Physics
Physics
Problem
State the formula for the magnitude of acceleration of an ideal two-mass system (Atwood machine) consisting of masses and connected by a light, inextensible string over a frictionless pulley, when .Intuitive explanation
The key is recognizing that both masses accelerate together at the same rate, even though they move in opposite directions. Write Newton's second law for each mass separately—the heavier one pulls down while the lighter one pulls up—then use the constraint that tension is the same throughout the string to eliminate it and solve for the common acceleration. The difference in weights drives the system, while the total mass resists that acceleration.
Intuitive explanation
The key is recognizing that both masses accelerate together at the same rate, even though they move in opposite directions. Write Newton's second law for each mass separately—the heavier one pulls down while the lighter one pulls up—then use the constraint that tension is the same throughout the string to eliminate it and solve for the common acceleration. The difference in weights drives the system, while the total mass resists that acceleration.