November 26, 2014:Angular Acceleration

Purpose: Analyze how different masses, different disk of different diameters , and different torque pulleys affect angular acceleration.

Apparatus: This device is known as the Pasco Rotational sensor.

What we did: First we had to take the measurements of several items to at least 3 significant figures.

• Diameter and mass of top steel disk: 126.6 mm, 1356 g

Diameter and mass of bottom steel disk: 126.6 mm, 1348 g

Diameter and mass of top Aluminum disk: 126.6 mm, 466 g

Diameter and mass of the smaller torque Pulley: 12.5 mm, 10 g

Diameter and mass of the larger torque Pulley: 25 mm, 25 g

the mass of the hanging mass supplied with the apparatus: 24.5 g

Second we opened up logger pro. Next we set up the pasco rotational sensor to 200 counts per rotation. Then we opened up the hose so that the bottom disk would be able to rotate independently form the top disk when the pin was plugged in its place. Next we wrapped the string around the metal plate as the picture above shows to position the mass at the highest point on the pulley. finally we turned on the air and captured the and collected the data onto logger pro. This gave us an angular velocity vs. time graph which we were able to use to find the angular velocity of the upward and downward motion.

We used this same process to find how the change in the hanging mass effects the angular acceleration, the change in the torque effects the angular acceleration, and how changing the rotating mass effects the angular acceleration.

Conclusion: The lab asked us to analyze three thing which were outlined in the hand out

EXPTS 1,2, and 3 Effect of changing mass: We found that the heavier the mass the larger the angular acceleration. 

EXPTS 1 and 4 Effecs of changing the radius and which the hanging mass exerts a torque:  We found that the larger the radius of the pulley the larger the angular acceleration

EXPTS 4,5, and 6 Effects of changing the rotating mass:  We found that the lighter the roraring mass, the larger the angular acceleration.

November 19,2014: Moments of Inertia

Purpose: To use the concepts of inertia to predict how long it will take for a 500 g cart to roll down a 40 degree decline track for 1 meter.

Apparatus: Large metal disk on a central shaft, a cart, ramp, and a camera. We must find the Moment of inertia of this apparatus.

Pic of apperat

What we did: First we took the measurement of all the desired pieces. We got the diameter of the large metal disk which equaled 20.04 cm, the length of the two small rods were 5.15 cm each, and the thickness of the large disk was 1.56 cm wide.Next we set up a camera to obtain a video capture of the disk as it decelerated. We made sure to give the disk a push soft enough for it to spin 2 revolutions. We captured the video and opened it into logger pro. We first set an axis. Then we plotted the points as it revolved around in circles until it came to a complete stop. Finally we scaled the disk and made the diameter of the disk our scale of 20.04 cm. 

What we did with this info: This video capture and points gave us a graph and we were able to get the velocities in the x and y direction. This enabled us to get the final velocity which equaled (Vy^2 +Vx^2)^.5. Then we made a linear fit which gave us a slope that turned our to be our acceleration. In this case our deceleration. It was equal to - 2.385 . We were able to find alpha with this since we now had an acceleration and the radius. Alpha=AxR  This allowed us to come up with the formulas below to find the moment of inertia. With the calculations below we were also able to predict how long it would take for the cart to travel 1 meter.

Conclusion: Our Pridiction was that it would take 7.83 seconds. 

This is a picture of three different times it took for our cart to travel 1 meter. The Average was 7.84 seconds. This gave us an error of less tan .128%.

November 17th 2014: Predicting the Height of a Meter Stick After a Collision.

Purpose: The Purpose of this lab was to figure out the height that the meter stick would go in a rotation system after it collides with clay and sticks onto the stick for some set height.

Apparatus:We used iron rods and clamps to give us a foundation for our meter stick and our clay to stand on. Next we got a rotary sensor and attached it to the rod using clamps. This sensor was not actually used to obtain data. It was only used since it gave us a good post to slide in our meter stick which allowed it to rotate. We Then grabbed a computer and plugged in a camera to obtain a video capture.

Our Set Up

What we did. First we weighed the meter stick. Then we crimped down our meter stick with the gasket onto the iron rod.. Next we got a piece of clay, wrapped it around a piece of tape and weighed it. Next we made a prediction of how high it would elevate.

Our Calcuations Say H=.108

After making our prediction we had to see how high it actually went. We Placed the clay on the bottom rod, lifted our meter stick to make it horizontal to the floor, we pressed video capture, and finally we let go of our meter stick. The camera took video of the whole rotation

.Next we opened up our video on logger pro. First we set an axis on our video which was where the collision took place and horizontal to the floor. Next we scaled our video so it could get a measurement of how high it went. After we clicked plot and followed the movement as it hit the clay all the way to the peak height. This last dot gave us the final height.

Conclusion: We were able to predict the height the meter stick would travel using the formulas above. Our prediction was that it would travel .108 meters high. Logger pro stated that it traveled .08 meters high. Our prediction was off by 2.8 cm which is significantly close to the actual. Things that may have caused this uncertainty may be friction,.

November 6,2015: Conservation of Energy

Purpose: The Purpose of this lab is to determine that Momentum and energy are conserved during a collision.

Apparatus:

 Camera for our video capture

Table for our collision 

What we did: In order to obtain the information that we need, we first had to get a video capture of our two collisions. We First took a video capture of two steel balls. The first ball was at rest at the center of our table. We gave the second steel ball an initial push so that it could collied with the ball at rest. Next we did the same process of obtaining the video capture, but with one steel ball and the other being an aluminum ball. Lastly we measured the weight of all three balls which we would later use to analyze our data.

How we collected our data: We logged onto logger pro and pulled out our first collision from the file. This put us directly into video capture where we clicked add points. This allowed us to click the position of the ball that we pushed up to the collision and through the collision. These points gave us a position vs time and a velocity vs time graph. Next we picked add point again and we followed the ball at rest before the collision and after the collision. Then we picked the scale button and scaled the table that we did our collision on. Lastly we set the axis on the table. This last step gave us a smoother position vs time and velocity vs time graph in which we analyed.PPPPP

 What we did with our data: First we obtained our x,y coordinates in respects to time. Then we got the slope of the graph by applying a linear fit. This gave us Velocity initial x (Vix) and Velocity initial y (Viy). Next we got the slope of the graph after the collision by applying a linear fit which gave us the Velocity final x (Vfx) and Velocity final y (Vfy) We did this for both balls and obtained a Vf1, Vf2, Vi1, and Vi2 in both x and y. This allowed us to make new calculated columns. One was P total x= m1V1fx+m2V2fx. The second being P Total y=m1V1fy+m2V2fy. The third was KE total= .5m1(V1x^2+V1y^2 )+.5m2(V2x^2+V2y^2)




Conclusion. After our analysis of two collisions, we were able to determine that momentum and energy are conserved during a collision.Here Are Our Calculations which Prove this statement. These are relatively close to what the Blogger pro claimed the momentum in the x and y.

November 1,2014: Impulse Momentum Theorm

Purpose:The Purpose of this lab is to verify the impulse momentum theorm. Momentum is equal to P=MV. Impusle is equal to the integral of the force in respects to time. Together  the Change in momentum is equal to impulse.

Apparatus: We used a track, two carts, a motion sensor and a force sensor. We attatched a force sensor on the back of one cart. The other cart had a peice of plastic attached to a spring which would obsorb the collison. The force sensor measured the force between the collisons and the motion sensor measured the velocity of the cart.

What We Did: We opened up logger pro and imputed our two sensors so that they could be read. We zerored out our force sensor and changed the direction of our motion sensor. Now we were ready to do our collisions. We left the cart with the plastic stick sticking out stationary. Next we gave the cart with the force sensor a push so that it could collied with the stationary cart. after the collision the cart that was pushed toward the stationary cart was pushed back by the plastic stick with the spring.

Our Data: Once we collected our data by collecting it in logger pro, we had to evaluate it. In order to find the impulse, we had to integrate over the period of the collison(the force). This integration is shown as a Red solid in the graphs below. Our data shows three graphs. One is a force vs time graph, the second is a position vs time graph and the third is a velocity vs time graph.


In order to prove that the momentum-Impulse theorm is true we had to set up the equation below.

mVf - mVi= Impulse     Where the impulse is simply the integral of the collision,

m(Vf-Vi)=Impulse

Above is the collision between the carts with the mass of the cart being .99kg
m(Vf-Vi)=Impulse

m=.99

vi=.428

vf=-.371

-.79=-.753

Above is the collision between the carts with the mass of the cart being .435 kg

m(Vf-Vi)=Impulse

m=.435kg

vi=.268 m/s 

vf= -.245 m/s

-.22315=-.2405

Above is our experiment of when our cart collied with the clay: This causes Vf to be equal to 0 

m(Vf-Vi)=Impulse

m=.435kg

vi=.728

vf=0

-.31=.277

Conclusion: Our Data above does have a bit of error. However, the error is so low which allows this theory to be true. Reasons for error may have been false readings by our motion or force sensors. Overall we conclude that The Change of momentum is equal to T

he impulse where the impulse is simply the integral of the collision.(The force)

m(Vf-Vi)=Impulse

October 20, 2014: Magnetic Conservation.

Purpose: The purpose  of this lab is to prove that the integral of magnetic force with respect to time is equal to the change in momentum.

Apparatus:We used an air source to blow air into our triangular track which makes the track friction-less. We used a red cart to move up and down the track. We also used a motion sensor to measure the distance between the motion sensor and the metal clip board. A magnet was also placed below the motion sensor so that their would be a repelling force between the magnet below the sensor and the magnet attached to the end of the cart.

 Track,cart,motion sensor, and magnet

Air sourse

What We Did: In Order to get the information we needed to derive a formula to prove that the integral of the force was equal to the change in momentum, we had to obtain a relationship between the distance of the cart to the magnet and the angle of the track. First we raised our track to a small incline and turned the air source on so that the cart could begin to slide down the track. it eventually came to a stop where the magnetic forces repelled and we turned off the air source so that the cart could stay in place due to friction. In order to get the angle of the incline we had to download an app from our phone that obtained angles to a 10th of a degree of accuracy. This made calculating the angle so much easier since we only had to place the phone onto the track and it would give us the angle we needed. Then we measured the distance between the magnet below the motion sensor and the magnet in front of the cart. We Did This processes 9 times and came up with a chart similar to the one below. We Obtained a smaller distance as we increased the angle of the track.

CM     Angle (In Degrees)   Mass of the cart 

3.3      2.35                                     356 grams

2.6      4.6

2.2      5.7

1.9      8.2

1.8      8.7

1.6      10.6

1.4      12.4

1.3      15.8

What We Did With This Data: We logged onto logger Pro and began to plot our information in an x,y system. Our X= the distance between the magnets. Our Y=The force, Where Force=mgsin(theta) This gave us a graph in which we had to insert a POWER FIT to connect our data points.

Next we found a formula for the separation between the motion sensor and the clip board by using total distance-X. Next we made a formula for UR which was the integral of the force. This equaled (.0003785/.792)*Position^(-.792). We got this integral from the formula above which used the power fit and gave the equation Ax^B. We plugged in the numbers and integrated. We then made a new calculated column for kinetic energy which equaled .5MV^2. Finally we made a new calculated column for total energy which equaled Ur+KE

BELOW IS OUR GRAPH OF THE INFORMATION ABOVE

Conclusion: As our chart above shows, total energy is constant and ranges beteween .30 and .50 This Shows that  that the integral of magnetic force with respect to time is equal to the change in momentum.