When bones are healing it is critical that they are held in

When bones are healing, it is critical that they are held in a fixed position. This is a primary purpose of the limb and cast in a fixed position. Consider the two cables suspending a leg with a cast. If the leg and cast weigh 150N and the angle of the ankle cable is 60degree above the horizontal, what are the cable tensions and the angle of the knee cable from the horizontal such that the leg is supported?

Solution

Here, it needs to be understood that the net forces along the horizontal and the vertical direction will remain balanced as there is not net motion for the leg and the cast.

We will assume that the angle at which the knee cable is held is . Now we have the ankle cable acting at an angle of 60 degrees from horizontal and is of 150 N magnitude.

Now we will balance the forces along the horizontal and the vertical direction to get the required values:

Hence, along the horizontal we get: TkCos = 150 cos60

or, Tk Cos = 75 [Equation 1]

Along the vertical we have: TkSin + 150 Sin60 = 150

or, TkSin = 20.0962 [Equation 2]

We divide the equation 2 by equation 1 to get:

Tan = 0.26795

or, = 15.0

Using this in equation 1 we get: Tk = 75 / cos15 = 77.646 Newtons

Therefore the tension in the knee cable is 77.646 Newtons while it is held at angle of 15 degrees with the horizontal.