Friday December 5, 2014: Mass Spring Ocillations.

Purpose: Find the relationship between period and oscillation.

Apperatus: Spring, motion sensor, a mass and logger pro.

What We Did: Professor wolf informed us that 1/3 0f the mass of a spring actually goes into the mass for a period of oscillation. We were part of group 1 where we all had to get our mass to equal 109g and had to find our spring constant so that we could see the relationship between period and oscillation. First we weighed our mass and found it to be 12 grams which meant that only 4 grams went into the mass for oscillation. This also meant that we had to attach 105 g on our spring so that every one would be using the same amount of mass but different spring constant. Next we had to find our spring constant. To do so we set up our motion sensor to get the change in y with two different masses. We found that the position of y was .330 meters with 100 grams attached and .229 meters with 50 grams attached. To find the spring constant we used the formula …. change in force/ change in y… force was equal to Massxgravity and change in y was =.101  meters. These numbers gave us a spring constant of K=4.851  We put these numbers on the board along with every one else's. We also found the period of one oscillation using the 109g mass by using logger pro. 

What we did with this information: We plotted these numbers in an xy graph in logger pro and applied a power fit to get what we were looking for. In the x axis we put the period in seconds of each group and in the y we put the spring constant.

Conclusion #1: We Found that the relationship between period and the spring constant is that the bigger the spring constant the the faster the period and vice versa.

Part 2:

What we did: Next we got the period of oscillation using our spring for our original 109 g, 209g ,209g, and 409 g. To find the period we used the formula. Change in time(s)/ Periods. 

this gave us this chart.

IN GRAMS             period in seconds

109                                .9625

209                                1.35

309                                 1.56

409                                 1.77

Finally we plotted this and evaluated the graph

Conclusion: We found that if you use the same spring with the same spring constant that as you increase the mass to the bottom of the spring that the period of oscillation also increases.

December 4,2014. Moment of Inertia of a uniform triangle about its center of mass

Purpose: To be able to calculate the moment of inertia of a uniform triangle about its center of mass.

Apparatus: We used a Triangle, disk, hanging mass, a sensor, and a piece of string.

What we did:  First we took the measurements of the triangle.

 Next we got the apparatus. We tied a string onto the apparatus  with a hanging mass on the other end. Then we got the string and put it over a pulley. Next we opened up the hose clamp so that the bottom disk could rotated independently from the top disk. After doing this we opened up logger pro and opened up our sensors. We used the Rorary motion sensor and used the setting to count 200 marks per rotation.  Finally we collected our data. The slope of these graphs were the angular acceleration/ deceleration. In order to get our alpha we used ( alpha of hanging mass rising + alpha of the hanging mass dropping and we divided it by two. This gave us an average alpha to use in our calculations. 

Part two: We mounted the triangle in a vertical position and used the same technique to find alpha for the apparatus to find the alpha of the apparatus with the triangle.

Next we mounted the triangle horizontally and used the same technique to find alpha for the system while the triangle is horizontal.

Finally we used all the alphas to calculate the moment of inertial of each situation based on the hanging mass and the angular acceleration (alpha) In order to get the inertia of the triangles alone we had to find the inertia of the system with the triangle and subtract the inertia of the system with out the triangle.

Below are all of our calculations

INERTIA

Conclusion: Using all these different formulas we were able to get the actual inertia of the triangle in both positions. My lab partners Isaac and Mathew had a major role in this Lab. They guided  and showed me how to get all of these calculations.

December 3, 2014: Conservation of Linear and Angular momentum

Purpose:  Prove that linear and angular momentum is conserved.

Apparatus: We used the model ME-9281 Rotational Accessory Kit and the ME-9279A Rotational Dynamics Apparatus.

used this to find the velocity of the ball when it reached the end of the ramp

Used this to the angular speed of the ball once it is in the ball catcher.

What we did: We set up the apparatus in picture one. We picked an initial launch point for the ball to roll down from and marked it on the ramp. Next we made a few measurements. We measured the height of the launch point to the bottom of the apparatus(19.2 cm), the height from the bottom of the apparatus to the floor(97.5) cm, and the horizontal distance the ball traveled once we let it go from our launch point(51 cm). We used kinematics to solve for the velocity at the end of the launch ramp which is known as the launch speed.(1.1433 m/s) This Velocity will be used in further calculations.

Part 2:  We used the aluminum top disk and mounted the ball catcher on top of a  small torque pulley. We used logger pro so that we could find the acceleration and deceleration of the torque pulley.  

The slope is equal to the acceleration/deceleration

We used the mass and the average angular acceleration to calculate the inertia(I) of the apparatus.

Part 3: Finally we set up the ramp and measured the radius at which the ball would hit the ball catcher. We released the ball from our initial release point. This would allow us to use our Velocity at launch in our next calculation. Finally we did the calculations to find the angular speed.

How we found I

How we got our angular speed.

Conclusion: We found that our Omega was equal to 1.74 rads per second theoretically and that our actual value for omega was 1.69 rads per second which is real close. Reasons for error may be rounding errors, went slightly higher than our initial drop point, or made have a small measurement error.

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.