Torque biomechanics

[Naucus]

TL;DR Summary: Solved the biceps, but having trouble finding the reaction force now.

I eventually calculated, using the moment, that the force exerted by the biceps is 1536 N (this is correct according to the model solution), but the calculation of the reaction force is more difficult. I was able to decompose the following forces into x and y components:


Fx Hand = 1.08 N
Fy Hand = 6.15 N


Fx Arm = 2.68
Fy Arm = 15.25


Fx Biceps = 125
Fy Biceps = 345


I'm unsure about the force in the rope; in the drawing, it's horizontal with the arm, so I thought the rope would only have a y-component.
But I also tried it with a 10° angle, and then my calculations still don’t work out.
→ Normally the force in the rope should be 367 N ((9.81 × 75)/2)."

 

[A.T.]

TL;DR Summary: Solved the biceps, but having trouble finding the reaction force now.

View attachment 359734
I eventually calculated, using the moment, that the force exerted by the biceps is 1536 N

I'm getting 1588 N for T in each arm, assuming both arms are loaded equally. This is ignoring the weight of the forearm & hand (since they are not given).

but the calculation of the reaction force is more difficult.

Ignoring the weight of the forearm & hand you have 3 force vectors acting on the forearm & hand:

F_biceps = T at 10° to vertically down
F_bar = half the bodyweight vertically up
F_elbow = contact force acting on the forearm in the elbow

These 3 vectors must add up to zero in both, X and Y direction. Then you solve this equilibrium equation for F_elbow and compute its magnitude.

 

[Naucus]

I'm getting 1588 N for T in each arm, assuming both arms are loaded equally. This is ignoring the weight of the forearm & hand (since they are not given).


Ignoring the weight of the forearm & hand you have 3 force vectors acting on the forearm & hand:

F_biceps = T at 10° to vertically down
F_bar = half the bodyweight vertically up
F_elbow = contact force acting on the forearm in the elbow

These 3 vectors must add up to zero in both, X and Y direction. Then you solve this equilibrium equation for F_elbow and compute its magnitude.

Thanks for the anwer!
Sorry forgot to add the weight of the arms and hand:
1. mHand: 0,64 kg
2. mforearm: 1,58kg
3.mupperarm: 2,48kg
And how/why can you ignore the rope force?

 

[A.T.]

Sorry forgot to add the weight of the arms and hand:
1. mHand: 0,64 kg
2. mforearm: 1,58kg
3.mupperarm: 2,48kg

Upper arm mass is not needed. Your vector equilibrium equation then also must include the combined weight of hand and forearm pointing vertically down.

And how/why can you ignore the rope force?

What rope? The person is hanging from a bar, see F_bar.

 

[Lnewqban]

Welcome, @Naucus !

Those numbers for x and y reactions that you show in your first post can't be correct.
Just like @A.T. , I'm getting 1588 N for each bicep.
The longitudinal compressing force in the Humerus bone should be 1227 N.

 

[A.T.]

Welcome, @Naucus !

Those numbers for x and y reactions that you show in your first post can't be correct.
Just like @A.T. , I'm getting 1588 N for each bicep.
The longitudinal compressing force in the Humerus bone should be 1227 N.

The OP was incomplete: The forearm & hand are not massless (see post #3).

But then I think the center of mass of forearm & hand should be given as well. Or are we to assume it's in the middle of those 34cm?

 

[Lnewqban]

The posted picture does not offer that additional information.
Then, maybe we should subtract those above-elbow four masses from the given total body mass.

Incorrectly perhaps, I just assumed no torque at shoulders or hands, and therefore similar lengths for elbow-hand grip and elbow-shoulder.

Then, I did the summation of forces at the elbow that is able to keep the shown static geometry.

Redoing it subtracting the above-elbow four masses from the given total body mass, I now get 94% less of each force:
The tension force should be 1493 N for each bicep.
The longitudinal compressing force in the Humerus bone should be 1154 N.

That value is far from the 1536 N according to the model solution.