Verified answer

The potential energy stored in the spring is:

Ep = k ∙ x² / 2

where

k = spring constant

x = spring compression

That Ep will be converted from the change in potential energy from the block

∆Ep = m ∙ g ∙ ∆h

where

m = mass

g = acceleration by gravity

∆h = chainge in height

Note that ∆h is NOT ONLY the 17 cm the block is above the spring, but ALSO the distance x that the spring is compressed, so

m ∙ g ∙ ∆h = k ∙ x² / 2

10 ∙ 9.8 ∙ (0.17 + x) = 5000 ∙ x² / 2

2500x² - 98x - 16.66 = 0

Solve this quadratic equation using the discriminant (abc formula)

√D = √( (-98)² - 4∙2500∙(-16.66) ) = 419.77

x₁ = (98 + 419.77) / (2∙2500) = 0.103 m

x₂ = (98 - 419.77) / (2∙2500) = -0.064 m

The spring will not be stretched by a falling block, so the only valid solution is

x = 0.103 m

The length of the spring at the moment of maximum compression wil be:

L = 0.2 - 0.103 = 0.097 m = 9.7 cm

The energy of the system is conserved.

=> the potential energy will be partially transferred to kinetic at the moment the block hits the spring.

Before the block is dropped the total energy is potential=mgh=10*9.81*(0.17+0.2)=36.297J

After the block in dropped and just before it hits the spring:

Energy=kinetic+potential this will all be transformed to elastic energy of the spring

=1/2kx^2=0.5*5000x^2=>x=radical 36.297/2500=0.1205m=12.05cm