Prosthetics: Forces Acting on a Femur

In a traction system three forces are applied to the femur as shown. The femur itself is positioned at an angle of 15° with the horizontal.

1. What is the resultant force of this traction system?
2. What impact, if any, will it have on the position of the femur?

Solution

In order to determine the resultant force R, which is a vector, we have to calculate both its magnitude and its direction. First, let us compute the magnitude of R. We accomplish this by resolving each force into its x and y components, and then summing up all the x components and summing up all the y components as follows:

Force x-component y-component
F1 = 10 lb 10 cos(-19°) = 10 × 0.9455 = 9.455 10 sin(-19°) = 10 ×(-0.3256) = -3.256
F2 = 10 lb 10 cos(17°) = 10 × 0.9563 = 9.563 10 sin(17°) = 10 × 0.2924 = 2.924
F3 = 10 lb 10 cos(61°) = 10 × 0.4848 = 4.848 10 sin(61°) = 10 × 0.8746 = 8.746
Resultant R Rx = 23.866 Ry = 8.414

Since we have calculated the x and y components of the resultant R, we can find its magnitude by using the Pythagorean theorem:

R2 = Rx2 + Ry2 = 23.8662 + 8.4142 = 569.586 + 70.795 = 640.381

which gives us:

R = 25.306 or rounded to 2 significant digits, the same as the original measurements: R = 25 lb.

The angle of the resultant can be calculated as follows:

From this:

Since the femur had an original orientation of 15° we can conclude that the effect of this traction system on the femur will be a rise of 4.42°.

Written by Erika Crema, October 10, 1997