Trouble with Static Equilibrium

[rtareen]

Homework Statement

You hold a 6.0-kg weight in your hand with your forearm making a 90° angle with your
upper arm, as shown in Figure 12-4. Your biceps muscle exerts an upward force Fm that acts 3.4 cm from the pivot point O at the elbow joint. Model the forearm and hand as a 30.0-cm- long uniform rod with a mass of 1.0 kg. (a) Find the magnitude of Fm if the distance from the weight to the pivot point (elbow joint) is 30 cm, and (b) find the magnitude and direction of the force exerted on the elbow joint by the upper arm

Relevant Equations

$\Sigma \Vec{\Tau }= 0$
$\Signma \Vec{\F} = 0$

My initial response to seeing the figure is what is $F_{ua}$ and where does it come from? How was i supposed to know it was there is they didn't give a picture?

So for part a, $F_{ua}$ doesn't play a role because it exerts no torque, and apparently we are supposed to use the torque equation to find $F_m$. Thats probably the only way to do this problem is to use the torque equation first, because if we used the force equations, we'd have two equations and three unknowns, I think. We would have to solve for the y component of $F_m$ and also both components of $F_{ua}$. But if there is another way to solve this problem please let me know.

So we can set $\Sigma \Tau = 0$ to find $F_m$ and we find that it is 560N. Then we can set the x and y components of force equal to zero and we find out that the x component of $F_{ua}$ is 0. That must mean that $F_{ua}$ is vertical only. And we find out that its 490 N downwards.

My main question is how was i supposed to know about $F_{ua}$.

Also there is this concept where you can set the net torque to be zero about any point on the object of interest, not just at O. Can someone explain how we could do that? These static equilibrium problems are hard.

Also in the preview my latex code isn't being converted. Can someone tell me why?

 

[andrewkirk]

My initial response to seeing the figure is what is $F_{ua}$ and where does it come from? How was i supposed to know it was there is they didn't give a picture?

I think that is the force exerted on the radius and/or ulna (forearm bones) by the humerus (upper arm bone). The end of the humerus provides the pivot point around which the forearm rotates, so it has to press down as the forearm rotates up.

That must mean that $F_{ua}$ is vertical only. And we find out that its 490 N downwards.

That sounds reasonable. In practice I'd guess it points down and a bit to the right, to counteract the sideways component from the bicep which will be pulling the forearm up and a bit to the left.

I have been encountering a few latex bugs on the forum recently too. However the red bold text in your above latex is because of misspelling and using upper case letters where all lower case is required. Latex is case-sensitive.

 

[Lnewqban]

... My initial response to seeing the figure is what is $F_{ua}$ and where does it come from? How was i supposed to know it was there is they didn't give a picture?
...
My main question is how was i supposed to know about $F_{ua}$.

Without that reactive force, all the other forces that were evident to you would create a clockwise rotation of the forearm.
The mechanism must be in static equilibrium, which means that all the forces and torques should be cancelling each other.
Having the reactive force in place, the net moment will be zero, regardless of where along the forearm you decide to locate its fulcrum.

Please, see:
https://www.engineeringtoolbox.com/equilibrium-d_943.html

http://www.engineeringcorecourses.c...ium/C2.1-freebodydiagram-and-supports/theory/

 

[rtareen]

Without that reactive force, all the other forces that were evident to you would create a clockwise rotation of the forearm.
The mechanism must be in static equilibrium, which means that all the forces and torques should be cancelling each other.
Having the reactive force in place, the net moment will be zero, regardless of where along the forearm you decide to locate its fulcrum.

Please, see:
https://www.engineeringtoolbox.com/equilibrium-d_943.html

http://www.engineeringcorecourses.c...ium/C2.1-freebodydiagram-and-supports/theory/

 

[rtareen]

Wow thanks for the helpful links!

 

[Lnewqban]

Wow thanks for the helpful links!

You are welcome