Solving Mass Ratios from Acceleration: The 3-Body Experiment

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SUMMARY

The discussion focuses on solving mass ratios from acceleration in a three-body experiment involving masses m0, m1, and m2 on a frictionless surface. When a compressed spring is released between bodies 0 and 1, the accelerations are related by a1=4a0, while for bodies 0 and 2, the relationship is a2=a0/3. The conservation of momentum and the equality of forces exerted by the spring on each mass are crucial for determining the mass ratios m2/m1 and m0/m1.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of conservation of momentum
  • Familiarity with basic concepts of mass and acceleration
  • Experience with spring dynamics in physics
NEXT STEPS
  • Calculate the mass ratio m2/m1 using the derived acceleration relationships
  • Explore the implications of conservation of momentum in multi-body systems
  • Investigate the effects of varying spring constants on acceleration
  • Learn about frictionless surfaces and their role in classical mechanics experiments
USEFUL FOR

Physics students, educators, and anyone interested in classical mechanics, particularly those studying dynamics and mass-acceleration relationships in multi-body systems.

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Consider three bodies with mass m0 m1 and m2 at rest on a frictionless surface. When we insert a compressed spring between bodies 0 and 1 and release the spring we notice that the magnitudes of their accelerations are related by: a1=4a0. When we do the same experiment with bodies 0 and 2 we find: a2=a0/3. What is the ratio of m2/m1?

Can anyone tell me how i should start this question?
 
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Start finding the ratios m0/m1 and m0/m2
 
what do you mean?
 
Karma said:
Can anyone tell me how i should start this question?
When the springs are released and the bodies fly apart, what physical quantity is conserved?

Alternatively, from a Newton's laws perspective, when two bodies fly apart what can you say about the force exerted on each body by the spring?
 
Last edited:
One object will be sent to the left and the other object will be sent out to the right. momentum would be conserved in this closed system..
 
Karma said:
One object will be sent to the left and the other object will be sent out to the right. momentum would be conserved in this closed system..

yes. and the force on each mass attached to the spring is the same. use the fact that the forces are the same to get the ratio of m0/m1 and m0/m2.
 

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