Restoring Couple When Floating Body In Stable Equilibrium Calculator

Restoring Couple Formula:

\[ \text{Restoring Couple} = (W_{\text{body}} \times x \times D \times (180/\pi)) \]

Weight of Body:

Newton

Distance from submerged to Floating Body:

Meter

Angle Between Bodies:

Radian

Restoring Couple:

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1. What is Restoring Couple?

Restoring couple is the torsional force that arises when a suspension wire is twisted, which tends to untwist the wire and restore the original position of a floating body in stable equilibrium.

2. How Does the Calculator Work?

The calculator uses the Restoring Couple formula:

\[ \text{Restoring Couple} = (W_{\text{body}} \times x \times D \times (180/\pi)) \]

Where:

\( W_{\text{body}} \) — Weight of Body (Newton)
\( x \) — Distance from submerged to Floating Body (Meter)
\( D \) — Angle Between Bodies (Radian)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula calculates the restoring moment that brings a floating body back to its equilibrium position after being displaced.

3. Importance of Restoring Couple Calculation

Details: Calculating restoring couple is essential for understanding the stability of floating bodies, designing marine vessels, and analyzing buoyancy systems in engineering applications.

4. Using the Calculator

Tips: Enter weight in Newtons, distance in meters, and angle in radians. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of restoring couple?
A: Restoring couple represents the torque that brings a floating body back to its equilibrium position when displaced, indicating the stability of the system.

Q2: Why is the angle converted using 180/π?
A: The conversion factor (180/π) is used to convert the angle from radians to degrees in the calculation, as the formula requires this conversion.

Q3: What factors affect the magnitude of restoring couple?
A: The restoring couple depends on the weight of the body, the distance from the submerged point to the floating body, and the angle of displacement.

Q4: How does restoring couple relate to stable equilibrium?
A: A positive restoring couple indicates stable equilibrium, where the body returns to its original position after being slightly displaced.

Q5: Can this formula be used for all floating bodies?
A: This formula applies specifically to floating bodies in stable equilibrium where the assumptions of the model hold true.