Finding Tension in a Quadriceps Tendon: A Static Equilibrium Problem

In summary, the conversation discusses a problem involving the tension in a tendon attached to the upper end of the tibia. The forces acting on the lower leg are modeled with T as the tension in the tendon, C as the force of gravity acting on the lower leg, and F as the force of gravity acting on the foot. The goal is to 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. The method used to solve the problem is discussed, including the use of torque to determine the reaction forces needed to maintain
  • #1
bjgawp
84
0
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!
 
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  • #2
HINT: The total moments of force about any point must be zero.
 
  • #3
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.
 
  • #4
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...
 
  • #5
To be honest, the medical context is killing me. :biggrin:
 
  • #6
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
 

1. What is static equilibrium?

Static equilibrium is a state in which all forces acting on an object or system are balanced, resulting in no movement or acceleration. This means that the object or system is at rest or moving at a constant velocity.

2. How do you determine if an object is in static equilibrium?

An object is in static equilibrium if the sum of all forces acting on it is equal to zero and the sum of all torques (rotational forces) acting on it is also equal to zero. This can be determined by using the equations of static equilibrium, which take into account the forces and distances from the pivot point of the object.

3. What are some examples of static equilibrium problems?

Some common examples of static equilibrium problems include: a ladder leaning against a wall, a book resting on a table, a person standing on a scale, and a bridge supporting the weight of cars and trucks. In all of these cases, the forces acting on the objects are balanced, resulting in no movement.

4. How do you solve a static equilibrium problem?

To solve a static equilibrium problem, you first need to identify all the forces acting on the object or system and their direction. Then, use the equations of static equilibrium to set up a system of equations and solve for any unknown variables. It is important to draw a clear and accurate free body diagram to help visualize the forces and their directions.

5. What happens if an object is not in static equilibrium?

If an object is not in static equilibrium, then it will experience a net force or torque, resulting in either linear or rotational motion. This means that the object will either start moving or accelerate in a certain direction. In order to achieve static equilibrium, the forces acting on the object must be balanced.

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