If spring 2 can only compress by 2 meters, what mass must the bock have, given the setup depicted in diagram 1, to compress spring 2 by exactly...

The energy required to compress a spring with spring constant Pk by x is equal to (1/2)*Pk*x^2.

In the diagram, the spring 1 is compressed by 5 m. The spring constant of this spring is 71 N/m. If the mass of the block is m, the potential energy stored in the spring is 0.5*71*25 = 887.5 N.

Spring 2 can compress only by 2 m. For this to happen, the block has to rise by 41 + 2 = 43 m. The gravitational potential energy of the block rises by m*9.8*43 = 421.4*m. The energy required to compress the spring 2 by 2 m is 0.5*m*37 = 18.5*m

As energy is conserved,

18.5*m + 421.4*m = 887.5

m = 887.5/439.9

m = 2.0175 kg

If the mass of the block is 2.0175 kg, the required conditions are met.

When the spring 1 is released, the block is accelerated. Its kinetic energy at a level x m from where it is released is: 887.5 - 2.0175*x*9.8

The velocity at that point is `sqrt(2*(887.5 - 2.0175*x*9.8)/2.0175)`

The maximum velocity of the block is equal to 29.66 m/s. It has this velocity when spring 1 is released.