Mass of Body B given Frictional Force Calculator

Formula Used:

\[ m_2 = \frac{F_{fri}}{\mu_{hs} \cdot [g] \cdot \cos(\theta_p)} \]

Mass of Right Body (m₂):

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1. What is the Mass of Body B Formula?

The formula calculates the mass of a body hanging from a string when the frictional force, coefficient of friction, and plane inclination are known. It's derived from the equilibrium conditions of forces acting on the system.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ m_2 = \frac{F_{fri}}{\mu_{hs} \cdot [g] \cdot \cos(\theta_p)} \]

Where:

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

Explanation: The formula accounts for the balance between frictional force and the component of gravitational force along the inclined plane.

3. Importance of Mass Calculation

Details: Accurate mass calculation is crucial for understanding mechanical systems, designing structures, and analyzing forces in inclined plane scenarios with friction.

4. Using the Calculator

Tips: Enter force of friction in newtons, coefficient of friction (dimensionless), and plane inclination in radians. All values must be positive (inclination can be zero).

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the cosine function in this formula?
A: The cosine function accounts for the component of gravitational force that acts parallel to the inclined plane surface.

Q2: Can this formula be used for any angle of inclination?
A: Yes, but for angles approaching 90 degrees, the cosine approaches zero, which would make the calculated mass approach infinity.

Q3: What units should be used for the inputs?
A: Force in newtons (N), coefficient of friction (dimensionless), and angle in radians. Make sure to convert degrees to radians if necessary.

Q4: Why is gravitational acceleration fixed at 9.80665 m/s²?
A: This is the standard gravitational acceleration on Earth. For calculations on other celestial bodies, this value would need adjustment.

Q5: What are typical values for the coefficient of friction?
A: Coefficient of friction values typically range from 0 (no friction) to about 1.0-1.5 for high-friction materials like rubber on concrete.