Atwood Machine Tension Calculator

Tension Formula:

\[ T = \frac{2 \times m1 \times m2 \times g}{m1 + m2} \]

Tension (T): N

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1. What is an Atwood Machine Tension Calculator?

Definition: This calculator computes the tension in the string of an Atwood's machine, which consists of two masses connected by a string over a pulley.

Purpose: It helps physics students and engineers understand and calculate the forces in simple mechanical systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T = \frac{2 \times m1 \times m2 \times g}{m1 + m2} \]

Where:

\( T \) — Tension in the string (newtons)
\( m1 \) — Mass of first object (kilograms)
\( m2 \) — Mass of second object (kilograms)
\( g \) — Acceleration due to gravity (9.81 m/s² on Earth)

Explanation: The formula accounts for the balance between gravitational forces and the system's acceleration.

3. Importance of Tension Calculation

Details: Understanding tension in pulley systems is fundamental for mechanical engineering, physics education, and designing lifting mechanisms.

4. Using the Calculator

Tips: Enter the two masses (must be different for meaningful results) and gravity (default 9.81 m/s²). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What if both masses are equal?
A: When m1 = m2, the system is in equilibrium and tension equals the weight of either mass (T = m1 × g).

Q2: Does this formula account for pulley mass?
A: No, this is the simplified formula assuming a massless, frictionless pulley.

Q3: What units should I use?
A: Use kilograms for mass and m/s² for gravity to get newtons for tension.

Q4: How does tension change with different masses?
A: Tension increases as the difference between masses decreases, reaching maximum when m1 ≈ m2.

Q5: Can I use this for real-world pulley systems?
A: This gives a theoretical baseline; real systems need to account for friction, pulley mass, and string elasticity.