Demo 01-16 Atwood's Machine

The classical Atwood's machine, consisting of two masses hanging on a light string over a light, frictionless pulley, is used to study force and acceleration. If the masses are nearly equal, the motion may be slow enough that accurate measurements can be made. We can do this by using large masses on each side and increasing the mass on one side by adding a smaller rider.For such a system, shown in Figure 1, we can formulate the equation of motion by considering the free-body drawings for each side. [Equation] [Equation]where M is the larger mass on each side, m is the lighter mass of the rider, T is the tension in the string, a is the acceleration of the system, and g is the acceleration of gravity. Eliminating T, the equation of motion is [Equation]Thus the two-mass system will move with a constant acceleration, with the side with the rider moving downward.We can determine this acceleration experimentally by using the difference method discussed in detail in Demonstration 01-10, where the position of either weight can be measured at a series of equal time intervals. A 10-cm grid is provided at the right of the Atwood's machine for determination of the vertical scale.In the video the net weight m is removed while the system is accelerating, causing the acceleration to cease and resulting in constant velocity for the system after that point. This can also be verified experimentally by determining the position of either weight at equal time intervals after the small net weight is removed