October 20, 2014: Magnetic Conservation.

Purpose: The purpose  of this lab is to prove that the integral of magnetic force with respect to time is equal to the change in momentum.

Apparatus:We used an air source to blow air into our triangular track which makes the track friction-less. We used a red cart to move up and down the track. We also used a motion sensor to measure the distance between the motion sensor and the metal clip board. A magnet was also placed below the motion sensor so that their would be a repelling force between the magnet below the sensor and the magnet attached to the end of the cart.

 Track,cart,motion sensor, and magnet

Air sourse

What We Did: In Order to get the information we needed to derive a formula to prove that the integral of the force was equal to the change in momentum, we had to obtain a relationship between the distance of the cart to the magnet and the angle of the track. First we raised our track to a small incline and turned the air source on so that the cart could begin to slide down the track. it eventually came to a stop where the magnetic forces repelled and we turned off the air source so that the cart could stay in place due to friction. In order to get the angle of the incline we had to download an app from our phone that obtained angles to a 10th of a degree of accuracy. This made calculating the angle so much easier since we only had to place the phone onto the track and it would give us the angle we needed. Then we measured the distance between the magnet below the motion sensor and the magnet in front of the cart. We Did This processes 9 times and came up with a chart similar to the one below. We Obtained a smaller distance as we increased the angle of the track.

CM     Angle (In Degrees)   Mass of the cart 

3.3      2.35                                     356 grams

2.6      4.6

2.2      5.7

1.9      8.2

1.8      8.7

1.6      10.6

1.4      12.4

1.3      15.8

What We Did With This Data: We logged onto logger Pro and began to plot our information in an x,y system. Our X= the distance between the magnets. Our Y=The force, Where Force=mgsin(theta) This gave us a graph in which we had to insert a POWER FIT to connect our data points.

Next we found a formula for the separation between the motion sensor and the clip board by using total distance-X. Next we made a formula for UR which was the integral of the force. This equaled (.0003785/.792)*Position^(-.792). We got this integral from the formula above which used the power fit and gave the equation Ax^B. We plugged in the numbers and integrated. We then made a new calculated column for kinetic energy which equaled .5MV^2. Finally we made a new calculated column for total energy which equaled Ur+KE

BELOW IS OUR GRAPH OF THE INFORMATION ABOVE

Conclusion: As our chart above shows, total energy is constant and ranges beteween .30 and .50 This Shows that  that the integral of magnetic force with respect to time is equal to the change in momentum.