Atwood Machine Calculator
This calculator helps you determine the acceleration and rope tension in an Atwood machine — a classic physics system consisting of two masses connected by a rope over a frictionless pulley. Enter both masses and the gravitational acceleration to instantly compute the system's acceleration and the tension in the rope.
Atwood Machine Calculator
Atwood Machine Formula
Where:
- $$a$$ is the acceleration of the system.
- $$m_1$$ and $$m_2$$ are the two masses.
- $$g$$ is the gravitational acceleration.
The tension in the rope is given by:
Where:
- $$T$$ is the tension in the rope.
These formulas describe the dynamics of an ideal Atwood machine with a massless, frictionless pulley and an inextensible rope.
Atwood Machine – Worked Example
An Atwood machine has two masses: $$m_1 = 5\ kg$$ and $$m_2 = 3\ kg$$. The gravitational acceleration is $$g = 9.81\ m/s^2$$.
- $$m_1$$ = 5 kg
- $$m_2$$ = 3 kg
- $$g$$ = 9.81 m/s²
Acceleration:
$$a = \frac{(5 – 3) \times 9.81}{5 + 3} = \frac{2 \times 9.81}{8} = \frac{19.62}{8} = 2.4525\ m/s^2$$
Tension:
$$T = \frac{2 \times 5 \times 3 \times 9.81}{5 + 3} = \frac{294.3}{8} = 36.7875\ N$$
Result: Acceleration = 2.4525 m/s², Tension = 36.7875 N
The Atwood machine is a fundamental apparatus used in physics to study classical mechanics, acceleration, and tension. It demonstrates how unequal masses create a net force that accelerates the system, while the rope tension keeps both masses connected. This calculator is useful for students, educators, and engineers analyzing pulley systems, force distributions, and Newton’s second law applications.