Arm problem, Static Equilibrium

[Bones]

Homework Statement

(a) 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.

(b) 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

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?

 

[LowlyPion]

Consider the effect of the cosine component of the deltoid force back into the joint.

 

[thomate1]

To calculate the magnitude of the force FJ exerted by the shoulder joint on the upper arm, we can use the principle of static equilibrium. This principle states that for an object to be in equilibrium, the sum of all forces acting on it must be equal to zero, and the sum of all torques acting on it must also be equal to zero.

In this case, we can consider the upper arm as a rigid body in static equilibrium. This means that the forces acting on the upper arm, including the force FM from the deltoid muscle and the force FJ from the shoulder joint, must be balanced out by an equal and opposite force from the lower arm. Additionally, the torques from these forces must also be balanced out by the torque from the weight of the upper arm.

Using this information, we can set up the following equations:

∑F = FJ - FM - mg = 0

∑τ = FJ(0.12m) - FM(0.12m) + (mg)(0.24m)sin15 = 0

Plugging in the values we know, we can solve for FJ:

FJ = FM + mg = (250N) + (3.3kg)(9.8m/s^2) = 282.84N

Therefore, the magnitude of the force FJ exerted by the shoulder joint on the upper arm is approximately 282.84N.