What is the correct condition for equilibrium when calculating torques about the elbow joint?
Understand the Problem
The question is asking which equation correctly represents the condition for equilibrium when calculating torques about the elbow joint. This involves understanding the relationships between the distances (r values) and forces (F and w values) acting on the joint.
Answer
The equation for equilibrium is $F \cdot r_F = w \cdot r_w$.
Answer for screen readers
The correct equation representing the condition for equilibrium when calculating torques about the elbow joint is:
$$ F \cdot r_F = w \cdot r_w $$
Steps to Solve
- Identify Forces and Distances
Identify the forces acting on the elbow joint. Typically, this includes the weight of the forearm ($w$) and the force exerted by the muscle ($F$). Also, identify the distances from the elbow joint: $r_w$ (distance to the weight) and $r_F$ (distance to the muscle force).
- Set Up the Torque Equation
The condition for equilibrium states that the total torque around the elbow joint must be zero. This can be expressed mathematically as:
$$ F \cdot r_F - w \cdot r_w = 0 $$
This means that the torque from the muscle force must balance the torque from the weight.
- Rearranging the Equation
To find the relationship between the forces and distances, we can rearrange the torque equation. This gives us:
$$ F \cdot r_F = w \cdot r_w$$
- Interpret the Result
This rearranged equation indicates that the product of the muscle force and its distance from the joint equals the product of the weight and its distance from the joint, establishing the equilibrium condition.
The correct equation representing the condition for equilibrium when calculating torques about the elbow joint is:
$$ F \cdot r_F = w \cdot r_w $$
More Information
This equation shows that for an object to remain in equilibrium, the torque produced by the muscle force must equal the torque produced by the weight of the forearm. This principle is crucial in biomechanics and physical therapy.
Tips
- Ignoring the Direction of Forces: It's important to consider the direction of the forces when calculating torques. Torques in the same direction should be added, while torques in opposite directions should be subtracted.
- Forgetting Units: Always check that force and distance are in compatible units to ensure the calculations are valid.
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