3-May-2015 Physical Pendulum

Purpose

The purpose of this lab is to find the period of a physical pendulums, we did this with a metal ring and a half circle at two different points.

Experiment

The set up for the first part of the experiment is to find the theoretical period of the ring though using our knowledge of torque, inertia, and periodic motion.

Once we found out the theoretical we then actually set up a stand with a nap sticking out and hanging the ring and see what the actual period of the ring is. We found the period of the ring by hooking it up to the lab pro and using a photogate. 

We then calculated the percent error of the period and see that we are the error was indeed very small. the cause for the error could be that is was not swinging perfectly side to side and may have had some diagonal movement. 

We then do the same for a semi circle, however the difference is that we have to find the center of mass of the semi circle first. After that we then find the moment of inertia of the semi circle about it edges, then use the parallel axis theorem to find the inertia of the semi circle about the center of mass with the shift being the center of mass of the semi circle. Once we have found the inertia about center of mass of the semi circle we then use the parallel axis theorem again to find the inertia about the outer edge of the semi circle. Once we have found the inertia at both points we the find the theoretical period like we did previously with the relationship between torque, inertia, and periodic motion. 

After our calculations we started the experiment by attaching the half circle to the top the and then the bottom and swinging it to see what the period would be. 

After we found out what the actual period was we then caculated the percent error between the theoretical and actual. What we found was the error was actually very small and that what caused the error was again that it may have not swung perfectly side to side and had some diagonal movement

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21-May-2015 Conservation of Energy/Conservation of Angular Momentum

Purpose

The purpose of this lab is to see how angular momentum and energy are conserved in a rotational collision. 

Experiment

This Experiment is done by attaching a clamp to the table with a rod protruding out, then at the end of the rod there is a rotation sensor at the end. The rotation sensor will not be used for collecting data only for the rotation it can produce, and to the rotation sensor we attach a ruler with a hole at one end to it. we then take a stand and put it under the other end of the ruler with a piece of clay in a way that then the ruler swings down it will collide.

In the experiment we know that momentum and energy are conserved therefore we take what we know, that being the mass of the ruler, mass of the clay, length of the ruler, and gravity to calculate the theoretical height that the clay and ruler went after the collision occurred.

Once we calculated how high the clay and ruler rise theoretically we take take a video capture of how the actual collision. From there we analyse the video by tracking the movement of the ruler and clay with points. From the video analysis we were able to find out the actual height which we compared with the theoretical height to get a percent deviation.

The source for our error in this lab was that the ruler was not completely perpendicular, some energy is loss to sound and heat, and lastly the scale and the point in the video capture. 

14-May-2015 Inertia of a Triangle

Purpose

The purpose of this experiment is to find the moment of inertia of the triangle with the air table.

Experiment

Before we use the air table to find the moment of inertia for the triangle we first derive a theoretical moment of inertia for the triangle. This is done by first finding the inertia for the triangle about the edge of the triangle, then using the parallel axis theorem to find out what the inertia about the center of mass is.  

Now that we have found the inertia of the triangle we set up the air table with the triangle on it, and connect the air table to a computer with logger pro. We then attache a hanging mass to end of a string and on the other end to the torque pulley which will cause the triangle on the air table to spin. one we let go of the hanging mass we start collecting the data on the position and angular velocity of the triangle. 

Once we have collected the data we analyze the graph and find the slope of the angular velocity of which would give us the angular acceleration. We take the slope of the velocity as the hanging mass rises and as it falls then take the average of the the two.

Once we have found the average acceleration we used a combination of tangential force and Torque to find the inertia of the triangle. 

After we did the percent error calculations we can see that we are very close, the cause for error can be cause by friction between the disks. the air pressure not being enough or being too much, and that the disk is not completely perpendicular to the disk.

11-May-2015 Moment of Inertia and Frictional Torque

Purpose

The purpose of this experiment is to calculate the moment of inertia of the large spinning disk as well as find the frictional torque of the disk. This is done so that we can predict how long it will take the cart to travel down the ramp.

Experiment

This experiment is set up with an apparatus with a large disk and to the disk we have tied a string to it that is then wrapped around the axis of the disk. This is so that as the cart goes down the ramp the disk will spin as well. We then set up a ramp and place the cart on the ramp, but the ramp is angled so that when the the sting is parallel to the track. 

Before we can conduct the experiment we first have to find the inertia of the disk, then the frictional torque of the disk, and finally the theoretical time that it will take the cart to reach the bottom of the track. To start off we found the inertia of the big disk by first finding the mass of the large disk by finding the volume of both the small and large disk. Then from there we used a ratio to find the mass of the small disk which is then used to subtract from the whole apparatus to ind the mass of the large disk. Once we knew the mass of the large disk we were able to find the inertia of the disk by using the formula for the inertia or a disk I= (1/2) mr^2

Next we had to find the rotational deceleration of the disk which we did by using rotational kinematics. We first counted how many times the disk spun and how long it took before it came to a stop then using rotational kinematics we found out the rotational deceleration, this was done a total of four time. After we got four rotational deceleration we took the average of them because we wanted to be more accurate instead of just using the first deceleration as is. There is a typo however in the picture where it is divided by three instead of four, but the answer is for the average acceleration is correct in that the sums are being divided by four not three.

From here we took our calculated values and solved for the tangential acceleration which is then used to find the theoretical time that the cart would reach the bottom of the track. The method we used to approach this was newtons second law and kinematics.

Now that we have our theoretical time we then actually conduct  the experiment by releasing the cart on the incline to see how long it takes for it to reach the bottom of the track. We did 2 trials of the run so that we can check how accurate the our calculations were. Once we have gotten the actual time of how long it too for the cart to reach the bottom of the track we finally calculate the percent difference between our theoretical time and the experimental time.

The sources of our errors would be that the track was not completely frictionless, the uncertainty from the measurement of the angle, the reaction speed of starting and stopping the timer, and the string was not completely parallel to the track.

5-May-2015 Angular Acceleration

Purpose
The purpose of this lab is to see how angular acceleration is changed when different known masses are pulling on a pulley, as well as how it changes as the diameter of the pulley varied.

Experiment

The set up for this experiment is an air table hooked up to a laptop with Logger pro which will read the angular displacement and velocity of the top disk. Then we hang various masses at the end a sting attached to a torque pulley and record the data, we do the same with a different sized torque pulley as well.

We then take the data collected from each trial and graph them, then from the graph we take use a linear fit to find the slope of the velocity going up and velocity going down. The slope of these lines represents the angular velocity of the hanging mass going up and going down. This was done with all the different trial and different scenarios.

We then took the accelerations and put them into a table along with weight of the masses we used, and the average acceleration calculated. From the table we see the trend that ass the weight of the masses increased so did the angular acceleration, also that as the size of the pulley increased so did that angular acceleration.

We used the acceleration to do two more comparisons for this lab, one in which we compared the angular acceleration to the tangential acceleration and then the theoretical inertia of the disk to the actual inertia of the disks. To compare the angular and tangential acceleration for our last trial we placed a motion sensor under the hanging mass so that logger pro can read it's velocity. We then do the same thing we did for the angular velocity graph for the tangential velocity, we take the slope on the velocity to get the acceleration. The way we compared he to is through the relationship between angular and tangential acceleration (a = αr).

By using the acceleration comparison we can see that they are both really close showing that the difference between the two is indeed by a factor of the radius. There is a slight error in both the accelerations as it rises and descends and that is caused by some friction in between the disks, and that the motion detector had a harder time to read is since the mass was not close enough ad some points.

We then compared the theoretical and actual inertia of the disk based on the acceleration we found, and we did this by manipulating the equations mg-T=ma, Tr=Iα, and a=αr. After we manipulated the equation to get what we wanted to we found the theoretical and actual inertia of the disks. After comparing the two theoretical and actual inertia of the disk we can see that they are very close and that the error is due to the errors in the calipers and scales used to find the radius and mass for each disk.

27-Apr-2015 Conservation of Energy and Momentum

Purpose
The purpose of this lab was to show that momentum and energy are conserved and using our knowledge of conservation of momentum and energy to find the the velocity initial velocity of the projectile.

Experiment
This simple experiment is done by loading a ball into the launcher then launching it into the block. The ball will then collide with the block and raising the block to a certain height at a certain angle. We then collect the data we need from the experiment that we need for our calculations, such as the angle, mass of the ball, the length of the sting holding the block, etc..

From there we then took the data and solved for the initial velocity of the ball as well as calculated the uncertainty for our answer. The uncertainties for this experiment came from the mass of the block, mass of the ball, length of the string, and the angle that the white block rose. 

22-Apr-2015 2D Collision

Purpose

The purpose of this lab is to observe a 2-D collision and to see if the momentum and energy of the balls colliding is conserved or not. In this experiment we are doing two collisions one with with a marble and a steel ball and the other with two steel balls.

Experiment

The setup for this experiment was a glass table where the ball could roll on with little to no friction and a camera above it to record the collisions. The video two collisions are then taken and analysed in logger pro. The collision is done by have one ball originally stationary and the the other is rolled towards the stationary one so that it causes a collision. 

 

The analysis of videos of the collisions were done by manually placing points along the path that the ball was traveling.  From the data gathered from the videos we are able to find the x and y velocities of the balls during the collision. Below we took the numbers we got from our data to calculate to momentum of each collision, the first set is for the steel and marble collision the second set it for the steel on steel collision. From the calculations that we made it can be seen that momentum is conserved in our collision.

After we compared the momentum for both collisions we then look at the energy for each collision to see if the energy was conserved during both collisions or not. From both of the graph the first one for steel with marble, and the second one with steel with steel, We see that energy is conserved because the potential energy in the x and y direction are in sync while the kinetic energy is almost a perfect mirror opposite.

From our momentum calculations it can be seen that there are some errors between the initial and final values. One of the reasons that cause this error would be the fact the lens for the camera is curved and that as the ball passes through the middle of the lens it would appear to move faster. Another would be that the surface is not completely frictionless on the table or the ball. Lastly the table was slightly slanted even though we tried to use note cards to level the table it may have still be slightly off. 

15-Apr-2015 Impulse-Momentum Activity

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

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

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

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

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

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

13-Apr-2015 Magnetic Potential Energy

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

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

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

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

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

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

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