A 0.150 kg block is placed on a light vertical spring...?

Question

A 0.150 kg block is placed on a light vertical spring (k = 5.40 103 N/m) and pushed downward, compressing the spring 0.100 m. After the block is released, it leaves the spring and continues to travel upward. What height above the point of release will the block reach if air resistance is negligible?

The answer I got is 0.184m which for some reason is "off by multiples of ten". What conversion do I use for this?

Answer 1

using conservation of energy
the energy stored in the spring will propel the block upward
The question is, was the block at rest on the spring when pushed downward an additional .1 000 m, or was the total compression of the spring .100 m?

I will assume the block was at rest since this is the more complicated

The initial compression of the spring
.15*g*x=.5*k*x^2

divide x from both sides and isolate x

.15*9.81*2/5400=x
x=.000545

The additional compression of the spring creates total energy in the spring of

.5*5400*.100545^2
27.295 J
The apogee will be the translation of all of this stored energy in the spring to potential energy in the block.
Recall that the block is at -.100545 from the release point so
(h+.100545)*.15*9.81=27.295
h=18.55-.100545
h=18.45 m

j