How to use this calculator
Enter both masses, the slope angle (0 for a flat table) and the friction coefficients. The calculator first checks whether static friction can hold the system, then finds the direction of motion, the acceleration and the tension.
Formulas
Accelerationa = |mBg − mAg sin θ| − μkmAg cos θmA + mB
TensionT = mB(g ∓ a)
Worked example
10 kg on a 30° slope (μs 0.25, μk 0.2) tied to 8 kg hanging (the default)
- Net pull: 8 × 9.81 − 10 × 9.81 × sin 30° = 78.48 − 49.05 = 29.43 N.
- Static friction can give 0.25 × 84.96 = 21.24 N, less than 29.43 N, so it moves: B falls, A slides up.
- a = (29.43 − 0.2 × 84.96)/18 = 0.691 m/s²; T = 8(9.81 − 0.691) = 72.95 N.
Frequently asked questions
Why is the tension less than the hanging weight?
Block B is accelerating downward, so the rope has to hold up less than its full weight: T = mB(g − a).
What if the pulley has mass?
Then the tensions on the two sides differ and the pulley’s rotational inertia enters; this calculator assumes a light pulley.