Calculating Spring Constant - Force or Energy?

AI Thread Summary
The discussion centers on two methods for calculating the spring constant (k) when a mass m stretches a spring by x meters. The first method equates the spring force (kx) to the gravitational force (mg), yielding k = mg/x. The second method involves using energy principles, equating the gravitational potential energy lost (mgx) to the energy gained by the spring (1/2 kx^2) and the kinetic energy of the mass. A discrepancy arises when using the energy method, resulting in a k value that is half of the one calculated using force. The correct approach for calculating k in this scenario is to use the force method, while the energy method is more suited for dynamic problems involving motion.
Cintdrix
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I've been being confused lately as to the 2 methods. The example I'm thinking of is when a weight of mass m is hung on a spring and it stretches x meters.

First of all, I know you can equate the spring force (kx) to the force of gravity (mg), to get
k = mg/x

But is it also possible to say that the gravitational potential energy lost (mgx) is equal to the energy gained by the spring (1/2 kx^2)? When I do this, I get a different k which is half the original k and probably wrong. How can you calculate K for this problem using energy?
 
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The first method F = mg = kx is what you would use to find the spring constant k. The second equation is used for the dynamic problem "How fast is the mass moving at distance x?". To solve, equate the potential energy "lost" by the downward motion to the potential energy of the spring AND the kinetic energy of the object: E = mgx = (1/2 kx^2) + (1/2 mv^2)
 

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