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Du57mi73
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Homework Statement
The device shown in the figure below (Figure 1) is one version of a Russell traction apparatus. It has two functions: to support the injured leg horizontally and at the same time provide a horizontal traction force on it. This can be done by adjusting the weight W and the angle θ. For this patient, his leg (including his foot) is 81.0 cm long (measured from the hip joint) and has a mass of 16.6 kg . Its center of mass is 41.0 cm from the hip joint. A support strap is attached to the patient's ankle 13.0 cm from the bottom of his foot.
What weight W(in N) is needed to support the leg horizontally?
Massleg=16.6kg
Radiusleg=81.0cm or .810m
Radiuscm=41.0cm or .410m
Radiuspulley=13.0cm from foot or 68.0cm from pivot=.680m
Homework Equations
Στ(torque) = 0
τ= T⋅R
F=ma
The Attempt at a Solution
Force of the center mass is equal to the mass times the acceleration(downward).
Fcm = m * a = 16.6kg ⋅ -9.8m/s2
Fcm = -162.68N
Fcm * Rcm = -162.68N * .410m = -66.988 N*m = τ
Now, I sum the torques and solve for Fpulley
Fpulley * Rpulley - Fcm * Rcm = 0
Fpulley*.68m = -66.988N*m
Fpulley = -98.08647N = -98.1N
I have tried inputing -98.1 and 98.1, both were wrong. Any suggestions? I've looked elsewhere online and this is pretty much the template they provide so maybe I'm getting my numbers wrong somewhere?