Momentum/Energy Conservation problem

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A massless spring with a spring constant of 20 N/m compresses between two carts, one with a mass of 5 kg and the other 3.5 kg, and is compressed by 1.2 m. The potential energy stored in the spring can be calculated using the formula 0.5k(x^2), which equals the kinetic energy of the carts after release. To find the speeds of the carts after they are released, conservation of energy and conservation of momentum principles must be applied. The force acting on the carts is derived from the spring constant, which is crucial for solving the problem. Clarification on these concepts is essential for successfully tackling the homework assignment.
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Exploding Spring

A massless spring of spring constant 20 N/m is placed between two carts. Cart 1 has a mass M1 = 5 kg and Cart 2 has a mass M2 = 3.5 kg. The carts are pushed toward one another until the spring is compressed a distance 1.2 m. The carts are then released and the spring pushes them apart. After the carts are free of the spring, what are their speeds?

Im sorry but I am utterly confused by this problem.. I am pretty sure that I must first use conservation of energy to find momentum then conservation of momentum to find velocity. Exactly how I apply all these concepts together is scrambling my brain..

please help! :cry:
 
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Start with a fbd showing the spring compressed and the spring force (the same force) acting on both carts. Do you know, or can you derive, the potential energy equation for a spring?

The energy stored in the compressed spring will equale the energy of motion for the carts. You know the force acting on the carts, the masses on the carts, and the initial enerty stored in the system.

Good luck.
 
The equation for the potential energy of a spring is .5k(x^2), with k being the spring constant and x distance compressed.

Sorry faust9 but i don't think your method will work because I do not have the force acting on the carts. You must have been looking at the spring constant and assumed that was the force. Thanks very much for the help though, any more suggestions would be GREATLY appreciated!

This homework is due in 3 hours and this problem is just killing me! Anyone else have any idea how to tackle it?
 
quatli said:
The equation for the potential energy of a spring is .5k(x^2), with k being the spring constant and x distance compressed.

Sorry faust9 but i don't think your method will work because I do not have the force acting on the carts. You must have been looking at the spring constant and assumed that was the force. Thanks very much for the help though, any more suggestions would be GREATLY appreciated!

This homework is due in 3 hours and this problem is just killing me! Anyone else have any idea how to tackle it?

You DO have the force acting on the carts. Reread the question you started this thread with.
 

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