1. Understand Torque

Torque is a twisting force that causes rotation. It's calculated as:

* Torque (τ) = Force (F) × Distance (r) × sin(θ)

* Force (F): The force applied. In this case, it's the weight of the steel ball.

* Distance (r): The distance from the axis of rotation (the shoulder) to the point where the force is applied (the ball).

* θ: The angle between the force vector and the lever arm (the distance).

2. Calculate the Force

* Weight (F) = Mass (m) × Acceleration due to gravity (g)

* F = (4.0 kg) × (9.8 m/s²) = 39.2 N

3. Calculate the Distance (r)

* r = 70 cm = 0.7 m (convert centimeters to meters)

4. Determine the Angle (θ)

* The problem states the arm is 30 degrees *below* horizontal. This means the angle between the force of gravity (acting downward) and the arm is 30 degrees.

5. Calculate the Torque

* τ = (39.2 N) × (0.7 m) × sin(30°)

* τ ≈ 13.72 Nm

Therefore, the magnitude of the torque about the man's shoulder is approximately 13.72 Nm.