Classical Physics - Pulley Problem

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SUMMARY

The discussion centers on the classical physics problem involving a massless string over a massless pulley with two hoops of masses M1 and M2. The tension in the string is derived as T = gM1M2/(M1+M2), where g represents the gravitational field strength. Participants explore the relationship between linear and angular accelerations of the hoops, emphasizing the importance of torque and the conservation of string. The conversation concludes with a collaborative effort to derive the correct equations governing the system's dynamics.

PREREQUISITES
  • Understanding of classical mechanics principles, particularly tension and torque.
  • Familiarity with the concepts of linear and angular acceleration.
  • Knowledge of moment of inertia for different shapes, specifically hoops.
  • Basic grasp of the conservation of string principle in dynamic systems.
NEXT STEPS
  • Study the derivation of tension in systems involving pulleys and masses.
  • Learn about the relationship between linear and angular motion, particularly in rolling objects.
  • Explore the concept of moment of inertia for various geometric shapes, focusing on hoops and disks.
  • Investigate the application of Newton's laws in rotational dynamics and their implications in pulley systems.
USEFUL FOR

Students and educators in physics, mechanical engineers, and anyone interested in understanding the dynamics of pulley systems and the interplay between linear and angular motion.

  • #31
3 unknowns and only 2 eqs
 
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  • #32
You have expressions for the a's in terms of T and you can get expressions for the alpha's in terms of T. Put them both into a1+a2=r1*alpha1+r2*alpha2. All that's left is T. Solve for it. You aren't going in circles. You are just giving up. Don't be a weakling! It's ONE equation in ONE unknown.
 
Last edited:
  • #33
you still there? i don't really feel like I am getting anywhere... in fact i think I've been here before heh..
 
  • #34
Yes, I'm still here. But I'm getting impatient. Solve this thing, ok?
 
  • #35
T = ((m1 + m2)G)/2
 
  • #36
I'll get you started. You have already told me in so many words a1=g-T/m1 and alpha1=T/(m1*r1). Same for the 2's. Read back if you don't believe me.
 
  • #37
danny271828 said:
T = ((m1 + m2)G)/2

You know that's wrong, right? How did you get that?
 
  • #38
ok heh got it...
 
  • #39
just been staring at this problem way too long...
 
  • #40
You may thank me now. :)
 
  • #41
Thank you much for your infinite patience... I appreciate it :D
 
  • #42
danny271828 said:
just been staring at this problem way too long...

You were missing the s'' thing. Conservation of string. If it's any comfort, I stared at it for a while myself.
 
  • #43
Yeh i should have stepped away from it for a while... after 3 hours or staring my brain went numb... thanks again man...
 

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