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# The forearm as an example of a third-class lever

## Problem

A lever is a simple machine that uses an applied force to rotate a rigid rod about a fixed pivot point / fulcrum with the purpose of lifting a weighted load. There are three major classes of levers, each defined by the location of the applied force/ effort in relation to the load / resistance and the fulcrum. A first-class lever has its fulcrum placed between the applied force and the load. An example of a first class-lever is a seesaw. In a second- class lever, the load is positioned between the fulcrum and the applied force. An example of a second-class lever is a wheelbarrow. Lastly, a third-class lever system has its applied force situated between the load and fulcrum. An illustration of the various classes of levers are shown in figure 1.
Figure 1: Examples of First, Second, and Third-class Levers
Most of the musculoskeletal levers of the human body are classified as third-class levers. For instance, the forearm, acts as a third-class lever. The biceps muscle, which originates from the scapula, inserts at the proximal part of the elbow. As the biceps contracts, it rotates the forearm about the elbow joint, bringing it closer to the body. This motion is called elbow flexion. Figure 2 shows a simplified lever representation of an arm holding a weighted load, W, in its hand. Other than the weighted load, the forces acting on this system are Fm , the force generated by the biceps muscle during contraction, and Fr , the reactive force at the fulcrum. These forces are oriented at a certain angle with respect to the horizontal axis as shown in figure 2.
Figure 2: Simplified Lever Representation of the Human Arm in Equilibrium With a Weighted Load
In figure 2, if the weighted load (W) is equal to 1 kg and if the biceps muscle attaches 4 cm from the elbow joint at an angle (ϴ) 30 degrees from the horizontal axis, then what is the value of Fm?