October 5th, 2014-

Purpose: To be able to prove the law of conservation of energy.
Apparatus: We used a spring, a mass,  a motion sensor and logger pro.

Our set up

What we did: We grabbed a mass that was attached to a hook which was a total of .5kg. Next we grabbed a spring and weighed it which gave us .1kg. We set up by hanging the spring with out the mass stretching it and measured the height from the floor to the bottom of the mass.(76cm) Next we measured the stretch of the spring by getting the distance to the floor to the bottom of the mass.(55cm) This gave us a delta x of 21 cm. We Then we found the K in the PEe=.5kx^2 formula by using the formula Mg/Delta x which gave us 23.53 After we set up our motion sensor and activated it onto logger pro. We let the mass start to oscillate and then we began to record the movement of the mass/spring system for ten seconds. This gave us two graphs on logger pro which consisted of a position vs time chart and a velocity over time chart.

What we did with this information: With this information we added 5 new calculated columns. These included gravitational potential energy(GPE), Kinetic energy (KE), Elastic potential energy(PE elastic),gravitational potential energy of the spring(GPE RED),  Kinetic energy of the spring(KE spring) and a final column for the Total Energy(Total. we set up a formula of each column as followed.

GPE: Mass*gravity*position

KE:.5*mass*velocity^2

GPE RED: (Mass of spring/2) *gravity*postion

KE Spring: .5*(mass of spring/3)*Velocity^2

PE elastic: .5*K*Delta Position

Total: Sum of all forms of energy

We finally graphed all of our new calculated columns together in out position over time chart which gave us multiple graphs that looked as followed.

Conclusion: The image above proves that energy is conserved. The yellow line above is the total energy of the spring as it oscillates up and down with the mass. As you can see, the total energy is relatively constant between .6 and .7 J.

October 9th, 2014- Work-Energy Theorem

Purpose: The purpose of this lab was to find the relationship between work and energy. We had to prove that Kinetic energy is equal to total work done.

Apparatus: We set up our apparatus which consisted of a cart, a track for the cart, a spring, a force sensor, and a motion sensor.

Our set up

What we did: We logged onto logger pro and connected both of our devices which included the motion sensor and the force detector. We first zeroed out our force sensor. Then we connected our motion sensor and reversed the direction of the motion sensor since the cart would be traveling away from the motion sensor rather than toward. Next we pulled the cart and pressed collect data on logger pro and let go of the cart. This gave us two charts. One was a position vs time chart and the other was a position vs force chart.

What we did with our data: The first thing we did was add in an extra curve for Kinetic energy. That is the purple curve above. In order to prove that kinetic energy was equal to force we had to find the integral of the force which is the red line above. We did this by clicking the integral function in logger pro. We integrated at three different locations. Below are our three charts already integrated.

Conclusion: The Graphs above prove that Kinetic energy is equal to the integral of force. This proves that kinetic energy is equal to total work since the integral of force is force over a specific distance. You can check this by looking at our graph and comparing the kinetic energy and the integral for force. This is extremely useful when finding energy problems and you are also given a force.

October 5th, 2014-WORK AND POWER

Purpose: The purpose of this lab was for us to learn how to calculate work and power. We did this by performing an outdoors activity and calculating our results.

What we did: Our lab asked us to find the amount of work and power it took for us to climb up the stairs. The first thing we had to do was to find the height of the stairs. to do so we measured the first step which was 17cm and multiplied it by the amount of stairs.(26 steps) This gave us a height of 442 cm or 4.42 Meters. Next we found the amount of time it took for us to walk up the stairs and to run up the stairs.  Below are my results

Time it took to walk up the stairs: 15.63 seconds
Time it took to run up the stairs: 5.03 seconds 

Part Two: The second part of the lab asked us to find the work and power it took for us to pull a bag from the floor up a pulley system. First we determined our height which was equal to the height of the stairs.(4.42Meters) Next we had to pick one of the three bags. I chose the bag that weighed 5 kg. Next one of my lab partners went up the stairs to calculate the time it took for me to pull the bag all the way up the pulley system. It took me 4.42 seconds.

What we did with this information: We used this information to calculate the amount of work and power it took for us to pull the bag up, walk up the stairs, and run up the stairs.

Work for the stairs project: We used the formula Work=force*distance. In order to calculate force we had to find our mass. I Converted my weight in pounds into kg. I weigh 170 pounds which converts to 77.11 kg.
1)work for walking and running up the stairs
W=Mass*acceleration*Height
W=77.11*9.8M/S^2*4.42M
W=3340.1 Joules.

2)Power for walking up the stairs:
Power=Work/Time
power=3340.1J/15.63S
Power=214.14 Watts

3)Power for running up the stairs:
Power=Work/Time
power=3340.1J/5.03S
Power=665.41 Watts

4)Work to pull mass up the pulley system:
Work=force*distance
Work=5kg*9.8M/S^2*4.42Meters
Work=216.5 Joules

5)Power needed to pull up mass
Power=work/Time
power=216.5J/3.5seconds
Power=61.88 Watts

Conclusion: We were able to calculate work and power in an everyday activity. This lab showed us how to approach any work or power problem. The main formulas used were Work=Force*Distance and Power = Work/Time

September 1st, 2014- Relationship between angular speed and Theta

Purpose: The purpose of this lab was for us to find the relationship between omega and theta using a conical pendulum.
Apparatus: 

This is our conical pendulum. This apparatus has a pole attached to the top of it and a string tied to the end of the pole. It is hooked up to a motor which cause the pole to pin in a clockwise direction. 

What we did:  First we took the measurements of the  few items we could obtain using a meter stick. We found that the Height of the Conical pendulum was 211 cm and the length of the string was 165 cm. Next we took the time for the weight at the end of the string to revolve around the apparatus 10 times. Once we got the time we recorded our data. After we had to determine the height of the mass by setting up a tripod and attaching a piece of paper onto it. To get the height we would have to position the tripod close enough for the weight to hit it and elevate the tripod to the point where the mass just hits the top of the paper.

Once the mass hit the paper we got the height of the paper relative to the ground by using a meter stick and recorded our data. That completed the experiment for one velocity. Professor Wolf would then raised velocity and we would obtain the same data for that speed. We continued this process for 7 different speeds. This is what we obtained

TIME FOR 

TEN ROTATIONS------HEIGHT OF MASS AT THAT VELOCITY

37 SEC                           49CM               

30 SEC                           72CM

26SEC                            92.3CM

25 SEC                          104CM

23 SEC                          119 CM

21 SEC                           132 CM

19 SEC                           174CM

WHAT WE DID WITH THIS INFORMATION: First we had to come up with a formula to be able to use our data. We set up an image of the apparatus and had to find out a few unknowns.

H= height of the apparatus.=211cm

L=length of string.

H2= the the height of the mass while spinning= column 2 above

H-H2=to the height of the string to the top of the apparatus.

Theta= acos(H-H2)/L 

We then made a body diagram of the mass and the tension. We separated the tension vector into x and y components. We set the x component= m*(V^2/R). We then found R using the Pythagorean theorem. Finally we manipulated and solved the equation to find the relationship between omega and theta.                                BELOW ARE ALL THE STEPS MENTIONED ABOVE.

Next we opened up Logger Pro and Inserted all the information we obtained.(Below)

We Then Graphed it and put a linear Fit (Below)

Conclusion: After an extensive lab we were able to find the Relationship between Omega(W) and Theta by finding the Height of the pendulum,the length of the string, the time it takes for the mass to revolve around the pendulum, and the height for that time period. We found that the relationship is that tan(theta)=(Omega^2*R)/G. 

September 1St,2014-Centripital Acceleration as a Function of Angular Speed

Purpose: To find the relationship between the acceleration of centripetal force and omega. In doing so we were able to find the radius of our apparatus from the information we used. We collectively  completed this lab as a class.
Apparatus: We used a spinning table, a motion sensor, and logger pro.

Spinning wheel and motion senor.

What we did:  First Professor Wolf handed us all a stop watch and told us to measure the amount of time it took for the sensor to revolve around the table four times.( obtaind time for four Periods) He would spin the wheel and we would measure the time.  After we measured the time for four revolutions he asked us for the time and he recorded it on the board. He took the average of all our times and used that time for our data. Logger pro recorded the spin and obtained an acceleration. We did this process of obtaining the time of four revolutions for five different accelerations and recorded the time and acceleration.

How this information was used: We put the information onto logger pro. On the first column we inserted the time for four periods.  In the second column we plotted the Acceleration for that time period. In the Third column we inserted the time for one revolution. In the final column we inserted a formula to obtain omega. After inserting our data we plotted it into an Acceleration Vs Omega Chart.

This is our chart  and graph.

Conclusion: We were able to obtain all the information needed just by measuring the acceleration and time for each revolution. However the data we obtained was faulty at first because we were unable to find the radius of our spinning table. What happened was that us students were actually giving the professor the time for three revolutions. After fixing all of our formulas by changing the time obtained from four periods to three, we were able to rind the radius of the spinning table. The function above is written as a=Ax. The A is said to be .18 meters which was close to the actual radius of our table. The function we derived is one of the equations needed to solve centripetal acceleration problems. This Equation states that  centripetal acceleration (a) is equal to the radius (A) times omega(x) where omega was squared before plotting.