26-April-2017, 3-May-2017: Ballistic Pendulum

Lab: Ballistic Pendulum
May Soe Moe
Lab Partners: Day 1: Steven Castro, Stephanie Flores, Henry Wang, Tomas Pacual, Garrett Giordano, Jesus Gonzalez, Ben Chen
Day 2: Steven Castro, Stephanie Flores, Henry Wang, Ben Chen
Date: 26-April-2017, 3-May-2017

Objective: To determine the firing speed of a ball from a spring-loaded gun and to determine how far the ball lands after it is launched horizontally

Introduction: There are two parts for this lab, which we performed on two separate days. For the first part, using a spring-loaded gun, we will fire a ball into a nylon block, supported with four vertical springs. The ball will be stuck into the block, and the block, together with the ball, will rise up to some angle, which we will measure with the angle indicator on the apparatus. To figure out the ball's firing speed, we will use conservation of momentum (momentum p=mv) to write an expression representing the initial speed of the ball, immediately after the collision. Conservation of momentum states that momentum is conserved if there is no net external forces acting on a system of objects, and those objects will have equal and opposite force acting on each other. For the second part, we lay out the apparatus above a pile of books. We estimate where the ball would land after the launch horizontally, and test it out. We put the carbon paper on the floor approximately at the point where it would land to mark out its final position. We will take appropriate measurements such as the height of the spring loaded gun from the ground, and the distance of the final position of the ball from the apparatus. We will use conservation of energy to get the initial firing speed of the ball and compare the two velocities we got from part 1 and part 2 of this lab.

Experimental Procedure:

Part 1: 
(1) Our apparatus looks like this:

(2) The ball is fired from the spring-loaded gun and it went into the nylon block, supported with four vertical strings.

(3) There is a hole inside the nylon block, so that the ball will stay inside the block after the collision.

(4) After the collision, the ball along with the block moved to some maximum vertical angle, that is indicated by an angle indicator from our apparatus.

(5) The collision also caused change in height of the block. 

(6) We repeated the process about six times to get an average angle. 

Part 1 Calculations:

Firing speed of the ball resulted as 4.9m/s.

(7) Our calculations give us the firing speed of the ball to be 4.9 m/s.

Part 2: 

Experimental Procedure:

(1) We set up our apparatus as below:

Our set up for Part 2 of the Ballistic Pendulum lab

(2) The height of the pile of the books to the spring loaded gun was measured as 20.5 cm (0.205m). 

(3) We estimated where the ball would land after firing it and put a blank sheet of white paper and carbon paper on top. We repeated this process for four times. 

(4) After that we removed the carbon paper and measured the distance of the ball's position after it landed from the apparatus, using a meter stick. 

Measuring the distance from the apparatus to where the ball landed

Part 2 Calculations:

Firing speed of the ball came out to be 5.175 m/s

Conclusions:

             The first part's initial firing speed is 4.9 m/s and the second part's initial firing speed is 5.175 m/s. There are uncertainties in our data that caused the difference in two firing speed of the ball. Our measurements of the angles, masses of the block and the ball, the height of the apparatus, height of the book pile, and the distances we measured away from the apparatus to where the ball landed were not exact numbers as we calculated. We used the average of he angles and distances we got from our trials to calculate it. The other factor to consider about the difference in firing speed is that we did this lab in two separate parts and two separate days. It is possible that we used different apparatus for two parts. But the difference between two results of the firing speed from the calculation was not large. 

26-April-2017: Lab 15-Collisions in Two Dimensions

Lab 15: Collisions in Two Dimensions
May Soe Moe
Lab Partners: Ben Chen, Steven Castro
26-April-2017

Objective: To determine if momentum and energy are conserved by looking at a two-dimensional collision

Introduction: The conservation of energy states that the total energy before the collision is equal to the total energy after the collision, which stays at a constant. The conservation of momentum states that if there is no net external force acting on objects, the momentum before the collision is equal to the momentum after the collision. We would use two steel balls to have a collision between those two balls for the first part. For the second part, we would use one steel ball and one marble and let them collide each other. For both parts, one ball is to be at rest while another ball moves toward the first ball, which is at rest, and collides. We would take two slow-motion videos of the collisions for both sets of balls. We would use the Logger Pro to trace their direction of motion and put it on a graph. We would get the velocities of the balls before and after collisions by getting the slopes from our graphs. Then we would use that velocities to calculate if the momentum and energy are conserved or not.

Our apparatus for this lab

Experimental Procedure:

(1) The glass table for this lab was already set up. We had to make sure if the table was leveled. We could check it by seeing if the ball stays at rest without rolling to the other side. If the ball stays at rest, then it is leveled.

(2) We set up the phone we would use to record the collision at the stand attached to the glass table. The stand is set up so that the phone is in the position of filming the process of collision clearly. The filming was done by using iPhone's slow motion capture feature in the phone's camera.

(3) Before we started filming the collision, we practiced rolling the steel ball toward other to make sure that the first moving steel ball hits the second ball at rest.

(4) Once we felt ready to film, we filmed the collision of two balls. We filmed two videos: One video involving the collision between one steel ball moving and one steel ball at rest, and another video involving the collision between one steel ball moving and one marble at rest.

Steel ball and Marble Collision

Steel ball and Steel ball Collision

(5) After we got the videos, we transferred the videos from our phone to the computer. We opened the video using Logger Pro and trace the direction of the balls before and after collision.

(6) Logger Pro allows us to plot the graph of the motion of the ball by transferring the tracing of the balls' directions.

(7) Once we got the graph, we did linear fit and got the equations for before and after collisions. The slope of those equations would give us the velocities of the balls. Logger Pro can also give us the positions of ball in x and y directions after they collide. So, in the graph, x and x2 are x-directions of motions for two different balls and y and y2 are the y-directions of motions.

Two Steel Balls Collision-Before the Collision Positions and Velocities
Red line for x-direction, Blue Line for y-direction of Moving Steel Ball
Green for x-direction, Brown for y-direction of Stationary Steel Ball

Two Steel Balls Collision- After the Collision Positions and Velocities
Red line for x-direction, Blue Line for y-direction of Moving Steel Ball
Green for x-direction, Brown for y-direction of Stationary Steel Ball

A Steel Ball and a Marble Collision-Before Collision Positions and Velocities
Red line for x-direction, Blue Line for y-direction of Moving Steel Ball
Green for x-direction, Brown for y-direction of Stationary Steel Ball

A Steel Ball and a Marble Collision-After Collision Positions and Velocities
Red line for x-direction, Blue Line for y-direction of Moving Steel Ball
Green for x-direction, Brown for y-direction of Stationary Steel Ball

(8) One question from our graphs was that how do we know if to certain position is before the collision or after the collision.

(9) We could figure that out by seeing their graphs. Before the collision, one ball was moving with a constant velocity, which we could see x2 moving in a constant slope. X on the graph pretty much stayed constant on a straight line, which we knew it was at rest. After the collision, you could see their slopes change, which means they moved, therefore, after the collision.

Data and Calculations for Collision between 2 Steel Balls

Checking if Kinetic Energy is Conserved in between 2 Steel Balls

Data and Calculations for Collision between a Moving Steel Ball and a Stationary Marble

Checking if Momentum and Kinetic Energy are conserved

Calculations and Analysis:
 I calculated the initial momentum, initial kinetic energy, final momentum, and final kinetic energy of the two steel balls to see if the momentum and kinetic energy were conserved. For conservation of momentum calculation, the difference between initial momentum and final momentum were 0.04325, which is about 5.8%. If we were to approximate our results, then, yes, the momentum of two steel balls are conserved. The percentage for momentum was not big. For conservation of kinetic energy, the initial kinetic energy and final kinetic energy were off by 0.0789, about 36.9%, which is way too off. For the second video, where the steel ball moves toward the stationary marble, I did the same calculations, which can be checked in the pictures above. There were also 2.18x10^-4 or 1.33% difference in initial momentum and final momentum. But this value is really small that we could say the momentum between the steel ball in motion and stationary marble are conserved. When we look at the conservation of kinetic energy calculation, we can see that the difference between initial and final kinetic energy is 8.019x10^-4 or 21.7%. Again, the differences for these can be considered small. But I noticed from our conservation of kinetic energy calculations that the percentages were high for both videos.

Conclusion: These differences in calculations might result from the glass table, which we assumed it was leveled after checking that the balls stay at rest. But the graphs that we got say something else. When I checked the graphs, the velocity of stationary balls were not exactly zero.
The other error could be that we did not click on the same point of the balls when we were doing the video analysis using Logger pro to produce our graphs. That could have affect our accuracy of the results. The other factor to think was that there was kinetic friction between the balls and the glass table when they were rolling on the table, which would turn into heat. We ignored the factor of kinetic friction in this lab. If we approximate our results, then we can say both momentum and kinetic energy are conserved.

19-April-2017: Impulse-Momentum Activity

Lab 14: Impulse-Momentum Activity
May Soe Moe
Lab Partners: Ben Chen, Steven Castro
19-April-2017

Objective: To observe and verify the impulse-momentum theorem

Introduction: According to Impulse-Momentum theorem, the change in momentum of an object equals to its net impulse. Momentum is when an object is in motion. Its equation is p=mv, where p is momentum, m is mass of an object, and v is the velocity of an object. Impulse is a force in change of time: J=FΔt. In this lab, we did 3 parts of experiments. One was elastic collision, where the moving cart with a spring plunger collides to the spring plunger of stationary cart mounted on a rod, which causes the moving cart bounced back. The second experiment was with the same set up but adding several hundred grams to the moving cart. For the third experiment, we set up an inelastic collision where the moving cart sticked to the clay and stopped. We would try to measure the impulse acting on the cart by taking the area under the force vs. time graph for the collision. We would also measure the change in momentum of the cart by knowing its mass and measuring its velocity before and after the collision using the motion detector. 

Experimental Procedure:

Experiment 1: Observing Collision Forces That Change with Time

(1) We set up the lab by clamping a cart to a rod, which was also clamped to our lab table. We attached the spring plunger on the cart.

(2) We set up a track and put a force sensor on the another cart, attaching another spring plunger to this cart. At the end of the track, we set our motion detector. 

(3) After this, we leveled our track to make sure the cart goes in a straight line at a constant speed when it is given a slight push. We calibrated and zeroed our force sensor. 

Our apparatus for Experiment 1 and 2

(4) After all setup, we began to collect our data using Logger pro. When we heard the clicking of the motion detector, we pushed the cart toward the stationary cart.

(5) Let the cart move, collided, and bounced back. We repeated until we got good graphs.

Impulse= the integrated value of the area under the Force vs. time graph
Initial Velocity

Final Velocity

(6) Now we can calculate the change in momentum since we know the mass of the cart, the final velocity and the initial velocity.

Comparison: When we compared the impulse--integrated value of the area under force vs.time graph and calculation of change in momentum, they are off by 13.7%. Our impulse was -0.4672 Ns and change in momentum was -0.350 kgm/s. Friction could have had some effects on the cart during its motion. May be the track was not re-level after each trial. But our percent error came out to be pretty large, therefore, the net impulse did not equal to the change in momentum from our results.

Experiment 2: A Lager Momentum Change

(1) This experiment was set up the same as experiment 1. But for this experiment, we added 200 grams to the cart and repeated the same steps in experiment 1.

Initial velocity

Final Velocity

Comparison: Our impulse from the area under the Force vs. time graph was -0.2437Ns while our calculated change of momentum came out to be -0.2936 kgm/s, which got 9.3% difference or 0.0499. This difference is within acceptable range, therefore, we can say impulse and change in momentum are equal. Compared to our last experiment, the impulse and change in momentum came out to be better using a more massive cart. 

Experiment 3: Impulse-Momentum Theorem in an Inelastic Collision

Experiment 3 Apparatus

(1) The setup for this experiment was almost the same as in experiment 1 and 2. But in this experiment, instead of a spring plunger attached to the force sensor, we put a nail. Instead of a stationary cart with a spring plunger, we put the clay sticked to the wooden stand.

(2) The cart was pushed, and we collected data, and graphed the force vs. time graph and velocity vs. time graph to give us the impulse and velocity values we want.

Initial Velocity

Final velocity

Comparison: Our impulse from area under the force vs. time graph was -0.8557 Ns and calculated change in momentum was -0.7674 kgm/s. They are off by 0.08833 or 5.44%, which can be considered not bad comparing to the first two experiments. Comparing the curves we got from experiment 3 with experiment, we saw that the two graphs are similar. 

Conclusion: From all three of our experiment, the first experiment was way too off, the second and the third experiments' results are acceptable since they are less than 10%. We could also see that the results get better. Therefore, the impulse-momentum theorem can hold true. The reasons why we got somewhat large percentage of errors are that our track might not have been re-leveled after each trial. The force sensor or the motion sensor readings can be off. 

17-April-2017: Lab13: Magnetic Potential Energy

Lab 13: Magnetic Potential Energy Lab
May Soe Moe
Lab Partners: Ben Chen, Steven Castro
17-April-2017

Objective: To verify that the conservation of energy applies to the system we came up for this lab.

Introduction: By turning on a vacuum, the air glider would glide along the air track and move toward the motion detector. Two magnets with same polarity at the end of the cart and the air track are attached. Since they have the same polarity, once the glider reaches to the end of the track, the magnet at the end would repel the glider, causing the glider to move to other direction of the motion. In this lab, we would like to show that our kinetic energy and potential magnetic energy of our apparatus is constant, therefore, energy is conserved. The problem of this lab was that we did not have an equation for magnetic potential energy. Therefore, by plotting a graph of Force vs. separation distance graph, we would get the power fit to the graph to get that equation that represents the magnetic potential energy. Once we get our equation for magnetic potential energy, we would use that as our model to figure out if our conservation of energy in our system or set up is conserved or not.

Experimental Procedure:

Apparatus:

Our Apparatus for this lab

 (1) The set up was already done by the professor.

(2) Air glider is used to move along an air track when the air is turned on. There are numerous holes in the air track. Through those holes, air would push up the glider, making it not really in contact with the track. That makes the track frictionless surface.

(3) One magnet was sticked to the end of the glider and another was sticked at the end of the air track. What would happen with this lab is that the glider would move toward the motion detector when air is turned on. When it reaches to the end of the track, the glider would bounce off and move to opposite direction due to the magnets. The magnets have same polarity-- like poles repel, and unlike poles attract each other. Because the magnets' poles are the same, it repelled and let the glider bounce off to other direction. This is almost the same as the spring; the spring would pull back an object when it is stretched to a certain distance and let go.

(4) Here, during the repel, we saw that the glider did not go to the very end of the track nor did it touch the magnet. There was a distance in between two magnets, which we called separation distance r. Like our previous labs before, we would approach this lab to find the force vs. position graph.

(5) We cannot find the force between the magnets directly. Therefore, what we used as a force between the two magnets was by representing force as mgsinθ since the glider was going in the x-direction. We would put the air track at a certain angle by adding books underneath. 

(6) We used bubble level app from our phones to measure the angle of the air track. 

(7) Then how do we get our position? Our position function was the distance between the glider and the motion sensor minus separation distance r between two magnets.

(8) Once we were ready with the setup, we gave a slight push to the glider after turning the air on. We started collecting the data and graphed our force vs. separation distance r graph.

(9) We repeated this procedure a few times by adding books underneath the track to raise the angle. 
And we collected new sets of data at those different angles.

(10) With our collected data, we graphed a velocity vs. time graph, and a position vs. time graph to help us with finding the kinetic energy.

Position vs. Time and Velocity vs. Time graph to help us find Kinetic Energy

(11) We put in all of our datas including our angles and separation distance r values. Then we graphed a force vs. separation distance r graph. 

This is how our force vs. separation of r graph should looks like.

Position and Angle are collected data and Force is calculated data.

How we calculated force for various angles

Our graph of Force vs. separation distance

(12) Doing the powerfit of the force vs. separation distance gave us a function that will represent the magnetic potential energy after doing the integral of this function.

(13) We knew that negative integral of the force and distance function equals to potential energy. Therefore, we integrated the function we got from the graph to get us the function of magnetic potential energy.

Integrating the function from the graph. U represents magnetic potential energy

Verifying the Conservation of Energy

We would try to verify the conservation of energy by putting kinetic energy, magnetic potential energy and the total energy of the system as a function of time onto one graph.

Kinetic Energy, Magnetic Potential Energy and Total Energy in one graph

This is how our Kinetic energy, magnetic potential energy, and total energy should looks like. (standard graph)

Conclusion: By comparing the standard graph and our resulted graph, we can see that they are quite similar, but not constant. We assumed that there was no friction force acting on the glider for our system. But when we assumed there is no friction between two surfaces, the graph should come out like the standard graph. But since it did not come out to be smooth line or curve, we could be sure that there was kinetic friction acting on the glider during the time of glider moving along the track. Although our graph was not smooth, kinetic energy and total energy stayed in that range, without moving up or down too much. Therefore, we can say conservation of energy for our system stayed conserved. 

10-April-2017: Work-Kinetic Energy Theorem Activity

Lab#11: Work-Kinetic Energy Theorem Activity
May Soe Moe
Lab Partners: Roya Bijanpour, Ian Lin
10-April-2017

Objective: To inspect and possibly confirm the statement of the Work-Kinetic Energy Theorem that the work done on a object is equal to the change in kinetic energy.

Introduction: We had done four separate experiments: (1) work done by a constant force, (2) work done by a non constant spring force, (3) kinetic energy and the work-kinetic energy principle, and (4) work-KE theorem. In this lab we wanted to confirm the Work-Kinetic Energy Theorem, which states that the total work done on an object is equal to the change in kinetic energy. We also knew that the area under the force vs. position graph is equal to work done on an object. Therefore, in this lab, we set up our apparatus so that we could get a graph of force vs. position graph, which would give us the work done on an object by finding an integrated value of an area under the graph and the kinetic energy at that position. When the two values we got from the kinetic energy and the integrated value of the graph are equal, we would compare them and see what we can conclude from our results.

Experimental Procedure:

Experiment 1: Work Done by a Constant Force

Apparatus:

The apparatus for first experiment: the string was not very visible in the picture.

(1) We set up our apparatus as above: we used a cart connected with a hanging mass with a string through a pulley. 

(2) Then we made sure the track was leveled, meaning the cart would roll along the track at a constant speed after giving a gentle push.

Leveling the Track

Our total mass of the cart and 500 grams-- We put in this mass in our kinetic energy in the table.

(3) After the setup and leveling, we would calibrate the force sensor by just vertically holding the force sensor at first and set it to zero. And then we would vertically attach the 500 grams mass to the force sensor and set it to 4.9 N. After it was done, if the force sensor described the force or the weight of the mass to be around 4.9 N, we know that the force sensor is calibrated and it is good to go on with the lab.

(4) We added 500 grams to the cart, hanged 50 grams to the end of the string and pull the cart back.

(5) After that we released the cart, started to collect data, and plotted force vs. position graph.

(6) After getting the force vs. position graph, we added a new calculated column for kinetic energy to our table in Logger Pro and added our equation of kinetic energy- KE= 0.5mv^2, where our mass here is 1.177 kg.

(7) Once we got all of this, we integrated the area under the force vs. position graph using Logger Pro to give us the work done on the cart and kinetic energy at the same point.

Getting the integral and Kinetic energy by highlighting a smaller area

Our Graph of Force vs. Position graph with integrated value and kinetic energy: Larger area highlighted

(8) Above is how our graph came out. In our first graph, we highlighted a smaller area and determined the integral value (0.1287 Nm) and Kinetic energy (0.109J). In our second graph, we highlighted a larger area. Our value of work done on an object was 0.1775 Nm and the kinetic energy was 0.150 J.

(9) When we compared the two values: the integrated value of the area under the force vs. position graph and the kinetic energy from the graph at the same point, we saw that the two values were off by 0.0197 in the first graph and  0.0275 in the second graph. Although we repeated the experiment a few times, we got similar results. Therefore, we suspected that there was friction along the track, and part of the errors might be due to the force sensor, which we had to calibrate after every trial because we saw different force readings.

Experiment 2: Work Done by a Non-constant Spring Force

Apparatus:

Apparatus of Experiment 2

(1) We set up our apparatus as above by attaching the spring to the cart and the force sensor while setting the motion detector on the other side of the cart and the force sensor. We made sure the track was leveled after the setup.

(2) We calibrated the force sensor by repeating the steps we did in experiment 1.

(3) We pulled the cart toward the motion detector until the spring is stretched about 0.6 m.

(4) Then we started collecting data for force applied by a stretched spring for 0.6m of distance.

(5) We began graphing the force vs. position graph as we pulled the cart.

(6) Once we got the graph, we integrated the area under the force vs. position graph.

Experiment 2: Work Done by a Non-constant Spring Force= the Area under the graph.

(7) The integrated value from the force vs. position graph is the work done on the cart by a spring force, which came out to be 0.2424 Nm. The spring constant of our spring is the slope of the equation Force=mx+b. It also makes sense that our spring force equation is F=kx. Therefore, the spring constant is 3.511N/m.

Experiment 3: Kinetic Energy and the Work-Kinetic Energy Theorem

Apparatus:

Our apparatus for experiment 3 was set up the same as in experiment 2.

(1) We measured the mass of the cart, which was 0.549 kg.

(2) We added a new calculated column for kinetic energy of the cart. The equation for kinetic energy of the cart KE=0.5mv^2 was put into the Logger Pro to calculate kinetic energy at different points. Here, our mass was 0.549 kg, the mass of the cart.

(3) We calibrated the force sensor again by repeating the steps in experiment 1 and 2.

(4) After calibration, we pulled the cart along the track so that the spring was stretched about 0.6m from its natural length position.

(5) We began graphing when we released the cart and the spring pulled back the cart to its natural length position.

(6) We would then find the work done by the spring force for the displacement of the cart between any two positions by finding the area under the curve between two points. We would also calculate the kinetic energy of the cart be finding directly from the Kinetic Energy Versus Position graph.

(7) For the change in kinetic energy of the cart, we found the kinetic energy between the same two points we used to find for the work done by the spring force.

(8) We calculated the work done by the spring and kinetic energy of the cart at different positions and repeated a few times.

Kinetic Energy at starting point for this area under the graph

Kinetic Energy at end point for this area under the graph

 (9) Below is the calculated value of change in kinetic energy and the integrated value of the area under the graph-- work done.

Conclusion: From the first two rows, we can see that the work done between 0.155m and 0.222m and change in kinetic energy between that two positions are off by 26.9%. The second set was off by 13.9%, and the third set was off by 3.38%. According to the work-energy principle, the total work done by the spring on the cart is equal to the change in kinetic energy. The work done and change in kinetic energy are not quite close to each other.  We speculated that there was some friction between the cart and the track. The force sensor was not functioning well, which might cause the different reading on the graph, because we had to calibrate it after each trial due to incorrect readings. Other factor that might cause error in our experiment was that the level is not leveled since the cart's velocity moved the track every trial.


Experiment 4: Work- KE Theorem

For this experiment, we watched the movie Work KE theorem cart and machine for Physics 1.mp4 in class. In this video, the rubber band was pulled back by using a machine and the force exerted on the rubber band was recorded by an analog force transducer onto a graph. The graph produced was as below. We calculated the total work done by the machine in stretching the rubber band by dividing up the graph into a triangle, trapezoids, and rectangles, and finding the areas under those shapes. We added all of the areas to get total work done.

The graph produced in the video

The values of displacement, time, mass of the cart are from the video.
The velocity and kinetic energy of the cart are calculated.

The total work done calculated from the Force vs. Position graph was 22.3 J. The final kinetic energy of the cart attached to the machine was calculated to be 23.8 J by using the data from the video.

Conclusion: From our all four parts of the lab, we saw that there were quite difference in between the work done and change in kinetic energy. We doubted that this difference was due to the possible friction between the track and the cart, and the unreliability of the force sensor. Despite of our numerous trials of each experiment, we got our best datas within 20 % range. Therefore, in our results and datas, the work done and the change in kinetic energy are not quite equal to each other. If we had a better reliable apparatus, we might have gotten better results. We can say that since other groups' datas turned out that the work done and change in kinetic energy were pretty close unlike ours.