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.
I set the relaxed state of the spring to be 0.
The Attempt at a Solution
[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
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]