Inclination of Plane for given Frictional Force Calculator

Formula Used:

\[ \theta_p = \acos\left(\frac{F_{fri}}{\mu_{hs} \times m_2 \times [g]}\right) \]

Inclination of Plane:

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1. What is Inclination of Plane?

Inclination of Plane is the angle between the plane of motion and the horizontal when a body is hanging by a string. It represents the slope angle at which the frictional force balances the component of gravitational force along the plane.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \theta_p = \acos\left(\frac{F_{fri}}{\mu_{hs} \times m_2 \times [g]}\right) \]

Where:

\( \theta_p \) — Inclination of Plane (radians)
\( F_{fri} \) — Force of Friction (N)
\( \mu_{hs} \) — Coefficient of Friction for Hanging String
\( m_2 \) — Mass of Right Body (kg)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)

Explanation: The formula calculates the angle at which the frictional force equals the product of friction coefficient, mass, and gravitational acceleration.

3. Importance of Inclination Calculation

Details: Calculating the inclination of plane is crucial for understanding equilibrium conditions in mechanical systems, designing inclined surfaces, and analyzing forces in hanging body systems.

4. Using the Calculator

Tips: Enter force of friction in newtons, coefficient of friction (dimensionless), and mass in kilograms. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the valid range for the acos function?
A: The input to acos function must be between -1 and 1 inclusive. The calculator will show an error if this condition is not met.

Q2: Why is gravitational acceleration fixed at 9.80665?
A: This is the standard gravitational acceleration on Earth. The value may be adjusted for different planetary bodies if needed.

Q3: What units are used for the result?
A: The result is displayed in degrees for easier interpretation, though the calculation is done in radians.

Q4: Can this calculator handle negative values?
A: No, all input values must be positive as they represent physical quantities that cannot be negative.

Q5: What if the denominator becomes zero?
A: The calculator will show an error message as division by zero is mathematically undefined.