We were able to find some information just by measuring, including the distance from the edge to the rubber band, the spring konstant in the rubber band, the mass of the block. From there our group was able to work with equations until we found the coefficient of friction. Then with the coefficient of friction we found the force of friction on the block which in turn allowed us to find the unbalanced force then the acceleration. With the acceleration of the block and the distance away, and knowing that the ending speed is 0, more equations helped us find the starting velocity.
Once all these elements were figured out, we knew that we had to somehow find how far to pull back the rubber band to give the block enough energy to give it the same initial velocity it needs to reach the edge of the ramp. To do this we had to move to energy equations. This was what was new for us at the time. We learned that the energy as it moved from elastic to kinetic had to be the same quantity. Therefor, using the equations for kinetic energy, E=1/2mv^2, and elastic energy, E=1/2kx^2, and setting them equal to eachother, we plugged what we knew and were able to find x in the elastic equation. X stood for the distance stretched for the rubber band and with that we were able to test out and see if it worked.
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