Final Challenge-Spring Compression

1. This final challenge was quite a success for our group as we thoroughly applied the skills we’ve learned throughout the year to solve the problem. Our goal for this challenge was to figure out how much we should compress two different springs so that carts of equal mass will come off at the same velocity. Below is a quick sketch of the set up

B. We did not have to take much data for this experiment as much of it was plug and chug after we figured out the equation. Because the energy for the system which consists of the cart, the spring, earth, and track, starts off all in elastic energy and finishes all in kinetic energy, our conservation of energy equation is Eel=Ek or 1/2kx^2=1/2mv^2. We were looking for the x value in the elastic energy formula which represents the amount the spring needs to be compressed and we had the other values to plug into the formula to solve. We set up 2 equations for each cart, and then weighed them both and converted their weights into kg. We were given the k constant for each cart, and then we picked a velocity we wanted the carts to come off at for consistency purposes. We chose .5 m/s for both and plugged all the values into the formula and solved for x for both carts. After getting the x value, we compressed each spring the given amount and using PASCO Capstone we preformed a final test to see if the carts would come off at around .5 m/s like we predicted and we were pretty accurate. Below is a table of all the variables we used:

C.  After we plugged all the variables into the formula pictured above and solved for the amount the spring needed to be compressed, there was not much analyzation that needed to be done. We were careful to be as precise as possible when measuring off the distance and we allowed the motion sensor to run for a bit before we ran the test so it would be more a little more calibrated. We then used the graphs on Capstone to find the exact velocities the 2 carts came off and they were well within out predicted velocity and very close to one another as well. 

D. Overall our prediction was a success and we were extremely close having a percent error of 1.69%