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.