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Nano-Passion

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## Homework Statement

A 1.20 kg piece of cheese is placed on a vertical spring of negligible mass and force constant k = 1800 N/m that is compressed 15 cm. When the spring is released, how high does the cheese rise from this initial position? (The cheese and the spring are not attached).

I looked up the solution to cramster, and the person did something bewildering (bewildering to me at least).

He set [itex] u=mgh=1/2kx^2[/itex] then solved for h and got [itex]s = 1.72m[/itex], but this doesn't make sense to me because he didn't take the acceleration of gravity in effect? I believe mine is more correct but I don't know too much in elastic potential energy.

## Homework Equations

[tex]v^2=V_o^2+2as[/tex]

[itex]K)1+u_g+u_{el}=k_2+U_{g2}+U_{el2}[/itex]

I set the relaxed state of the spring to be 0.

## The Attempt at a Solution

[tex]mgh_1+1/2kx^22=1/2mv^2+mgh_2+1/2kx^2[/tex]

[tex]mgh_2[/tex]and [tex]1/2kx^2_2[/tex] go to 0

[tex]1.2(9.8)(-.15) + 1/2(1800)(-.15)^2 = 1/2 (1.2)v^2[/tex]

Solve for v accordingly

[tex]v=5.55 m/s[/tex]

Then I use a simple kinematics equation to see how high it will go in the air.

[itex]v_o = 5.55m/s[/itex] [tex]a=9.8m/s^2[/tex] [tex]v_f = 0[/tex] [tex]s=?[/tex] [tex]v^2= v_o^2 + 2as[/tex] When we solve for s we get [itex]s=1.57m[/itex]

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