50 Forces in the Elbow Joint

In the previous chapter we found the biceps force in our example problem to be 430 lbs! You may have noticed that when we found the biceps tension we completely ignored the forces acting at the elbow joint. We were allowed to do this because those forces cause no torque.  Forces  acting on the fulcrum of a lever don’t cause the lever to rotate.  Just because the forces on the elbow don’t cause rotation, that doesn’t mean they aren’t important. Those forces can certainly damage the joint if they get too large. Let’s try to find out how big those forces are for our example problem.

Figure is a schematic drawing of a forearm rotated around the elbow. A 50 pound ball is held in the palm. The distance between the elbow and the ball is 13 inches. The distance between the elbow and the biceps muscle, which causes a torque around the elbow, is 1.5 inches. Forearm forms a 60 degree angle with the upper arm.
The elbow joint flexed to form a 60° angle between the upper arm and forearm while the hand holds a 50 lb ball . Image Credit: Openstax University Physics


The forearm is holding still and not moving so it must be in and all the vertical forces must be canceling out. If the vertical forces didn’t cancel out the forearm would begin to move up or down.  We already know that the of the ball is 50 lbs downward and the bicep is 433 lbs upward. The downward weight cancels 50 lbs worth of the upward muscle tension, leaving behind a remaining 383 lbs of upward force. The forearm is in static equilibrium, so the vertical force on the end of the forearm at the elbow must cancel out this 383 lbs upward force,  meaning that the vertical force on the elbow end of the forearm is 383 lbs downward. This force comes from the upper arm bone (humerus) pushing down on the end of the forearm bones (radius and ulna). Adjusting our , we should report this force as 380 lbs.

Reinforcement Exercises

Draw a of the elbow showing the forces from the ball , the bicep , and the upper arm pushing on the forearm. The values for all of these forces are given in the previous paragraph.

Horizontal Elbow Forces

The horizontal forces must all cancel out because the forearm is in , but there are no horizontal forces in our example to begin with, so that’s it. We’re finished analyzing the forces on the forearm while holding a 50 lb ball!

  1. OpenStax University Physics, University Physics Volume 1. OpenStax CNX. Jul 11, 2018 http://cnx.org/contents/d50f6e32-0fda-46ef-a362-9bd36ca7c97d@10.18.


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