The Atwood Machine A classic rotational motion problem! Rhine.

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Presentation transcript:

The Atwood Machine A classic rotational motion problem! Rhine

The Problem massless frictionless pulley m M Two masses, m and M, are hung over a massless, frictionless pulley using a massless rope, all purchased from the Lowell Physics Store in Diagon Alley. a.What is the significance of a massless, frictionless, pulley (you might want to think what would happen if the opposite were true)? b.At what rate will each mass accelerate? c.Find the tension in the rope on each side of the pulley? d.No numbers were provided above because you should be able to develop a general solution. Once you do so, find a and F T using m = 2 kg, M = 4 kg. Then quadruple each of mass and repeat, then try reversing the values.

Initial Assumptions & Intuition massless frictionless pulley m M a.What is the significance of a massless, frictionless, pulley (you might want to think what would happen if the opposite were true)?

Solution Process massless frictionless pulley m M i. Draw a FBD for each mass: m M ii. Apply Newton’s 2 nd Law to each mass: ii. Solve for a and F T :

Analyzing the Results massless frictionless pulley m M i. What are a and F T if M = 2m? v. What are a and F T if M >> m ? ii. What are a and F T if M = 4 kg and m = 2 kg? iii. What are a and F T if M = 16 kg and m = 8 kg? iv. What are a and F T if M = 2 kg and m = 4 kg?

What happens if pulley has mass?? (still no friction) massless frictionless pulley m M Two masses, m and M, are hung over a frictionless pulley with mass m P using massless rope, all purchased from the Lowell Physics Store in Diagon Alley. a.At what rate will each mass accelerate? b.Find the tension in the rope on each side of the pulley? c.No numbers were provided above because you should be able to develop a general solution. Once you do so, find a and F T using m = 2 kg, M = 4 kg. Then quadruple each of mass and repeat, then try reversing the values. We’ll be able to tackle this problem after studying torque!