Solving Mass Ratios from Acceleration: The 3-Body Experiment

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In the three-body experiment involving masses m0, m1, and m2 on a frictionless surface, the accelerations are related as a1=4a0 and a2=a0/3 when a compressed spring is released. The discussion emphasizes the conservation of momentum in this closed system, as the bodies move apart in opposite directions. It is noted that the forces exerted on each mass by the spring are equal, which allows for the calculation of mass ratios. Participants are encouraged to derive the ratios m0/m1 and m0/m2 based on these relationships. Understanding these principles is essential for solving the mass ratio problem effectively.
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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?
 
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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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