Solve Atwood's Machine Problem: Acceleration of Weights

[claudio315]

Problem: There is this pulley, pulley A. On one end is another pulley, pulley B, and on the other end is a weight of mass X. On one end of pulley B is a weight of mass Y and on the other end is a weight of mass Z. How do you get the acceleration of the system? I mean the acceleration of the weights.

 

[arildno]

What have you done so far?

 

[ogb p]

To solve this problem, we can use the principles of Newton's second law of motion and the concept of tension in a pulley system. First, we must determine the net force acting on each weight. For the weight of mass X, the net force is equal to the tension in the string connecting it to pulley A. Similarly, for the weight of mass Y, the net force is equal to the difference between the tension in the string connecting it to pulley B and the weight of mass Y. For the weight of mass Z, the net force is equal to the weight of mass Z minus the tension in the string connecting it to pulley B.

Next, we can use the equation F=ma, where F is the net force and a is the acceleration, to find the acceleration of each weight. For the weight of mass X, we have F = T - 0 = T, where T is the tension in the string. For the weight of mass Y, we have F = T - Y, where T is the tension in the string and Y is the weight of mass Y. For the weight of mass Z, we have F = Z - T, where Z is the weight of mass Z and T is the tension in the string.

Now, we can set up a system of equations by equating the net forces to the respective masses multiplied by their accelerations. This will give us three equations, which we can solve simultaneously to find the acceleration of each weight. Once we have the accelerations, we can also find the acceleration of the system by taking the average of the three accelerations.

In summary, to find the acceleration of the weights in this Atwood's machine problem, we must determine the net forces acting on each weight and then use Newton's second law to find the accelerations. Solving a system of equations will give us the accelerations of each weight, and taking the average will give us the acceleration of the system.