Question

For serious fractures of the leg, the leg may need to have a stretching force applied to it to keep contracting leg muscle from forcing the broken bones together too hard. This is often done using traction (see the picture) The rope must make the same angle on both sides of the pulley so that the net force of the rope on the pulley is horizontally to the right, but the angle can be adjusted to control the amount of traction. The doctor has specified 50N of traction for this patient, with a 4.2 kg hanging mass. What is the proper angle?(Start by drawing a FBD for the pulley).

Answer 1

The proper angle will be "52.6°".

The given values are:

Fraction force,

• $F_{Pulley \ on \ leg} = 50 \ N$

Mass,

• $m = 4.2 \ kg$

Let,

The tension in rope be "T".

For equilibrium of mass,

→ $T = mg$

Now,

→ $F_{Pulley \ on \ leg} = 2T Cos \theta$

or,

→ $F_{Pulley \ on \ leg } = 2 mg Cos \theta$

By substituting the values, we get

→                 $50 = 2\times 4.2\times 9.8\times Cos \theta$

→            $Cos \theta = 0.6074$

→                  $\theta = 52.6^{\circ}$

Thus the above solution is correct.

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