Physics Pulley and Tension Question?
An accident victim with a broken leg is being placed in traction. The patient is wearing a special boot with a pulley attached to the sole. The combined mass of the foot and boot is 4.0 kg. To provide the necessary traction, the doctor has decided to hang a 6.0 kg mass from the rope. The boot is suspended by the ropes and does not make contact with the bed.
a) To ensure the net traction force pulls straight along the leg, what is the proper angle, θ, for the upper rope?
b) What is the magnitude of the net traction force pulling on the leg?
Here is a link to the diagram for reference: http://session.masteringphysics.com/problemAsset/1...
2 Answers
Feb 19, 2025
The tension in the rope T = Mwg = 6.09.8 = 58.8 N
For the leg to be pulled straight out, the vertical components of forces on the leg must sum to zero.
The vertical component from the lower part of rope is -T*sin15º
The vertical component from the upper part of the rope is T*sinθ;
The vertical force from the weight of the foot and boot is -4.0*9.8 = -39.2 N
Then
-Tsin15º + Tsinθ - 39.2 = 0
sinθ = (39.2 + 58.8*sin15º)/58.8 = 0.925
θ = 68º
The net traction force is the sum of the horizontal components:
T*cosθ + T*cos15º = 79 N
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