What torque must be maintained by a worker at the elbow to hold a 2-kg mass, if the worker's forearm (3 kg) is at a 40% length from the elbow?

To determine the torque that must be maintained by the worker at the elbow to hold the 2-kg mass, you begin by considering the forces involved and the distances from the pivot point, which is the elbow.

First, we need to calculate the torque due to the mass being held at a specific distance from the elbow. Torque ((\tau)) is calculated using the formula:

[

\tau = r \times F

]

Where (r) is the distance from the pivot (elbow) to where the force is applied, and (F) is the force applied.

1. Calculate the weight of the 2-kg mass:

[

F = mass \times g = 2 \text{ kg} \times 9.81 \text{ m/s}^2 = 19.62 \text{ N}

]

2. Determine the effective length where this force acts. If the forearm is at 40% of its length, let’s denote the full length of the forearm as (L). The force acts at a distance of (0.4L) from the elbow.

3. **Calculate the torque due