Magnetic Potential Energy Lab ( Daniel Guzman) Physics 4A. lab partners( Rodrigo Uribe and Dylan Valencia).

Daniel Guzman
Physics 4A.
Magnetic Potential Energy Lab


The purpose of this experiment was to demonstrate that the energy in the system is is conserved at every single moment, in this particular experiment the purpose was to realize that the kinetic energy of the glider and the potential magnetic energy was conserved in the system.

Apparatus description

The apparatus used in this particular experiment consisted of an air track, which had a magnet attached to it, a glider that also had a magnet attached to one of its ends, a motion sensor, a laptop, and a cellphone to measure the different angles at which the glider was moving when approaching the magnet that was fixed in the air track.

Experimental Procedure

The experimental procedure of this particular experiment consisted on making different measurements for angles, distances and mass. The first measurements made by my lab group and I were measurements of distance, which were going to allow us to determine how far does the glider was going to be from the magnet that was put on the track, to come out with good accurate measurements we first measured the distance at which the magnet had been put on the track, so it would be easier to use the entire length of the track to make all the measurements desired. After we measured this first distance we measured the distance at which the glider would stop from the magnet. Once having these two measurements we would have a reference of the position of the glider and by having this reference we would only measure the distance at which the glider would stop. Once these measurements of position were made we proceeded and started to make measurements of the angles at which we would let the glider slide for it to approach the magnet on the track. once these measurements of the angle were made we had to use different objects to maintain the track at that precise inclination so the glider would move at a constant angle, right when the track was fixed we would turn on the air track and the glider would approach the magnet, which made the glider bounce back a certain distance, which we would measure and record, the distance measured was the distance using the entire length of the track, which was possible and easier due that we had already measured the distances described previously. Once this was measured and recorded, we proceeded and repeated the same process six more times in order to have enough data to plot a graph of the magnetic force and the separation distance. The data recorded was necessary to determine the magnetic force, which had to be graphed in order to determine a function that would describe the relationship between the magnets in terms of distance.
After the data was plotted and some calculations were made we proceeded to second part of the experiment which was to compare the kinetic energy of the cart and the potential energy of the system, to do this we used the motion sensor to determine the velocity of the glider at any point when it was moving and we set the function found as a parameter on the computer to be able to compare the graphs of the kinetic energy of the cart to the potential magnetic energy.

Measured data and calculated data

Measured data (red) and calculated data (blue)

Sample calculation for the magnetic force and derivation of the potential magnetic energy in terms of distance (r)
The magnetic force was calculated using the following equation Fmag= mgsin(theta), the angle theta changed for every trial.

To come up with the function of Potential energy in terms of distance, a plot of the magnetic force and the distance r had to be done. Once this plot is done one can obtain the values for A and b to then do the integration that will yield the function the function of potential energy in terms of distance (r).

Graphs

The values for this particular plot were the magnetic force calculated and the distance r measured .
This graph represents the relationship between magnetic force and the distance(r) between the magnet on the glider and the magnet on the track. As this graph shows, as the glider gets closer to the magnet. In this graph we used a power fit and obtained the values for A and B, which are really important because they are used when coming up with the equation of the potential energy in terms of r.

This is the most important graph of the experiment because it demonstrates that the total energy of the system is conserved thorough the experiment. For example, the potential energy increases to a maximum when the kinetic energy completely decreases, and vice-versa when the potential energy of the system decreases to zero there would only be kinetic on the system, this is observed on the graph when the potential energy in red decreases the kinetic energy of it increases.

Conclusion

This experiment was trying to show one that the energy on any system is conserved, in this particular experiment one was trying to demonstrate and realize that energy of the system was conserved, after collecting data and doing calculations we were able to show that the energy is conserved. Obtaining accurate results in this experiment was very amazing because it allows one to realize that energy was never lost, and that the total energy of the system was conserved every single moment. The goal of this experiment was accomplished because when one analyzes the graph one notices that when there's no potential energy in the system the energy in the system is all kinetic energy, and vice versa when there is not kinetic energy in the system all the energy is potential. The sources of uncertainty and error in this experiment might come from the measurements made, for instance measuring the angles or the distance were the glider would stop can bring some error, nevertheless the error obtained in these measurements was very small, this can be proven to the uncertainty values in the graph of magnetic force vs distance. Another source of error can come from making wrong assumptions about the system such as ignoring air friction and assuming that the track was perfectly friction-less, yet the error that comes from making these assumption is minimal because the air resistance and friction were minimal. The goal of the experiment was achieved due that one was able to obtained a graph that shows that the total energy of the system is conserved thorough the entire experiment

Lab 11 ( Work kinetic energy theorem activity) Daniel Guzman

Daniel Guzman
Physics 4A.
Work kinetic energy theorem


The purpose of this experiment is particular experiment is to understand and prove that the change in kinetic energy of any system is equal to the total work done in the system.

Experimental procedure and apparatus description

Description of apparatus for experiment #1: The apparatus for this experiment consisted of a track, a motion sensor, a force sensor, a pulley a cart and a hanging mass. The apparatus in this experiment used two different sensors, a motion sensor that will record the position, and velocity as the car is moving, and a force sensor that will record the force that is being exerted on the cart by the tension on the string.

Experimental procedure for experiment  #1 (work done by a conservative force) : The experimental procedure for this particular experiment was simple, yet at the same time very interesting due that different data is being collected at the same time, The procedure for this experiment consisted on setting up the apparatus correctly, which means to calibrate the force sensor correctly so it will read and record appropriate values for the force. Once the force sensor is calibrated one had to set up the apparatus by attaching a string to the cart and the hanging mass so the tension created in the string will make the car accelerate and move. Once this was set up the group was able to collect the desired data, which consisted of three graphs, one for force, one for position and the last one for velocity, once these graphs were collected we analyze the data and verify that the data collected was appropriate for the assumption of this experiment which is the work done on the cart by the tension force in the string should equal the kinetic energy gained by the cart.

Description of the apparatus for experiment #2 (work done by a non constant spring force) : The apparatus for this particular experiment consists of a spring, a motion sensor, a force sensor, a cart and a track. The set up for this experiment is very similar to the set up in the first experiment, the only thing that changes is that a spring is now used instead of the string a hanging mass used in the first experiment. In this experiment the force sensor was attached to a clamp and to the spring so it will record the force that the spring is exerting on the cart.

Experimental procedure for experiment #2: The experimental procedure for this particular experiment was quite simple. The procedure consisted on attaching the force sensor to a clamp that was placed at one end of the track, after the force sensor was put at the end of the track one attached the force sensor to the end of the spring and the other end was attached to the cart, once this is done one can proceed and stretch the spring by moving the cart, so some data force will be collected, once this data is collected we analyzed it and found the K constant of the spring, which is very important when finding the work done stretching the spring.

Description of the apparatus for experiment #3: The apparatus for this particular experiment is the same as the apparatus for the other experiment

Experimental Procedure #3: The experimental procedure for this experiment was quite simple, due that the set up was the same for the last two experiment. We started by stretching the spring, which is done by moving the cart forward, once the cart is moving forward one would start collecting date then when the cart reaches approximately 60 cm we let the car go so the spring would pullet it back and the data for the position and force of the cart would be recorded at the same time, which would allow one to have data for the position and the force at the same time. Once the data is collected one will find the area under the curve of the graph of force vs position, once this is done one can compare the kinetic energy at any position to the work done by the spring, so one can compare the work done by the spring to the change of kinetic energy of the system.


Data Collected

Graphs for each experiment

For this part of the experiment the area under the graph represents the work done by the constant force and if one was to compare the value obtained for the integral and the point at the end of the area of the integral one would find either that they are exactly the same or relatively close to each other, which lets one infer that the work is equal to the change of kinetic energy of the car.

This graph represents the same exactly relationship; nevertheless these graph was integrated over a longer interval the value for the integral is 0.1335 and value for the kinetic energy of the cart is 0.135, which is the same. This lets one infer that the change in kinetic energy is equal to work. because the values are exactly the same, which is amazing because by knowing the change in kinetic energy, one can find the work done.

For this part of the experiment one was asked to compare the value obtained for the area under the graph to a point at the end of the graph, what one would notice is that the values are relatively close, which once again holds true that the change in kinetic energy is equal to work, if one compares these two values by doing the percentage error one would find that the percentage error is 1.123% which is relatively small.

For Part # 2 the only thing that one had to find was the K constant for the spring this was found by graphing force vs position of the spring and by doing this one would be able to find the K for the spring because on would only have to calculate the slope of the graph in this case the K value was 3. 197, the other part that one had to find in this case was to calculate the work done in stretching the spring, which came out to be 0.5948 joules. 

For the third part of the laboratory on had to find the change in kinetic energy of the cart after it is released from the initial position where the kinetic energy is zero, so the kinetic energy and the work had to be find in three different places.

In this case the integral gave 0.4343 ,which would represent the work and when one calculates the change in kinetic energy one would find that the two values matched perfectly , which once again proves that the change in kinetic energy is equal to work.

The same approach was used for this particular graph and once again it gave almost a perfect relationship which is good because the point of the lab was to prove that the change in kinetic energy is equal to work, for the third point picked in this part had a value for the work of 0.6054 joules and for the kinetic energy of 0.638

The work done on the cart by the spring is equal to the change of energy of the cart at different point, if it is not equal it is relatively close.

Part #4

In this part of the lab we watched a video and extracted the data from it, the pint of it was to confirm that the area under the graph was the same as the change of kinetic energy. in order words work equals the change in kinetic energy, in this case it was done by calculating the area under the graph an then calculating the change in kinetic energy to see it they were equal

Conclusion

In this particular lab the work energy theorem was proven or confirmed because every single relationship attempted showed that the change in kinetic energy is equal to the work done. multiple examples were tested and different experiments were done, and every single one of them held that the change in kinetic energy equals to work, the sources if uncertainty in this lab can come from overstretching the spring, which would change the results when comparing the work to the change in kinetic energy, another source of error can come from not calibrating the force sensor correctly, this would definitely alter the results because the work done on the system depends on the force, so it the force sensor does not read accurately the force, the area under the graph would not be the result that one would like to have. This lab was very interesting because my group and were able to collect good data and to prove that work energy theorem is true by using different approaches.

Lab (10) Activity- Work and Power Daniel Guzman

Daniel Guzman
Physics 4A.
Lab 10 ( Activity- work and power).


The purpose of this particular experiment was to measure the power at which different members of the group would do different activities such as lifting a backpack using a pulley, walking upstairs and running upstairs, to then compare the powers achieved by each member of the group.

Experimental procedure and description of the apparatus: The apparatus for this particular experiment consisted of a pulley that was assembled by the professor, the pulley had attached to it a backpack that weighted 9 pounds. For the other two parts of the experiment an apparatus was no needed due that each member of the group was only required to go up some stairs running and walking.

The experimental procedure for this particular experiment was quite simple. The first part of the experiment required each member of the group to use the pulley to be able to lift the mass 4.4 meters above the ground, while a member of the group was trying or attempting to lift the backpack another member of the group would time how long it took the person to complete the activity, the same exact process was repeated for each member of the group. The other activity for this experiment consisted each member of the group to walk upstairs, while a member of the group was walking upstairs the other members would time how long it took the person to get to the top of the stairs, the same exactly process was repeated for each member of the group. The last activity done for this particular experiment was very similar to the previous one the only thing that changed was that the activity had to be done as fast as possible; nevertheless, the activity was the same, it consisted to get to the top of the stairs as fast as possible, while the other members of the group would time how long would it take the person to get to the top of the stairs.

Data table

This was the data taken during the different trials and activities. TL= time lifting.  TW= time walking        TR= time running

Calculated Results for power of each activity (Power lifting, power running, power walking)

Example calculations

Conclusion (the conclusion is all completed by hand, due to the calculations and questions)

Lab 9: Physics 4A (centripetal force with a motor) Daniel Guzman

Daniel Guzman
Physics 4A.
Lab 9: Centripetal force with a motor



The objective for this particular experiment is to come with a clear model, which shows the relationship that exists between the angular velocity and the angle theta for an object that is rotating.

Description of the apparatus and the experimental procedure:

The apparatus for this experiment consisted of an electric motor that was mounted on to a surveying tripod, a long shaft that was oriented vertically, a horizontal rod that was mounted on a vertical rod, a long string that was attached to the horizontal rod, a rubber stopped attached to the end of the string  , and a ring stand that that had a piece of paper sting out.This apparatus was powered electrically and was used for the entire class to repeat multiple trials.
The experimental procedure for this particular experiment consisted first in taking measurement of the apparatus described above due that the dimensions are important to come up with the desired  model. Once the measurement of the apparatus were taken, we had to come up with a mathematical expression, which would relate the angle theta at which the object is rotating to the angular speed of the object,Once this mathematical expression was approved by the professor the entire class started to record the measurements using the apparatus. The measurements recorded included the time for ten rotations passing a fixed mark so one would know precisely when to to start and stop the timer, the other measurement that we had to do was to measure the height at which the the stand was because the height at which it is at every trial would be important when determining the angle theta at which the object is rotating, the same exactly process was repeated for another 5 trials in which the height and the time for ten rotations changed due that the power at which the motor was functioning was increased, which changed the data for the other trials; nevertheless, the same process was done for all the trials.

Mathematical expression that relates the angular speed to the angle theta

Data Table

The data collected for each trial was the time to complete 10 rotations and the height at which the rod will hit the paper that was sticking out on the rig clamp. These were the only two measurements necessary to be able to model the relationship that exists between the angle theta and the angular velocity.

Example Calculations

These calculation were done on the the excel data sheets using the data collected in the experiment, the same calculations were done for every single trial.

Conclusion

This particular lab yielded very precise results due that the apparatus used worked very well, reason why it yielded very precise results for the desired model. Some of the main aspects or reasons why the results were accurate was that the angular speed at which the rod was rotating was kept constant, which is very important when measuring the period of the rod. If the period was correct the theoretical angular speed would be correct, and this would allow one to make a correct comparison between the theoretical and experimental angular speeds. The model that related the angle theta and the angular speed was very accurate, this was proven by plotting the actual omega and the theoretical omega and obtaining a slope of one, which lets one infer that the values compared are equal. Also the percent error calculations were very small, which lets us assume that the model attempted was correct. The sources of error in this experiment can come from measurements made by the group for instance. measuring how tall was the apparatus, or the length of the string. Another source of error for this lab can come from doing a miscalculation or from imputing a wrong value in the data sheets, the error that comes from the apparatus is minimum due that the apparatus worked very consistently through the entire experiment.

Percent error calculations

Lab#8 (Demonstration - Centripetal acceleration vs angular speed) Daniel Guzman

Daniel Guzman
Lab#8 (Centripetal acceleration vs angular speed)
Physics 4A.

The purpose of this particular experiment is to determine the relationship that exists between the force that makes an object spin and the angular speed of the object that is rotating.

Summary of the apparatus and experimental procedure.
The apparatus in this particular experiment consisted of a big wooden disc that was placed on top of two scooter wheels, which were connected to a motor that would make the wheels spin in different direction so the big wooden disk could spin with respect to its center. this apparatus also consisted of different weights, a wireless motion sensor, a photo gate and a laptop were all the measurements were being recorded in logger pro.

The experimental procedure for this experiment consisted first, on taping or securing a mass to the rotational disc some distance r in inches from the center of the circle, so we would know what was the radius when the mass was rotating, after the mass was secured on the rotational disc, the professor secured the wireless motion sensor so the computer would record the centripetal force when the disc was rotating; also a piece of paper had to be taped to the disc, so when the disc was rotating a photo gate could count or measure the frequency of the disc and the mass that was put on it. Once this was all set up the entire class proceeded and observed the data, which was being recorded in real time by the force sensor and the photo gate. Once the measurements were collected the professor repeated the same process, but moved the mass that was attached to the disc so it would have a different radius than the last trial.
Multiple trials were done where the same mass was kept but the radii changed, the same mass and same radius but different rotational speeds, the same radius and same rotational speed, but different masses.
The same exactly process was repeated for all the other masses which were 50, 100, 200 and 300 grams. a total of 11 trials were done in this lab.

Data Table

Data collected of the eleven trials

Calculations for the Frequency and Angular Frequency

Calculations and graphs of the data

These calculations were done in the spreadsheets in excel

Data table repeated to show the frequencies calculated based on the data collected.

Graphs of data

For trials 6,7 and 8  we plotted force vs mass , then set a liner trend through the points and force the line to go through zero to obtain a better correlation, the slope that we obtained for this plot is the radius times angular velocity raised to second power. the slope that we obtained was 9.4956, nevertheless the slope obtained in this particular graph does not model the system very well due that the apparatus was not able to sustain a constant angular velocity, which makes the results nor precise.

For trials 1,2 and 3  we plotted force vs radius and forced the trend line through zero to obtain a better correlation the slope of the line is mw^2 , which is 5.092, the value obtained in the graph can be compared to the values in the data table for the specific trial recorded. when force vs radius is plotted the slope that one would obtain is mass times angular velocity raised to the second power. This particular model of the system also fails to give accurate data, due to the same reason as the previous plot, the apparatus used in this experiment was not able to keep the same angular speed therefore the information one obtains in this graph is not precise as one would like; therefore this model fails at providing accurate results or close results to what one would like.

For the third graph,  we plotted force vs the angular velocity, the slope of this particular graph is mass times radius, the slope for this graph was the only slope that was constant for all the graphs plotted. This particular slope was constant because the only value changing was the angular velocity, which is a correct model for the system because as explained before the apparatus was not able to keep the same angular speed, so when one compared the slope of this particular graph one would find that it matches perfectly the value that one is expecting, this model is more accurate due that keeping the mass and radius constant for the trials is possible, not like in the other trials were more than one variable was not constant,

Conclusion

For this particular experiment, not all the models attempted were accurate or precise, due that for two of the models two variables were not constant, in the first model the angular speed and the mass varied and in the second model the angular speed and the radius varied, reason why the information obtained in the graphs were not accurate. On the other hand the information obtained  in the third graph was very accurate because there was only one variable changing and it was the angular speed, the radius and the mass were held constant reason why the graph provided very accurate  results. The sources of error for this experiment basically come from the apparatus used in this experiment because the apparatus could not spin uniformly which brings error to the calculations and models that one is trying to do, nevertheless, when the angular velocity was the only changing variable the results were very accurate and precise.

Lab # 7 Physics 4A Modeling friction forces

Daniel Guzman

Physics 4A.

Lab #7 Modeling Friction Forces


Modeling Friction Forces

The purpose of this particular experiment was to model different friction forces, under different circumstances, to then compare and analyze if the model predicted for the friction forces was correct when comparing it to theoretical results.

Summary of Apparatus and Experimental Procedure.

The apparatus changed slightly in this lab due that there were five different experiments.

Instead of a water cup a hook with weights was used

Apparatus for experiment #1: The apparatus consisted of a block, a pulley, weights and a hook. The weights were placed on the hook so the car could accelerate due to the tension created in the string.
 The experimental procedure for this part of the lab was quite simple due that my group and I only had to attach a string to the wooden block and to a hook that was hanging from the pulley. Once this was done we proceeded and and put wights on the hook util the block started to move. After the block started to move we stopped it and measured how much weight was hanging from the pulley and recorded it. The other trials for this experiment were the same, but the only thing that changed was that the 220 grams were put in the block every time so the hanging mass changed each trial. After the data was all recorded it was used to create a plot on logger pro.

Apparatus for experiment #2: The apparatus consisted of a force sensor, a wooden block, and a string , which was attached to the bock and sensor, so one member of the group could pull the block at a constant speed and the force would be recorded on logger pro.
The procedure for the second part of this experiment was quite simple, the first thing that we did was to calibrate the force sensor using 500 grams until the reading in the sensor reads 4.9 Newtons. Once this is calibrated a member of the group pulled the string with the car at constant speed, the data for this particular experiment was saved automatically into the laptop, the only thing I had to do was to use the statistics tool of logger pro to obtain the mean of the force exerted on the car by the person who was pulling it.

Apparatus for experiment #3: For the third experiment of this lab the apparatus consisted of a phone which measured the angle of the slope, the same wooden block used in the other parts of the experiment and a wooden board,which was the slope on which the block would slide down.
the experimental procedure for this experiment was the simpler of all experiments because we only had to tilt the board and measure the angle at which the block would slide down, to then calculate the coefficient of static friction between the block and the wooden board.

Apparatus for experiment 3 and 4 was pretty similar the only thing that changed was that in the apparatus for experiment four a motion sensor was used to measure the acceleration of the block sliding down.

Apparatus for experiment #4: For the fourth experiment of this lab the apparatus was the same as the third's experiment the only thing that was added was a motion sensor so we could measure which was the acceleration as the block slides down.
Experimental procedure:  The experimental procedure for this experiment of the lab was pretty much the same as the experimental procedure for last part the only thing that changed was using the motion sensor, which helped one record the position and velocity graphs. On the velocity graph we put a trend line, which ends up giving one the acceleration that the block had as it was sliding down the slope.


Data collected for all the experiments of this lab

Graphs of plots and explanations

First plot for first experiment

On logger pro we plotted the data collected in the first experiment. on the x axis we used the mass of the block n grams and in the y axis the weight required for the block to start moving. Once this was plotted we put a linear fit throughout the points and the slope of this linear fit would give us the coefficient of static friction.

For the second experiment the force sensor provided a mean value of the force that was exerted by the person that was pulling the wooden block at a constant speed. In the x axis we used the weight of the wooden block and in the y axis we used the average force recorded by the motion sensor. After these different points were plotted we used a linear fit, and from this linear fit we obtained the slope of the plot,which tells us the coefficient of kinetic friction, which in this case is 0.3096

For part three of the experiment we just calculate the angle at which the block would start sliding and found out that the angle is 27 degrees from the horizontal.

For part four the procedure was the same the only thing that changed was that a motion sensor was used to find the acceleration of the block as it was sliding down.

Once this acceleration is found one can proceed and calculate the coefficient of kinetic friction

Using the data collected from the previous parts, one was able to predict the acceleration for the system, which it came out to be 2.267 m/s^2 Theoretical acceleration. The experimental acceleration came out to be 2.311 and it was found using the motion sensor which recorded the position and velocity as a function of time on logger pro.

Conclusion: The prediction of the acceleration of the two mass system using the data collected trough the experiments was not as accurate as one would have liked to have it due that there are parts for this particular experiment where the sources of error are very big. For instance, the first experiment is not consistent, which means that it is almost impossible to collect similar data twice. Another source of error for this particular lab comes from the second part of the experiment were the force is basically changing every second because it is really hard to pull the car at the same speed all the time, which affects the theoretical calculations for the acceleration of the system. The percent error between the theoretical and experimental values was calculated and it came out to be 1.9408 %, which lets one infer that is not accurate enough due to the sources of error described previously.