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.