Newton's second law 3 pulley problem.

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SUMMARY

The discussion focuses on solving a Newton's second law problem involving three pulleys with no friction and massless strings. The equations derived include tension (T) and acceleration (a) for three masses (m1, m2, m3). Key equations include +T - m1g = m1a, m2g - 2t = m2a, and +T - m3g = m3a, leading to the relationship g(-m1 + m2 - m3) + 2a2 = (m1 + m2 + m3)a + a1 + a2. The tension between the 2kg and 5kg masses remains constant due to the absence of friction.

PREREQUISITES
  • Understanding of Newton's second law of motion
  • Basic knowledge of pulley systems and tension
  • Familiarity with algebraic manipulation of equations
  • Concept of massless strings in physics
NEXT STEPS
  • Study the principles of tension in pulley systems
  • Learn how to apply Newton's laws to multi-body problems
  • Explore the effects of friction on pulley systems
  • Investigate advanced topics in dynamics, such as rotational motion
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in solving complex pulley problems using Newton's laws.

travisdass123
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There is no friction and the strings are massless. Find Tension and acceleration.

3. The Attempt at a Solution

1. +T-m1g = m1a
2. m2g-2t= m2a
3. +T - m3g =m3a
4. 2a2 = a1+a3

g(-m1+m2-m3) + 2a2 = (m1 + m2 + m3)a + a1 + a2

-29.4 + 2a2 =11a +a1+ a2
 

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travisdass123 said:
There is no friction and the strings are massless. Find T1 T2 T3 and acceleration.

If there is no friction, then the tension in the string connecting the 2kg and 5kg masses should be constant throughout.
 

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