The Atwood Machine A classic rotational motion problem!

1
The Atwood MachineA classic rotational motion
problem!

• Rhine

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The Problem

• 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.
• What is the significance of a massless,
  frictionless, pulley (you might want to think
  what would happen if the opposite were true)?
• At what rate will each mass accelerate?
• Find the tension in the rope on each side of the
  pulley?
• No numbers were provided above because you should
  be able to develop a general solution. Once you
  do so, find a and FT using m 2 kg, M 4 kg.
  Then quadruple each of mass and repeat, then try
  reversing the values.

massless frictionless pulley
M
m
3
Initial Assumptions Intuition

1. What is the significance of a massless,
   frictionless, pulley (you might want to think
   what would happen if the opposite were true)?

massless frictionless pulley
M
m
4
Solution Process
i. Draw a FBD for each mass
M
m
massless frictionless pulley
ii. Apply Newtons 2nd Law to each mass
M
ii. Solve for a and FT
m
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Analyzing the Results
i. What are a and FT if M 2m?
massless frictionless pulley
ii. What are a and FT if M 4 kg and m 2 kg?
M
iii. What are a and FT if M 16 kg and m 8 kg?
m
iv. What are a and FT if M 2 kg and m 4 kg?
v. What are a and FT if M gtgt m ?
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What happens if pulley has mass?? (still no
friction)

• Two masses, m and M, are hung over a frictionless
  pulley with mass mP using massless rope, all
  purchased from the Lowell Physics Store in Diagon
  Alley.
• At what rate will each mass accelerate?
• Find the tension in the rope on each side of the
  pulley?
• No numbers were provided above because you should
  be able to develop a general solution. Once you
  do so, find a and FT using m 2 kg, M 4 kg.
  Then quadruple each of mass and repeat, then try
  reversing the values.

massless frictionless pulley
M
m
Well be able to tackle this problem after
studying torque!