Spring problem on work and force

AI Thread Summary
To determine the speed of a 0.4 kg mass after it is released from a compressed spring with a spring constant of 400 N/m, energy conservation principles apply, where the potential energy stored in the spring converts to kinetic energy. The initial potential energy of the spring can be calculated using the formula PE = 0.5kx^2, where x is the compression distance. After the spring decompresses, the mass's speed can be found using the kinetic energy formula KE = 0.5mv^2. For the second part of the problem, clarification is needed regarding whether the hill is 0.5 m high and if the speed is being asked for at the top of the hill. The discussion emphasizes the importance of understanding energy conservation in solving the problem.
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Homework Statement



a .4 kg mass compresses a spring of .2m. The spring constant is 400n/m How fast is the mass moving after the mass is released and the spring uncompresses? If the mass is going up a .5m hill, how fast is it going?



Homework Equations



PE+KE=w

PE=mgh

KE=.5mv^2




The Attempt at a Solution



PE=.5(9.8)(x)
 
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To find how fast its moving right after the spring decompresses, use energy conservation. Elastic potential energy is lost, and kinetic energy is gained.

You'll have to clarify the second part -- is the hill 0.5m high? Do you mean how fast is it going at the top?
 
The hill is .5m high
 

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