Static Equilibrium of the Arm

[Kalie]

You are able to hold out your arm in an outstretched horizontal position because of the action of the deltoid muscle. Assume the humerus bone has a mass m=3.6, length L=0.66 and its center of mass is a distance L1=0.33 from the scapula. (For this problem ignore the rest of the arm.) The deltoid muscle attaches to the humerus a distance L2=0.15from the scapula. The deltoid muscle makes an angle of 17 degrees with the horizontal, as shown.
http://session.masteringphysics.com/problemAsset/1011051/15/MTS_st_20_a.jpg
http://session.masteringphysics.com/problemAsset/1011051/15/MTS_st_20_b.jpg
Use throughout the problem.

A. Find the tension in the deltoid muscle.

I solved this T= 256, because the some of the torques is equal to 0 which is equal to mL1g-Tsin(theta)L2

B.Using the conditions for static equilibrium, find the magnitude of the vertical component of the force exerted by the scapula on the humerus (where the humerus attaches to the rest of the body).

This is whre I am lost. I know that there are three vertical forces in this problem: the force of gravity acting on the bone, the force from the vertical component of the muscle tension, and the force exerted by the scapula on the humerus (where it attaches to the rest of the body), but i don't know what to do with this.

C.Now find the magnitude of the horizontal component of the force exerted by the scapula on the humerus.
Same thing don't know what to do

Please Help I have been sitting here for hours
Thanks

 

[OlderDan]

Apply the weight of the humerous at its center of mass. Resolve the deltoid tension into horizontal and vertical components. Include the horizontal and vertical components of the force exerted by the scapula. Write two equations of equilibrium; one for vertical and one for horizontal.

 

[kyle8921]

for your question! Let's break down the problem step by step to help you find the answers for parts B and C.

First, let's review the concept of static equilibrium. In order for an object to be in static equilibrium, the net force acting on it must be zero and the net torque (rotational force) must also be zero. This means that the object is not moving and is not rotating.

In this problem, we are looking at the static equilibrium of the arm, specifically the humerus bone. We know that the deltoid muscle is exerting a force on the humerus, which allows us to hold our arm in an outstretched horizontal position. This force from the deltoid muscle is represented by the tension T in the muscle.

Now, let's look at the forces acting on the humerus bone. We have the force of gravity acting downwards, and the force from the deltoid muscle acting upwards at an angle of 17 degrees from the horizontal. We also have the force exerted by the scapula on the humerus (where it attaches to the rest of the body).

To solve for the magnitude of the vertical component of the force exerted by the scapula on the humerus, we need to use the condition for static equilibrium: the net force acting on the humerus must be zero. This means that the vertical component of the force exerted by the scapula must be equal in magnitude and opposite in direction to the force of gravity acting on the humerus. We can set up an equation to represent this:

Fscapula + Fgrav = 0

We know the mass of the humerus (m=3.6) and the acceleration due to gravity (g=9.8). We also know that the angle between the force of gravity and the horizontal is 90 degrees, so we can use trigonometry to find the vertical component of the force of gravity:

Fgrav = mgcos(90) = 0

Therefore, we can simplify our equation to:

Fscapula = 0

This means that the magnitude of the vertical component of the force exerted by the scapula on the humerus is zero, because the scapula is exerting an equal and opposite force to counteract the force of gravity.

Now, for part C, we need to find the magnitude of the horizontal component of the force exerted by the scapula on the humerus.