Calculate the force required of the "deltoid" muscle, Fm, to hold up the outstretched arm shown in the figure below. The total mass of the arm is 3.31kg. Assume that alpha = 15.2°, d = 12.0 cm and D = 24.0 cm.

Figure: tinyurl com/hszqaqw

Any help (at least how to set up the problem) would be great, thanks!

To calculate the force required of the deltoid muscle (Fm) to hold up the outstretched arm, we need to consider the equilibrium of forces acting on the arm. First, let's set up the problem by identifying the forces involved:

1. Weight of the arm (W): The total mass of the arm is given as 3.31 kg. We can calculate the weight using the formula: W = mg, where g is the acceleration due to gravity (approximately 9.8 m/s^2).

2. Force exerted by the deltoid muscle (Fm): This is the force we need to find.

3. Torque due to the weight of the arm (τw): Torque is the tendency of a force to cause rotation. The torque due to the weight of the arm acts around the shoulder joint. We can calculate it using the formula: τw = r × W, where r is the distance between the shoulder joint and the line of action of the weight force.

4. Torque due to the deltoid muscle force (τm): Similarly, there is a torque due to the deltoid muscle force. We can calculate it using the formula: τm = D × Fm × sin(alpha), where D is the distance between the shoulder joint and the line of action of the deltoid muscle force, and alpha is the angle between these two.

The arm is in equilibrium when the torques due to the weight and the deltoid muscle force are balanced.

Once we set up the problem with the forces and torques, we can solve for the force required of the deltoid muscle (Fm).