An adult person is holding their arm straight out to their side. Their kid is hanging from their wrist, dangling. The kid has a mass of 20 kg. The length of adult’s arm between the shoulder and the wrist from which the kid is hanging is 0.7 m. The mass of the arm is 2.5 kg, and its center of mass is halfway along its length. The deltoid muscle is supporting all of this, generating a force directed at 14° above the arm and toward the body’s centerline. The deltoid muscle attaches to the arm at 15 cm from the shoulder. Find the magnitude of the force generated by this muscle.

The sum of torques about the shoulder is zero =>

mg•0.35 +Mg•0.7 -F•sinα•0.15 =0
F= g(m•0.35 +M•0.7)/ sinα•0.15=
=9.8(2.5•0.35+20•0.7)/0.24•0.15=
=4049 N.

To find the magnitude of the force generated by the deltoid muscle, we need to consider the forces acting on the system.

1. Weight of the kid: The weight of the kid is given as 20 kg. We can calculate the force due to gravity acting on the kid using the formula F = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, the weight of the kid is 20 kg * 9.8 m/s^2 = 196 N.

2. Weight of the arm: The weight of the arm is given as 2.5 kg. Using the same formula as above, the weight of the arm is 2.5 kg * 9.8 m/s^2 = 24.5 N.

3. Tension force in the arm: The deltoid muscle generates a force to counteract the weight of the kid and the arm. This force acts along the line connecting the attachment point of the deltoid muscle to the arm and the shoulder joint.

Now, let's break down the forces acting along this line:

- The vertical component of the tension force should be equal to the sum of the weight of the kid and the weight of the arm.
- The horizontal component of the tension force can be determined using the length of the arm and the angle between the deltoid force and the arm.

To calculate the vertical component of the tension force, we have:
T_vertical = Weight of the kid + Weight of the arm = 196 N + 24.5 N = 220.5 N.

To calculate the horizontal component of the tension force, we have:
T_horizontal = T_vertical * tan(14°)

Now, we need to find the total tension force using the components T_horizontal and T_vertical. To do this, we use the Pythagorean theorem:

T_total = sqrt(T_horizontal^2 + T_vertical^2).

Therefore, T_total = sqrt((T_vertical * tan(14°))^2 + T_vertical^2).

By substituting the known values into the equation, we can find the magnitude of the force generated by the deltoid muscle.