General Rule for Spring Compression?

AI Thread Summary
To determine how much a spring compresses when a block slides on a frictionless table, the principle of conservation of energy is applied. The kinetic energy of the moving block, represented as 1/2 mv^2, is converted into the potential energy stored in the compressed spring, given by 1/2 k x^2. The equation set up for this scenario equates the initial kinetic energy to the spring's potential energy at maximum compression. The correct relationship to use is that the kinetic energy of the block equals the spring energy when the block comes to rest. Thus, the compression distance x can be calculated using the formula derived from this energy conservation principle.
FrenchAtticus
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Homework Statement



A block of mass m slides on a horizontal frictionless table with an initial speed. It then compresses a spring of force constant k and is brought to rest. How much is the spring compressed x from it's natural length.




Homework Equations



??
 
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Conservation of energy.
Whats the energy of a moving block
Whats the energy of a compressed spring
 
Conservation of energy is mgh1 + 1/2mv1^2 = mgh2 + 1/2mv2^2

energy of a moving block is 1/2mv^2

energy of a compressed spring is potential?

How do I apply these to find how much the spring will compress.
 
FrenchAtticus said:
Conservation of energy is mgh1 + 1/2mv1^2 = mgh2 + 1/2mv2^2
No this is only for a falling object mgh2 = gravitational potential energy.

energy of a compressed spring is potential?
Whats the equation for the energy in a compressed spring?
 
energy in a compressed spring is F = -Kx

and is conservation of energy m1v1 = m2v2?
 
No that's momentum.
Spring energy = 1/2 k x^2
Kinetic energy = 1/2 m v ^2

For conservation of energy you have the ke of the block at the start and the spring energy at the end. So the ke just equals the spring energy.
 

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