What is the formula used to solve for the tension in the tendon in rotational equilibrium?
Understand the Problem
The question is asking for the specific formula that is used to calculate the tension in a tendon when the system is in rotational equilibrium. The provided options suggest that different formulas are being considered to determine which is the correct one.
Answer
The formula for tension is: $$ T = \frac{\text{other torques}}{r_{T}} $$
Answer for screen readers
The formula for calculating the tension in a tendon in rotational equilibrium is: $$ T = \frac{\text{other torques}}{r_{T}} $$
Steps to Solve
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Identify the General Concept The tension in a tendon when a system is in rotational equilibrium can typically be analyzed using concepts from physics related to torque and equilibrium.
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Understand Rotational Equilibrium In rotational equilibrium, the sum of torques acting on the system must equal zero. This can be stated as: $$ \sum \tau = 0 $$ where $\tau$ is the torque.
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Torque Calculation Torque is calculated using the formula: $$ \tau = r \times F $$ where $r$ is the distance from the pivot point to the point where the force is applied, and $F$ is the force applied (in this case, the tension in the tendon).
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Set Up the Equation If we have a tendon exerting tension $T$, we would analyze the torques around the pivot point. Setting the sum of clockwise torques equal to the sum of counterclockwise torques allows us to find the tension: $$ T \cdot r_{T} = \text{other torques} $$ where $r_{T}$ is the distance from the pivot to the point where the tension is applied.
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Rearranging for Tension To solve for tension $T$, we rearrange the equation: $$ T = \frac{\text{other torques}}{r_{T}} $$
The formula for calculating the tension in a tendon in rotational equilibrium is: $$ T = \frac{\text{other torques}}{r_{T}} $$
More Information
This equation shows that the tension can be calculated by dividing the sum of all other torques in the system by the distance from the pivot to where the tendon’s tension is applied. It is a fundamental concept in biomechanics and engineering.
Tips
- Confusing linear equilibrium with rotational equilibrium where the sum of forces is used instead of the sum of torques.
- Forgetting to convert all forces and distances to the same units, which can lead to incorrect calculations.
- Not accounting for all torques acting on the body, which can result in an incomplete analysis.
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