Conservation of mechanical energy

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SUMMARY

The discussion centers on the conservation of mechanical energy in a system involving two blocks connected by a massless string over a frictionless pulley. Block 2, which is lighter, is released from a height, while Block 1 is at a higher elevation. The key equations used are Emechf = Emechi and Emech = Ug + K, leading to the conclusion that the blocks meet at a height determined by their respective masses and the distance they travel. The height at which they meet is derived from the relationship that one block lowers by the same distance that the other rises.

PREREQUISITES
  • Understanding of mechanical energy conservation principles
  • Familiarity with gravitational potential energy (Ug) and kinetic energy (K)
  • Basic knowledge of pulley systems and massless string dynamics
  • Ability to manipulate algebraic equations involving multiple variables
NEXT STEPS
  • Study the principles of conservation of energy in mechanical systems
  • Learn how to apply the equations of motion in pulley systems
  • Explore gravitational potential energy calculations in varying mass scenarios
  • Investigate the effects of friction on mechanical energy conservation
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators seeking to explain the concepts of energy conservation in dynamic systems.

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Homework Statement



I have two blocks attached by a string (massless) over a pulley (frictionless, massless). Block 2 (which weighs less than block one) is released and the two blocks meet momentarily at the same height. I have the find the speed at which the meet at that moment. The blocks are separated by a distance of 1m.

I have drawn a figure in paint (sorry for this pic): http://i36.tinypic.com/2076at1.png

Homework Equations



Emechf = Emechi
Emech = Ug + K

The Attempt at a Solution



Emechf = Emechi
<=> (m_1gh + m_2gh) + (1/2m_1v^2 + 1/2m_2v^2) = m_1gH (where H = 1m, and h is the height at which they meet)

But then I have this h which is unkown and I can't figure out.

Thanks a lot in advance.
 
Physics news on Phys.org
If the lower (and lighter) block starts out at height "h", the higher (heavier) block starts out at height "h + 1".

At what height will they meet? Hint: One block lowers by the same distance that the other rises.
 
Thanks a lot, I see it clearly now. I really appreciate you help.
 

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