Atwood Machine Calculator

How it is calculated

Enter the two hanging masses in kilograms. The tool models an ideal setup: a string that does not stretch and a pulley with no mass and no friction. The acceleration is the net force divided by the total mass being moved, a = |m1 − m2| · g ÷ (m1 + m2), and the string tension is T = 2 · m1 · m2 · g ÷ (m1 + m2), with g = 9.80665 m/s². Acceleration is a positive magnitude in m/s², tension is in newtons, and a note tells which mass goes down. Both masses must be above zero; zero or negative values give no result. Equal masses give acceleration 0 and a tension equal to one weight. Results are rounded to three decimals. Real pulleys have mass and friction, so measured values come out a little lower.

Common mistakes

• Entering weights in newtons, or masses in grams. The fields take kilograms, so a 500 g mass is 0.5.
• Expecting a negative acceleration when mass 2 is heavier. The tool reports only the size; the note shows which side descends.
• Assuming the tension equals the weight of the heavier mass. When the masses differ it is lower than the heavier weight and higher than the lighter one.
• Expecting a real lab result to match exactly. A pulley with mass or friction slows the motion, and the tool ignores both.
• Entering 0 for a missing mass. Zero or negative masses give no result; a single hanging body is simply in free fall at g.