibrium of a Suspended Leg?

[needhelp83]

Calculate the mass, m, needed in order to suspend the leg shown in Problem 12-5. Assume the leg (with cast) has a mass of 15.0 kg, and its CG is 35.0 cm from the hip joint; the sling is 80.5 cm from the hip joint.


How do I set this up? What equations should be used with this?

 

[teknodude]

Any chance you can post a diagram of the figure?

The only equations you need are the ones for static equilibrium.

 

[needhelp83]

Here's the diagram

 

[needhelp83]

What are your static equilibrium equations?

 

[needhelp83]

I meant what are the static equilibrium equations that I need for this

 

[trajan22]

what does static equilibrium mean?

 

[kaitamasaki]

uh from what i learned..

1.draw a free body diagram
2. in an equations u sum the forces (in this case in the vertical direction) and they add up to 0 since its static equilibrium
3. pick a Point on the free body diagram and sum the torques around it

I don't know if you learned this yet, but that is the way I do it. I am half confused abou the diagram so my answer was 1.73 kg

I am thinking that a force CG is applying up on the "leg", and so is the force of mass of weight x 9.8 through the cable/string, and that at the centre of the leg there is a gravitational force pulling down.

so i sum the forces in y direction: CG + (mass of weight)g - (mass of leg)g = 0

I don't know if I am on the right track, but basically all forces add up to equal ZERO, because in static equilibrium NOTHING MOVES

its not FN = ma

 

[teknodude]

Start out with a free body diagram of just the leg + sling. You will have forces from the weight of the leg(acting at CG), the hipjoint and the tension from the sling. Note that you have a pulley and probably assuming it is frictionless.
Once you have the diagram set up, you should see how to solve it. Anything else will just give too much of the problem away.

The equations of static equilibrium are the sum of x and y forces equal zero. Also the equation of moments or torques in your case.

 

[needhelp83]

Et=(35.0 cm)(g)(x)-(15 kg)(80.5 cm)(g)
x=34.5 kg

Is this what you mean?