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.

September 29 2014: Angular speed for a particular rotating apparatus

Purpose: To find a relationship between angular speed(w) and angle created by the string relative to the vertical on a particular rotating apparatus.

This is the rotating apparatus that the class used to calculate the rotations and the time for this lab. There is a string attached to one of the ending of this apparatus, where a weight is located, and it was our reference.

First, we took some time to calculate the measurements of this apparatus such as height, length of each arm, length of the string, etc... Then we calculated the time of 10 rotation at 8 different speeds and we are going to attempt to find the angular speed for each trial by utilizing the given equations and using a computer to calculate the values for us.

This is the model that our professor drew on the board for us to use as reference of what measurements to take from the apparatus.

We drew our own model of the apparatus, and as possible to see, we have the measurements of each relevant part of the apparatus, and we are going to solve for h2, and theta according to each trial.

This is the picture of the values that we got for each of the eight different trials that the class did. Each time was taken for 10 rotations of the object.

 These equations were the ones that we found relevant to finding the angular speed for each trial. From those equations, we expected to get numbers to create a graph for the lab.

In order for us to perform the calculations easily, instead of finding each angular speed for each different trial by hand, we plugged the numbers in excel and created formulas to calculate the values faster.

This is a graph of w(rad/s) vs. f(theta). Our expectation was to get the slope close enough to 1, which would show that our calculations for the angular speed would be accurate, we got 0.9987, a number really close to 1.

Summary: First, we got the measurements of each relevant part of the rotating apparatus. Then the professor turned on the apparatus and we timed 8 different trials at different speeds. We drew a model of the apparatus with our measurements and tried to find a equation where the angular speed(w) would be a function of theta. We got w^2=g*tan(theta)/d+l*sin(theta) to be our equation. We used each different trial to get a different value of w, and we plugged those numbers in the computer. After that we used the equation w=2*pi/time to calculate the angular speed(w(rad/s)) relative to the time for each rotation. We also plugged this numbers in the computer and created a graph w(rad/s) vs. w=function of theta. The slope of that graph had to be close to 1 to indicate that our calculations were accurate, and we got 0.9987 which is considered close. This showed that our calculations/measurements were good.

September 24 2014: Centripetal acceleration as a function of angular speed

Purpose: To find the centripetal acceleration as a function of the angular speed of the system.

This is a picture of the apparatus, which is an accelerator with the disk, the picture is not clear because our group was not close to the professor's desk, and we forgot to take a closer picture.

The whole class did this lab together, each group got a stop watch, and the professor set up an accelerator with a disk that rotates. Each group was supposed to find the time in which the disk did four rotations. We did this five times, with different speed in each trial. With the average of times, we attempted to reach to a centripetal acceleration by plugging our data into the computer and creating a graph.

This is a graph that the professor obtained when plugging the data in his computer, we got this graph because he posted in moodlerooms. 

This is the average of time that the class had for the different speeds when executing the lab.

This lab was more of a consensus of data information between the groups. Each group had to time four rotations, and of course, this lead to human errors plus uncertainty. Another factor that contributed to errors was that some groups did not calculate the time for the rotations. With the average from the groups who timed the lab, we created a graph and from it we were able to calculate the centripetal acceleration of the system, showing that exists a relationship from the angular speed and the centripetal acceleration.

Sep 17 2014 - Modeling friction forces

Purpose: Utilize wooden blocks to find the friction forces acting on the blocks in various situations, and also calculate the acceleration of the system.

This is a motion sensor, which is the apparatus that we used in order to get our data into our computer, such as position, time, velocity, etc.

This is a force sensor, which is the apparatus that we used to calculate the kinetic friction acting on the wooden blocks as we dragged them.

Explanation: First we are going to find the static friction force acting on the wooden blocks by attaching a string and a pulley connecting the blocks and a cup filled with water. After that, we are going to connect a force sensor to the wooden blocks to calculate the kinetic friction that acts on the blocks. Then we are going to build a ramp and find at which angle the blocks start to slide so that we can calculate the static friction of that system. After finding the static friction, we are going to increase the angle of the ramp so that the block slide with constant speed so that we calculate its kinetic friction. The finalize, we are going to create a system using weights, and a pulley that will pull the wooden block from the bottom of the ramp to the top of it, and by doing this we are going to calculate the acceleration of the system.

This is the system that we created using the wooden block and the cup of water to find the static friction.

 This data table shows the friction force obtained from, 1,2,3,4 wooden blocks respectively. We used those numbers to create a graph where we would find the coefficient of the static friction.

This is the graph from the data table above, as we can see, points 2 and 3 are a little off, probably due to uncertainties and irregular surface.

This is a graph obtained from using the force sensor to calculate the kinetic friction of the wooden blocks, we did the same calculations for all 4 blocks.

This is the ramp that we created to find the angle which the block starts to move and find the static friction. We also used this ramp to calculate the kinetic friction by increasing the angle of the ramp.

This is the graph that we used in calculating the kinetic friction for the angled ramp.

 This is how we calculated the acceleration of the system, as possible to see, the weight on the right will pull the wooden block if I stop holding it.

 This is the data table from the system that we run to calculate the acceleration.

This is the graph of the system used to find the acceleration obtained by the wooden block being dragged.

 These calculations were used in the first part of the lab, where we utilized the cup of water to find the static friction of the system. Notice that part two did not require calculations, because all we did was use a force sensor to find the kinetic friction.

 These calculations were used in the third part, where we found the the static friction of the system by creating a ramp inclined with certain angle.

 These calculations were used in the fourth part, where the increased the angle of the ramp in order to find the kinetic friction of the system.

The handwritten part of top of this picture are the calculations used for us to find the acceleration in the last part of the lab, where weights pulled to wooden block from an inclined ramp.

Summary: We started this lab by using a cup of water attached to 1,2,3,4 wooden blocks to find the static friction of them. By using those numbers in a data table, we could find the coefficient of static friction in the system. We then, attached the wooden blocks to a force sensor and by using those numbers in the computer, just like the first part, we were able to find the coefficient of kinetic friction. After this, we created a ramp with certain angle, where the block would start to move, and that would give us the maximum static friction in the ramp system. When the angle and friction were found, we increased the angle significantly, such that the wooden block would slide with certain speed, and from that we were able to calculate the kinetic friction in the ramp system. To finish the lab, we attached a string connecting some weights and the wooden block in order for us to find the acceleration in which the block was pulled by the weights.