Understanding the Concepts
* Torque: Torque is a rotational force that tends to cause an object to rotate. It's calculated as the product of the force applied and the perpendicular distance from the pivot point (in this case, the shoulder) to the line of action of the force.
* Force of Gravity: The force acting on the steel ball is its weight, which is determined by gravity (9.8 m/s²).
* Lever Arm: The perpendicular distance from the shoulder to the line of action of the weight force is the lever arm.
Calculations
1. Calculate the weight of the steel ball:
* Weight (W) = mass (m) * acceleration due to gravity (g)
* W = 4.0 kg * 9.8 m/s²
* W = 39.2 N
2. Determine the lever arm:
* The arm is 70 cm long, which is 0.7 meters.
* Since the arm is 50 degrees below horizontal, we need to find the perpendicular distance from the shoulder to the line of action of the weight force. This distance is the length of the arm multiplied by the sine of the angle:
* Lever arm (L) = 0.7 m * sin(50°)
* L ≈ 0.536 m
3. Calculate the torque:
* Torque (τ) = Force (W) * Lever arm (L)
* τ = 39.2 N * 0.536 m
* τ ≈ 21.0 N·m
Answer: The magnitude of the torque about the man's shoulder is approximately 21.0 N·m.
