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springs

A massless pan hangs from a spring that is suspended from the ceiling. When empty, the pan is 47 cm below the ceiling. If a 95  g clay ball is placed gently on the pan, the pan hangs 60 cm below the ceiling. Suppose the clay ball is dropped from the ceiling onto an empty pan. What is the pan's distance from the ceiling when the spring reaches its maximum length?

so i think i have an answer but i was wondering if you could check it before i submit it

k=(.9316)/,11=8.4694
(1/2)kx^2=mgh
x=2.7636m
I added .47
3.2336m
i converted to cm
323.36
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First, solve for k.  Make sure to convert everything to kilograms and meters.
Force(normal) = k * x(distance the pan hangs extra when clay ball is in the pan)
k = (9.81*0.095) / 0.13
k = 7.1688

Now use conservation of mechanical energy for when the clay ball strikes the pan.
ME = KE + PE
KE(intitial) + PE(initial) = KE(final) + PE(final)
initial potential energy is 0 and final kinetic energy is 0, so
KE(initial) = PE(final)
0.5mv^2 = 0.5kx^2
you are solving for x here since it is the final displacement
x = sqrt( (mv^2) / k )
initially, velocity is the velocity of the clay ball when it strikes the pan which is sqrt(2gh)

x = sqrt( (m*2*g*h) / k )
x = sqrt( (0.095 * 2 * 9.81 * 0.47) / 7.1688 )
x = 0.349572 meters
add the initial 0.47 meters
total distance from ceiling is 0.819572 meters, or 81.9572 centimeters
initially, velocity is the velocity of the clay ball when it strikes the pan which is sqrt(2gh)

but the velocity of the ball is NOT as given here. when it strikes the pan it has fallen a distance less than h,     (by the distance that it stretches the spring)
My initial posts stand.
I made the same mistake in my other springs post, I didn't notice it until you pointed it out. I also didn't realize that this is probably homework and we aren't supposed to give answers with homework. Either way, it won't matter much, the question is almost a year old.  
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the question was answered within the homework restriction. several suggestions were given. Work was critiqued
see aburr

ID: https:#a33846971
ID: https:#a33847005
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