October 29 2014: Angular Acceleration

Purpose: Find the factors that affect the angular acceleration of the system.

This is the rotating apparatus that we used for the lab experiment.

Explanation: After we set up the rotating apparatus, we connected it to LoggerPro for it to read the information. We also configured LoggerPro in the form given in the lab sheet, so we would get accurate data. Then, we attached a string into the rotating apparatus and a mass with certain weight. We ran the experiment a series of times, releasing the mass from a high point, so that the mass would accelerate downwards. We changed the equipment, such as torque pulley, top disk, and weight of hanging mass a couple of times to see how the acceleration would change in each experiment.

This picture shows the data table obtained when we ran the experiment for the first time, our idea was to use the velocity vs. time graph and find its slope, which would give us the acceleration of the system.

 This is the graph velocity vs. time for the first trial.

 This is the graph of velocity vs. time for the double weight of the hanging mass.

 This is the graph velocity vs. time obtained for tripling the mass of the hanging object.

 This is the graph we obtained by changing the size of the torque pulley.

These are the values that we got for each type of experiment. We did six of them, and we got the graph for four of them, the other two we didn't take a picture of the graph because they all look familiar, except for the value of the slope.

Summary: We can say that this lab was successful because we found out that by doubling the mass of the object, the acceleration also doubled, and tripled when we used 3x the hanging mass. When we switched the top steel disk into and aluminum disk, we got an acceleration that was about 5 times faster that with using the steel disk. When using the large torque pulley, the acceleration doubled. By looking at this, we can conclude that there exists a relationship between the torque pulley, the rotating disk and the weight of the object with the acceleration of the system.

10 November 2014: Moments of Inertia

Purpose: Determine the time which a cart slides a ramp attached to a rotating apparatus by using the moment of inertia of the apparatus.

This picture shows the apparatus' that we used for the lab. On top in the rotating disk with cylinders, in the middle is the ramp inclined at certain angle, and on the bottom, the cart.

Explanation: First, we calculated the relevant measurements to find the moment of inertia of the whole rotating apparatus, from that, we used video capture to calculate the angular deceleration of the apparatus. After this, we were able to find the frictional torque of the system. We then, were given a problem where a cart attached by a string to the apparatus was sliding down the ramp by 1 meter at certain angle and we needed to find the time of it. We had to do the calculations before actually setting up the experiment. After the calculations were done and revised by the professor, we set the experiment and ran it a couple times to see if our calculations matched the real life situation.

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This is the data table obtained by using video capture and logger pro.

This graph shows the velocity in the x and y direction as the rotational apparatus spins.

This is the graph of the tangential velocity of the system found by the equation Vt=sqrt(Vx^2+Vy^2)

 These are the calculations that we did to find the moment of inertia of the total system. It came out to be 1.92*10^-2 kg*m^2

This are the calculations that we did to find the frictional torque, the angular acceleration and the time in which the cart would drop 1 meter.

Summary: Unfortunately, our conclusion did not come as expected, because we calculated the time to be at around 9.5 seconds with the ramp angled at 46 degrees, however when we did the experiment, we were getting around 12.5 seconds. This 3 seconds difference is more than the percentage expected, which was around 4%. However, these were the values that we got, and the professor revised the calculations and apparently, they were correct; so the error could be either when plugging the numbers incorrectly in the calculator, which has little chance, given that various members of the group punched the numbers in their own calculator, or some external force changed the system.

13 October 2014: Air track with magnetic potential energy

Purpose: To verify that conservation of energy applies to this system.

This is the glider on top of the air track system. As possible to see, we have some books ready to place under the track to find angles and distances of equilibrium.

Explanation: First, we set the system where a glider is able to move on an air track, and when its turned on, the surface becomes "frictionless." The glider has a magnet on top of it, and on the end of one side of the air track, there is another magnet, so when they get closer, the glider rebounds. We used a motion sensor on top of the magnet in one of the sides to calculate our values when performing the experiment. To start, we measured the distance which the glider stays in equilibrium away from the magnet. By measuring the distance from the magnet on top of the glider away from the motion sensor, and subtracting by the distance that the glider is away, we got our true distance. After that, we placed books under the air track, creating an angle which we measured with our phones, and we measured the equilibrium distance again. We repeated this eight times, with eight different angles. With the angle and distance, we were able to do a graph of Magnetic force vs. distance and by measuring the slope, we found the force equation. We integrated the area of the graph to get a value for F. From that, we are able to do a graph containing the energies of the system, where KE, PE and total energy were shown.

 This data table shows the angles and forces obtained in our eight different trials.

 This is the graph that we plotted with the values of the Force vs. distance of the system.

This is the integration of the area of the graph Force vs. distance.

 This is the data table including the Energies in the system such as Kinetic Energy(KE), Potential Energy(PE), and Total Energy(T).

This is the graph of the three Energies, where KE(purple), PE(green), and Total(orange).

These are the values that we got for each trial with a different angle. The picture also shows the equation that we used to calculate the force at equilibrium point. The actual numbers were found by plugging the angles in the computer to generate a table.

Summary: After we did all the trials, and got our values, we were able to create graphs, and generate numbers to the Energies and specific times. From those numbers, a graph containing the three energies was able to be created. By looking at it, it is possible to see that the Total Energy is not exactly a straight line, but it does not have extreme oscillations, and most of the time it is close to a straight line of top of the other two energies. This shows that our experiment and values were accurate, because energy is supposed to be conserved. I believe that the oscillations in the graph are due to the fact that the air track surface is not completely frictionless, so friction does affect on the total energy, and also because the table in which the experiment was done was not fully straight, also contributing to a margin of error.

13 October 2014: Impulse-momentum with two carts

Purpose: To verify the impulse-momentum theorem.

This is the track and cart that we used to calculate the momentum of the system.

 This is the cart with a certain weight on top of it, to calculate the new momentum.

This is the cart stuck on the mass of clay, to calculate a third momentum in inelastic collision, where the cart does not repulse back.

Explanation: First, we set the system just as the pictures above. The first two pictures show a system where the cart is repulsed back by the red cart. To calculate the force of repulsion, we attached a force sensor on the blue cart. To calculate thing such as distance, time, we used a motion sensor on the end of the track. The idea is to push the blue cart with some force, where the red cart will repulse it back, from that, we are going to calculate the momentum by doing a force vs. time graph and calculating the integration of that area. To make sure our numbers are accurate, we also did calculations by hand, where we got the velocity before and after collision to find the momentum. For the third experiment, using the clay, we did the same procedure, but in the calculations by hand, the final velocity is 0.

These are the graphs that we got in our first experiment, with only the blue cart and the red one. The last graph shows the force vs. time graph, and the momentum is the area of it. It came out to be -0.2723 s*N

 These are the graphs that we got in our second experiment, the blue cart had some weight on it on this trial. The last graph shows the force vs. time graph, and the momentum is the area of it. It came out to be -0.6706 s*N

These are the graphs for the last experiment, where the cart glues on the mass of clay. The last graph is the force vs. time graph, and the momentum came out to be -0.2351 s*N

This are the calculations by hand that we did to show that the values that we got for each momentum was accurate. The equation used was mass*velocity(final) - mass*velocity(initial) = momentum.

Summary: To start, we set the cart, track, motion sensor and force sensor system. We calibrated the motion and force sensor to give us accurate values. We run each experiment, where the blue cart was pulled into a red cart on the first two experiments, and into a mass of clay of the third experiment. The force and motion sensor gave us values to work with. We created a force vs time graph for each experiment, and the area of that graph would give us the momentum of the system in each trial. To ensure that the momentum value was accurate, we also performed calculations by hand, and because the numbers were close, we can say that our experiment was successful.

October 8 2014: Works acting on a spring system

Purpose: To find the works acting on a spring system with a hanging mass in movement for 10 seconds.

  This is our spring system with a hanging mass. We also have a motion sensor on the ground to calculate data such as position, velocity, time, etc...

Explanation: First, we are going to measure the spring stretched and not stretched to find the constant k of the spring. Then we are going to obtain data by letting the system move up and down for 10 seconds and allowing the motion sensor to capture that. With those information, we are going to create a data table containing the KE of the system, the GPE of the system, the Elastic PE, the GPE of the spring, the KE of the spring, and the Total Energy in the system. We have equations to find the values of these energies.

 This is the data table that we have for the energies present on the system at certain time.

 These two graphs are one for the position vs. time of the system and one for the velocity vs. time of the system.

This is the graph of all the energies on the system, the top(purple) energy is the total energy. We made a mistake probably on finding the constant K, because the total energy should be a straight line, since energy is barely lost while the system is in movement.

 These calculations show how we found each type of energy present in the system. The professor made the derivations with us in class.

This picture shows just what are the equations for each one of the energies.

Summary: First, we derived, with the professor, all the energy equations that were necessary to complete this lab. Then we set our spring system to perform the experiment. We calculated the constant "k" by stretching the spring with the mass, and then we allowed the spring to stay in movement for 10 seconds, so that the motion sensor could obtain the information necessary to the computer. Having the equations for the energies, with the data information from the motion sensor, we created a graph by using the values of the energies at certain time. From that, we were able to know the energies present in the system at specific moments. However, I think we made a mistake in calculating the constant "k," because the total energy was supposed to be a straight line, since energy is not lost in the system, but our total energy was in oscillation form. We can conclude that our lab was almost successful, we got values for all the energies, but the total energy did not come out as expected.

September 29 2014 - Finding the Power used out of class

Purpose: To find the power required to go up a staircase and to pull a backpack up to a certain height by using a pulley.

This is the staircase that we used to time how long it took us to go up. We had to times, one for going up slow and one for going up fast.

This is the system with the pulley and the backpack. We used the 9 kg backpack system.

First we are going to calculate the time needed to go up the staircase in two scenarios, one going up slow and the other going up fast. Then, we are going to calculate the height of each step and count how many steps are in the staircase, so we can find the total height. After done with that, we are going to go to the backpack system, where each one of us is going to pull the cable holding the backpack and we are going to time how long it take us. The height pulled will be the same as the staircase.

 These are the calculations used to find the height of the staircase which is 3.74 m, the gravitational potential energy of going up the staircase which is 1832.6 J, and the power used in each execution, one slow and one fast.

This is the calculation to find the power used in pulling the backpack up to the top of the staircase, the power that I used was 21.7 Watts.

Summary: After we calculated the time for each execution and height of the staircase, I found the work(mgh) of me going up to be 1832.6 J. Dividing my work by the time of each execution(slow=15 seconds, fast=8.9 seconds), I found out that I used a power of 122.17 Watts when going slow, and 205.9 Watts when going fast. After that, we timed how long it took us to pull the 9 kg backpack. I found the work in that backpack going up to be 329.87 J. Again, by dividing the work by the time it took me to pull up (15.2 seconds), I found that the power required to pull the backpack was 21.7 Watts.

October 1 2014: Finding the kinetic energy of a cart being pulled by a spring system

Purpose: To find the work done  by the spring on the cart during the execution of the experiment.

This is the spring-cart system that we used to perform our lab. There is a motion sensor on one the ends to calculate the data needed to create a graph of this system. Attached to the string there is also a force sensor to calculate the force which the spring in pulling the cart.

Explanation: We are going to calibrate the force sensor, so that the data obtained is more accurate. From that, we are going to pull the cart with certain force and release it. This will allow the force sensor and the motion sensor to calculate our data information such as force, position, time, velocity, etc... By using the graphs that the computer will give us, we plan to the graph force vs. position and calculate random areas to know the work done by the spring on the cart.

This is the data table for our graph, it contains information such as Force, time, position, velocity, and kinetic energy.

These are the graphs that we got when performing the experiment. The first graph is position vs. time, the second is velocity vs. time, and the third is Force(blue) and Kinetic Energy(purple) vs. time.

This is the 1st area that we calculated the integration to find the work done, it gave us a value of  0.79m*N

This is the 2nd area for the integration, it gave us  0.896m*N.

This is the 3rd area for integration, it gave us 0.625m*N.

 This picture is a hand-made drawing by the professor to explain how the system should work. Our experimentation was similar to the one expected.

This is an expectation of what the graph Force and Kinetic Energy vs Position should look like. The fact that our  sensor had reference to the opposite way made our graph have the Force reaching zero as the position increased, but the integration gave us a good expectation for the work done, it did not affect the process at all.

Summary: First we created a system where the cart could be dragged by the string force without any problems. Then we calibrated the force sensor, so that our graphs would be accurate. We then, perform the experiment, letting the cart go from a certain distance and have the spring force drag the cart. With the force and motion sensor in position, they provided us data information from which graph could be generated. By analyzing the graphs, specifically the Force and Kinetic Energy vs Position graph, we were able to find the area of the graph at random points to calculate the work done by the spring on the cart at specific positions.