Atwood Machine on an Incline

A block on a ramp is joined by a string over a pulley to a hanging mass. Work out the acceleration and the tension, then release the system to check.

Time0.000 s

Speed0.00 m/s

Acceleration? m/s²

Ramp block (M₁)50 g

Hanging mass (M₂)50 g

Ramp angle (θ) 30° Friction on the ramp (μ = 0.20) Show the force arrows

Your task: draw a free-body diagram for each mass, then calculate the acceleration (a) and the tension (T) in the string. Release the system to check your acceleration. Use g = 9.8 m s^-2.

Show the answers and the working

Forces on M₁ along the ramp: the weight component M₁g sinθ pulls it down the ramp, the string pulls it up the ramp, and friction opposes the motion. The normal force is N = M₁g cosθ, and friction is f = μN.

If M₂g > M₁g sinθ (M₂ goes down):
a = (M₂g - M₁g sinθ - f) / (M₁ + M₂) and T = M₂(g - a)

If M₁g sinθ > M₂g (M₂ goes up):
a = (M₁g sinθ - M₂g - f) / (M₁ + M₂) and T = M₂(g + a)

If the difference between M₂g and M₁g sinθ is not bigger than the maximum friction, nothing moves: a = 0 and T = M₂g. This lab uses the same value of μ for static and kinetic friction, a simplification. The string is light, the pulley has no mass and no friction.

Learn more in the Forces and pulleys lesson.