The arm in the figure below weighs 44.5 N. The force of gravity acting on the arm acts through point A. Determine the magnitudes of the tension force t in the deltoid muscle and the force s of the shoulder on the humerus (upper-arm bone) to hold the arm in the position shown.

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We are unable to help, since we don't have the figure to determine where point A is or what position the arm is in.

To determine the magnitudes of the tension force t in the deltoid muscle and the force s of the shoulder on the humerus, we can start by analyzing the forces acting on the arm in equilibrium.

In this case, we have three forces acting on the arm: the weight of the arm acting downward, the tension force t in the deltoid muscle acting upward, and the force s of the shoulder on the humerus acting downward.

Since the arm is in equilibrium, the sum of the forces acting on it must equal zero. This can be expressed as:

ΣF = 0

Considering the vertical components of the forces, we have:

t - s - 44.5N = 0

The weight of the arm is acting downward and is given as 44.5N, so we can substitute it into the equation. Rearranging the equation, we get:

t - s = 44.5N

Now, let's consider the moments (or torques) acting on the arm. Since the arm is not rotating, the sum of the moments acting on it must also equal zero.

In this case, we can consider the moments about point A, where the force of gravity acts. The moment due to the weight of the arm is given by:

Moment due to weight = weight * distance from A to weight

Since the weight acts through point A, the distance from A to weight is zero. Therefore, the moment due to weight is zero.

The moment due to the tension force t can be calculated as:

Moment due to tension force t = t * distance from A to t

We don't have the distance from A to t provided, so we cannot determine the exact value of this moment.

Lastly, the moment due to the force s can be calculated as:

Moment due to force s = s * distance from A to s

Again, we don't have the distance from A to s provided, so we cannot determine the exact value of this moment.

Since the arm is in equilibrium, the sum of the moments acting on it must equal zero. Therefore, we can write:

ΣM = 0

Moment due to weight + Moment due to tension force t + Moment due to force s = 0

0 + Moment due to tension force t + Moment due to force s = 0

Moment due to tension force t + Moment due to force s = 0

From this equation, we can see that we need more information (the distances from A to t and to s) to solve for the magnitudes of the tension force t and the force s of the shoulder on the humerus.