15-Apr-2015 Impulse-Momentum Activity

Purpose
The purpose for this lab is to observe the impulse during a collision and how it changes the momentum. This is going to be done by colliding a cart in an elastic collision at different with carts of different mass then an inelastic collision.

Experiment
The first part of this experiment is to observe two elastic collisions each with different mass carts. this is set on a track with one cat held down with it's spring projecting out while the other cart will be pushed towards it and bounce back, this is done twice with carts of different mass. There is a force probe that is on the cart which will collide with the spring during the collision and give us how much force occurred, as well as a motion detector on the other side of the track which will give us velocity and position versus time.

Impulse of a collision is calculated by taking the mass and multiplying it by the change in velocity before and after the collision. From the data we gathered we go to the graph and find the integral of the dip of the force graph, which is the beginning of the collision to the end of the collision. This give us the impulse of the collision, and this is done with the cart with a greater mass as well.

The next part of the experiment has the same set up, but instead of a cart at the end it is a clay wall also the cart that is going to collide with a wall has a nail on it as well. The purpose of the nail is so that it will get lodged into the clay and stop the cart from bouncing back thus creating n inelastic collision. Just like in the previous part we push the cart and collect the data on the collision.

 From that data we once again take the integral of the dip to find the impulse of the inelastic collision. Once we have done all the impulses from the graphs we then calculate what the theoretical momentum should be. This is done by going the the velocity graph and finding out when the collision started and when it ended, then we multiply the mass of the cart by the the difference between the final velocity and initial velocity.

When we compare the values we got from the the graphs and put calculated values we can see that they are very close, therefore we can say that the impulse is equal to the change in momentum. The reason the the values were not exactly the same were due to error that occurred during the experiment. Some of those errors being that there is friction on the track and the collision did not hit the force probe dead center.

13-Apr-2015 Magnetic Potential Energy

Purpose
There was two purposes to this lab was to determine the conservation of energy for a magnetic system.

Experiment
The set up for this experiment is an air track with an air glider on it and a motion sensor on the end of the track on where the magnet is. For the first part of the lab we raise the track to different angles, then let the glider get as close to the end of the track as possible until it stops. We do this process six times so we get six sets of data.

We then take the six sets of data and graph them in logger pro, and from that graph we power fit it. Next we enter a new calculated column for the force which in this case would be gravity (mgsinθ) and then graph the force against the separation distance. Since we know that the area under the curve for a force vs position graph is work we can then find an equation of the line and integrate it. We use a power fit curve for the line since it fits the cure the best and the equation given is the equation for the magnetic force, and then we integrate that force to get the equation for the magnetic potential energy. In our case however we strike through the last point because it was too far off from the curve making it an outlier.

Now that we have found the equation for the magnetic potential energy we can now start the second part of the experiment. The second part of the experiment has the same set up as the first part, except that instead of being raised at and angle it is left leveled. We then start the glider at the end of the track and give it a push towards the magnet while recording the collision.

After the data collection is over we created new calculated columns for kinetic energy, separation, magnetic potential energy, and total energy. For separation we take the position that the motion detector reads and subtract it from the difference between the distance between the position the motion senor reads and the distance between the two magnets. We then graph all the energies together on the y-axis against time to compare and see if energy is indeed conserved within the system.

From our graph we can see energy is conserved by in that as the kinetic energy decreases it is becoming magnetic potential energy thus the magnetic potential energy increases. The total energy reflects that by being a constant line across; however in the above graph it is hard to see since the range are very small, but if we increased the ranged from 0-0.02 to 0-0.4 we can see that it relatively a straight line.

The reason that the total energy is slightly tilted when we zoomed out would be cause by error when we calculated magnetic potential energy. The cause for this error would be from the uncertainty that in the ruler used, the uncertainties that logger pro gave us when we generated the graph magnetic force, and the uncertainties of the phone when measuring the angle. Another source of error would be in part two of the lab there was interference with the motion sensor as can be seen by the kinetic energy line. The cause for this error could be from interference from the the motion sensor bouncing off part of the glider instead of only the steel plate, another reason would be that there was some friction on the track.

8-Apr-2015 Spring Energy

Purpose
The purpose for this lab is to see if the energy within a spring system is conserved or not; however, for this lab the spring's mass is no longer negligible.

Experiment
For this lab we used a spring hanging from a force sensor which is attached to a rod on one end and a hanging mass on the other end of the spring. The whole system was attached to the side of a table with a clamp and also with a motion detector below it.

Before we began the experiment as a class we came up with what energies were in the system, as well as derived how we were able to find those energies. The energies that we found in the system were elastic potential energy, gravitational potential energy of the mass, kinetic energy of the mass, gravitational potential energy of the spring, and kinetic energy of the spring.

Once we found have figured out what energies we are trying to find we can then begin the experiment. We first find the spring constant of our spring with the force sensor by pulling the spring and finding the slope of the force vs position graph. The reason we need to find the spring constant is because it will be needed for finding the elastic potential energy. Once we have found the spring constant we conduct the experiment by hanging a mass at the end of the spring and letting it oscillate.

We then take the data we collected from logger pro and make new calculated column for each of the energies that are in the system with an additional column for the total energy of the system. Once all the energies have been calculated we then graph them all on the y-axis against time.

The reason we graph all the energies together is because it gives us a better picture to see if energy is conserved in the system and in this case it was. One reason we know this for example is because through conservation of energy we know that the as the mass fall the gravitational potential energy becomes elastic potential energy. Meaning that as the mass fell the gravitational potential energy decreases and becomes elastic potential energy which means it the elastic potential energy increases. The graph shows this relationship very clearly as one dips the other peaks. Another reason we know that energy is conserved is because if we look at the total energy we can see that the oscillation is constant and that no energy is gained or lost.

6-Apr-2015 Work Kinetic Energy System

Purpose
The purpose of this lab was to see how force was related to the work of the system. This was done with two experiments, one was the force and work done on the spring and the other being the force and work done by the spring.

Experiment
The first part of the lab was set up with a cart attached to a spring which is in turn attached to a force sensor, all on a track with a motion detector at the end of the track. What we did for this part was to start to data collection on logger pro and slowly push the cart and stretch the spring, this will help us find how much work is done on the spring.

We then take the data and generate a force vs position graph, which we then take a section of and integrate it to find out how much work is done. The reason that we integrate the the line because we learned that the area under the curve will give us the work done. We also linear fit the curve to help us find the spring constant for our spring which is given as the slope.

For the second part of this lab we use the same set ups as we did in part one except that instead of pushing the cart and stretching the spring, we are going to have the spring already stretched out by the cart and have it pull the cart back. By doing this small change we can then find how much work is done by the spring.

Just like before we integrate the force graph to find the work done by the spring, but to double check that the work done we got is within reason we then compare it to a kinetic energy graph along with it for a comparison. This was done by adding a new calculated column used to calculate the kinetic energy. The reason we compare the work to the kinetic energy is because the change in kinetic energy is equal to work.

As seen above we compared the work and kinetic energy of the work done by the spring at three different position within the experiment to see if they are consistent. We can see that the kinetic energy and work are not exactly equal, which would mean that there was a source of error during this experiment. The cause of this error was concluded to be friction caused by the track slowing down the cart during the experiment and because kinetic energy relies on the velocity of the cart this is one cause for the difference between the work and kinetic energy.

4-Apr-2015 Centripetal Force Motor

Purpose
The purpose of this lab was to find out the angle the string makes as the rubber stopper spins, and also how long it takes for the stopper to make one rotation. This is done with an apparatus that the professor made with a motor that will spin a rubber stopper on a piece of string that is tied to a meter stick.

Experiment
Before we actually conduct the experiment we draw a diagram to figure out an equations for the angel that is going to be created, and how long it will take the rubber stopper to make one revolution.

Now we conduct the experiment with the apparatus, but before that we take measurements of the dimensions of the apparatus. After the measurements are taken we then conduct the experiment and spin the rubber stopper at six different speeds. At each speed we timed how long it would take for the rubber stopper to make ten revolutions, then divide by ten to fins how long it would take the rubber stopper to make one revolution. Along with the time it takes the rubber stopper to make one revolution, we also measure how far off the ground the rubber stopper was from the ground.

Once we have collected all the data we needed for all six trials we the take that data and plug it into the equations we found prior to the lab. The values that those equations give us are theoretical values of what the angle the string makes as it spins, and how long it takes for the rubber stopper to make one rotation.

To make any sense out of the data we collected and calculated we plot the theoretical data against our experimental data to see if they have a a slope of one. We want a slope of one because otherwise it would mean that in our theoretical calculations were off. This in turn would mean that we are off by a certain factor or that our whole equation was wrong.

For the graph we did a proportional fit and you can see that our slope is very close to one, and so we decided that even with the error that our model for calculating period was an accurate one. We decided that it was okay because the errors were very small and explainable. One source of error would be that there is a limit to how fast our reaction time is when we start and stop the timer for the each trial. Another would be that the meter sticks also have a margin of error, also uncontrollable factors such as the air drafts caused by vents.