How Do You Calculate Final Velocities in a Spring-Mass System?

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SUMMARY

The discussion focuses on calculating final velocities in a spring-mass system involving a 1-kg mass and a 3-kg mass on a frictionless table. The minimum work required to compress the spring is determined to be 150 joules using the work-energy principle. For the second part of the problem, participants suggest applying both the conservation of energy and conservation of linear momentum to derive the final velocities of each mass when released simultaneously. The key equations involved are the kinetic energy formula and momentum conservation principles.

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  • Understanding of Newton's laws of motion
  • Familiarity with the work-energy theorem
  • Knowledge of conservation of momentum
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Homework Statement


a massless spring is between a 1-kg and 3-kg mass as shown.but it is not attached to either mass. Both masses are on a horizontal frictionless table. In an experiment, the 1 kg mass is held in place and the spring is compressed by pushing the 3 kg mass. the 3 kg mass is then released and moves off wiht a speed of 10 m/s.

a. determine the minimum work needed to compress the spring in this experiment.

b. the spring is compressed again exactly as above. but this time both masses are released simultaneously. determine the final velocity of each mass relative to the table after the masses are released.



i've found a. by using work done=change in kinetic energy and got 150 joules.


B. i have no real idea how to start this problem, i think that the amount of work may stay the same but I am not sure. my thought is work done=totat kinetic energy so, 150 joules= 1/2(1)v^2 + 1/2(3)v^2
 
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I have not done one of these in a long time, but it appears that you will now have two unknowns. This means you NEED to have two equations. You have one. Is there another theory (equation) that you cab apply to this problem?
 
One of the equation involve the conservation of energy, the other would involve the conservation of linear momentum.
 

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