Static Equilibrium of deltoid muscle

In summary, the problem asks for the calculation of the magnitude of the force, FM, required by the "deltoid" muscle to hold up an outstretched arm with a total mass of 3.3 kg. The force FJ exerted by the shoulder joint on the upper arm also needs to be calculated. To solve this problem, equations for the X and Y directions are used, taking into account the force of weight and the force of the object. In the X direction, the equation is Fjcos(theta)-Fmcos15=0, while in the Y direction, the equation is -Fjsin(theta)+Fmsin15-32.3N-83.3N=0. By solving
  • #1
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Homework Statement


Calculate the magnitude of the force, FM, required of the "deltoid" muscle to hold up the outstretched arm shown in the figure. The total mass of the arm is 3.3 kg. Then, calculate the magnitude of the force FJ exerted by the shoulder joint on the upper arm.
http://www.webassign.net/gianpse4/12-56.gif



Homework Equations





The Attempt at a Solution


We did a problem similar to this in class, but there was a 8.5kg object in the hand.
X direction:
Fjcos(theta)-Fmcos15=0

Y direction: Force of weight=32.2N
-Fjsin(theta)+Fmsin15 Force of object=83.3N
-32.3N-83.3N=0

tnet=Fm(0.12m)(sin15)-32.3N(0.24m)(sin90)-83.3N(0.52m)(sin90)=0
Fm=1644N

How would you this problem change is there is no weight in the hand like the above problem suggests?
 
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  • #2
If there was no weight, you would not include the force of gravity from that weight or the torque caused by that force in your calculations.
 
  • #3
Does this mean I just leave it out or do I alter the equation in some way?
 
  • #4
I got part a:
tnet=mg(24m)-Fmsin15(0.12m)=0
Fmsin15(0.12m)=(3.3kg)(9.8m/s^2)(0.24m)
Fm=(3.3kg)(9.8m/s^2)(0.24m)/0.03106m
Fm=250N

How do I figure out Fj for part b?
 

1. What is the deltoid muscle?

The deltoid muscle is a large, triangular-shaped muscle located in the shoulder region. It is responsible for various movements of the arm, including shoulder abduction, flexion, and extension.

2. How does the deltoid muscle maintain static equilibrium?

The deltoid muscle maintains static equilibrium by balancing the forces acting on the shoulder joint. This is achieved through a combination of isometric contractions and coordination with other muscles in the shoulder and arm.

3. What factors affect the static equilibrium of the deltoid muscle?

The static equilibrium of the deltoid muscle is affected by several factors, including the position and movement of the arm, the angle of the shoulder joint, and the strength and coordination of other muscles in the shoulder and arm.

4. How does the shape of the deltoid muscle contribute to its static equilibrium?

The triangular shape of the deltoid muscle allows for a wide range of movements and provides stability to the shoulder joint. It also allows for the distribution of forces across different regions of the muscle, helping to maintain static equilibrium.

5. What are the potential consequences of an imbalance in the static equilibrium of the deltoid muscle?

An imbalance in the static equilibrium of the deltoid muscle can lead to shoulder instability, decreased range of motion, and increased risk of injury. It can also affect the overall function and performance of the arm, as the deltoid muscle is involved in many activities and movements.

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