How would I be able to estimate the energy and power of a torsional spring (similar to one used in a mouse trap)?

Any help is appreciated.

 

From your drawing: What is stationary and what rotates? Can you place a bearing in the center bore, front and back; attach a crank to an axle thru the bearing ,with a hole for the pin[#1] ?? Wind up the spring ,counting the turns.Measure crank arm from axle to handle,measure force needed to keep crank from turning from start to fully wound. use spring scale or a container of weights. Two X crank length X ∏ X turns willgive a good indication of work that spring can do. Need something greater than 10,000 cm-grams.

 

This may be of some use: http://www.engineersedge.com/spring_torsion_calc.htm

 

Woops...I thought your drawing was a nice encased spring mech. The same approach can be used with linear tortional springs. Thanks to thingmaker3 you can put real numbers on your spring. For Deg, use 360 X turns.
Not only does trolley want to go 2 m, but in a hurry.
What are size limitations.
What do you have to work with, drill press, table saw,etc.??

 

Have you considerd using a sling-shot? Place a two Kgram weight on the trolly, shoot it of with strong springs; weight goes 1/2 meter trolly goes other direction like a bat out of Carlsbad Caverns. Might earn brownie points or disqualification.