Vertically Stretched Spring w/ Hanging Mass.

[rmiller70015]

Homework Statement

A spring with a k=53N/m hangs vertically next to a ruler. The end of the spring is next to the 15cm mark on the ruler. If a 2.5kg mass is now attached to the end of the spring, where will the end of the spring line up with the ruler marks?

k=53 N/m
m=2.5m
y₀=0.15m

Homework Equations

Potential Elastic Energy =1/2kx^2
1/2kx = Fnet

The Attempt at a Solution

Drew a diagram with a spring and mass at two different positions. Having trouble getting the force of tension when the spring is at equilibrium (F_T1. But I've tried using conservation of energy, but can't figure out how to get either the acceleration at equilibrium or the force of tension at the spring's equilibrium. I've also tried using kinematics, but without either a time interval or acceleration I can't get a value for V₁. Other than that I've tried a number of different ways of substituting equations into other equations to try to get some of these missing values, but I can't seem to get what I am looking for. I'm looking for a blueprint for how to get the answer to this question.

 

[Chestermiller]

If x₀(=15 cm) represents the location of the bottom of the spring when no weight is attached, and x represents the location of the bottom of the spring when the weight is attached, how much has the spring stretched? What is the force exerted by the spring on the mass? From a FBD, how does this compare with the weight of the mass (assuming the mass has been moved downward by hand)?

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