Question

A massless pan hangs from a spring that is suspended from the ceiling. When empty, the pan is 50cm below the ceiling. If a 100g clay ball is placed gently on the pan, the pan hangs 60 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?

Answer 1

Here is what I thought should be done:
F=mg and Fsp = k(x1) x1 is the distance we get when placed gently


\[mg = kx _{1}\]\[\frac{ mg }{ x _{1} } = k\]

then I said ,

Potential energy lost =Kinetic energy gained
\[mgh = \frac{ 1 }{ 2 }k(x _2)^{2}\]
\[x _{2} = \sqrt{\frac{ 2mgh }{k }} =\sqrt{\frac{ 2mghx _{1} }{ mg }}\]

and then
\[x _{2} = \sqrt{2 \times 0.1 \times 0.5}= 0.316m\]

I then added the 31.6cm to the original 50 cm, to get 81.6. But then the answer at the back of the book says its 93cm ????? Please help!