Tension force with pulleys and weights

AI Thread Summary
The discussion focuses on calculating tension force in a pulley system used for a patient in traction. The tension in the rope was determined to be 58.8 N using the weight formula W=mg. The correct angle for the upper rope, necessary for the net traction force to pull straight out on the leg, was found to be approximately 47.58 degrees. The total horizontal force acting on the leg was calculated as 99.429 N, combining the horizontal components of the forces. The analysis emphasizes the equilibrium of forces in the system and the application of Newton's laws.
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Homework Statement



An accident victim with a broken leg is being placed in traction. The patient wears a special boot with a pulley attached to the sole. The foot and boot together have a mass of m = 3.4 kg, and the doctor has decided to hang a 6.0 kg mass from the rope. The boot is held suspended by the ropes and does not touch the bed. ϕ = 10°.

p5-33alt.gif


(a) Determine the amount of tension in the rope by using Newton's laws to analyze the hanging mass.

(b) The net traction force needs to pull straight out on the leg. What is the proper angle θ for the upper rope?

(c) What is the net traction force pulling on the leg? (Hint: If the pulleys are frictionless, which we will assume, the tension in the rope is constant from one end to the other.)

Homework Equations



F=ma
W=mg

The Attempt at a Solution



I was easily able to use W=mg to find the tension in the rope to be 58.8N.
After that, I am lost.

I know the Fnet(y) should be zero since the boot is pulling straight out, but I can't get any further than that...

I also imagine somehow that i will find acceleration along the x-axis, then because the system is in equilibrium (the leg will not move), I will use acceleration and the mass of the boot to find the net traction force.

I really need some help finding the angle theta. Thanks!
 

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Okay guys, I started out with a free-body diagram showing the forces on the boot. I found the force of weight on the boot to be 33.32N. I then set fnet(y) equal to zero, which showed that 58.8 sin(theta)=33.2+58.8sin(10) and found the angle to be 47.58 degrees, which was correct.

Now I just can't figure out the third part and have no idea how to go about it. Thanks.
 
The new traction will be the total horizontal force acting on the leg, ie the sum of horizontal components of the forces. We already found the angles for the forces to be balanced. Now the total horizontal force will be,

Tcos(10) + Tcos(47.558)

as T = 60N (I take g = 10),

Total HF = 99.429N
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

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