Comparing Spring Compression in Two Trials with Different Release Heights

[phzzo]

Homework Statement

Students in a physics class set up an experiment to examine the behavior of springs being compressed under various conditions. In the first trial of the experiment, students released a 1.5 kg block from rest at the top of a ramp. The block slid down the ramp, across a horizontal surface, and then collided with an uncompressed, massless spring. Students attached a marker to the spring so they could see how far it was compressed in bringing the block to rest. All surfaces in trial 1 were effectively frictionless.
In trial 2, the block was dropped from the same height directly above an identical spring. This spring was placed such that its bottom had the same height as the spring in trial 1 (as shown in the diagram). Again the students recorded the maximum compression of the spring in bringing the block to rest. Indicate which of the two springs experienced a greater compression in bringing the block to rest.

Homework Equations

E_g = mgh
E_sp = 1/2kx²

The Attempt at a Solution

Each block will have a potential energy that is conserved as elastic energy. The blocks have the same mass and the springs have the same k. For each block and spring, mgh = 1/2kx², but I'm not sure about the h for Trial 2. Would it be the same as Trial 1?

 

[CWatters]

I'm not sure about the h for Trial 2. Would it be the same as Trial 1?

Try assuming that in both cases the spring is compressed some amount (say 50%?) after the collision. Draw that and work out the height that you would use to calculate the PE that has been converted into energy stored in the spring. Can they be the same?