Atwood Machine
Two masses hang from a string over a pulley. Work out the acceleration and the tension, then release the system to check.
Each mass is a 50 g hanger plus 25 g slotted masses.
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 each mass: the weight (mg) pulls down and the string tension (T) pulls up. The tension is the same all along the string. The heavier mass speeds up downwards and the lighter mass speeds up upwards, with the same size of acceleration.
If M2 > M1 (M2 goes down):
For M2: M2g - T = M2a
For M1: T - M1g = M1a
Add the two equations, so T cancels:
a = (M2 - M1)g / (M1 + M2)
T = M1(g + a) = 2M1M2g / (M1 + M2)
Change grams to kilograms before you calculate (1 kg = 1000 g). If M1 > M2, swap the labels. If the masses are equal, a = 0 and T = Mg. The string is light and does not stretch, and the pulley has no mass and no friction.
Learn more in the Forces and pulleys lesson.