Finding Tension in a Quadriceps Tendon: A Static Equilibrium Problem

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Homework Help Overview

The problem involves analyzing the forces acting on the lower leg in a static equilibrium scenario, specifically focusing on the tension in the quadriceps tendon. The context includes the forces due to gravity acting on the lower leg and foot, as well as the angles involved in the setup.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply static equilibrium principles by setting up equations based on the forces and angles involved. Some participants question the correctness of the approach, suggesting that additional considerations regarding equilibrium in the x-direction are necessary. Others express uncertainty about the implications of the forces and whether reaction forces are present to maintain equilibrium.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the problem. Some have provided hints regarding the need to consider moments of force, while others are questioning the assumptions made about equilibrium and the role of reaction forces.

Contextual Notes

There is mention of the medical context being challenging for some participants, and the original poster expresses uncertainty about their method. The discussion includes considerations of angles and the positioning of forces, which may affect the analysis.

bjgawp
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Here is the problem I am attempting to solve:
http://img227.imageshack.us/img227/2747/problempr4.jpg

The large quadriceps muscle in the upper leg terminates at its lower end in a tendon attached to the upper end of the tibia. The forces on the lower leg when the leg is extended are modeled as shown where T is the tension in the tendon, C is the force of gravity acting on the lower leg, and F is the force of gravity acting on the foot. Find T when the tendon is at an angle of 25.0° with the tibia, assuming that C = 30.0 N, F = 12.5 N, and the leg is extended at an angle of 40.0° with the vertical. Assume that the centre of gravity of the lower leg is at its centre and that the tendon attaches the lower leg at a point one-fifth of the way down the leg.

What I am uncertain is my method of solving this question. I'm quite sure that I'm missing something. Here is what I did:
Fnet = 0
Angle between quadricep and the dotted line is equal to 40.0°. Therefore, the angle between the quadriceps and T is equal to 65.0°.
0 = Tsin65.0° - C - F
T = 46.9 N

Merci d'avance!
 
Last edited by a moderator:
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HINT: The total moments of force about any point must be zero.
 
bjgawp said:
Angle between quadricep and the dotted line is equal to 40.0°. Therefore, the angle between the quadriceps and T is equal to 65.0°.
0 = Tsin65.0° - C - F
T = 46.9 N

This is not correct, since you could write a scalar equation for the 'x-direction', too, which would be T*cos65 = 0 => T = 0. If you try to sum up the vectors graphically, you'll easily see that there's no state of equilibrium for this set of vectors.
 
If they aren't in the state of equilibrium, does that mean the leg is moving down? Or are there reaction forces that help keep the equilibrium?

*sighs* Torques...
 
To be honest, the medical context is killing me. :biggrin:
 
Hmm .. as I'm thinking about this, there would have to be reaction forces to balance all the vectors. But where would they be situated? At the tendon? =S
 

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