Magnetic Potential Energy Lab

Ana,  Jonathan, and Andrew

4/17/17

For this experiment we are trying to show that the energy is conserved when the cart moves from one end of the cart to the other. In order to do this we will get our kinetic energy and our magnetic potential energy and show that they are constant at every location. In order to do this we will first have to do some experiments that will allow us to find our potential energy.

To start off this experiment we first have to set up a track with a frictionless cart with a magnet on one end, and a magnet attached to one end of the track. We then leveled the track and checked to see what the repulsion distance is between the two magnets. Then we lifted the track to a certain angle and then once again measured the distance of the repulsion. We repeated this again four more times each time doing it at a different height. The magnetic repulsion force between the two magnets will be equal to the gravitational force component parallel to the track. We then plotted a force vs repulsion distance graph and used this to get values for our equation F=Ar^n.Then we used this equation to get our potential energy by integrating it. This gave us the equation for the potential energy. Once we were done with this we verified the conservation of energy by using a motion detector to measure both the speed of the cart and the separation distance between the two magnets. Then using the data that the motion detector gave us we were able to get graphs for the Kinetic Energy and the Potential Energy.

How we calculated our F value

The Magnetic Force

The equation for the Potential Energy of the magnet

Our expectation for the graph of the kinetic energy magnetic potential energy and the total energy was that we would get a nice straight line for the total energy (dark green) and the inverse of the red line for the kinetic energy however this wasn't the case. The line for our kinetic energy decreased as the time went on this is due to our cart slowing down. This means that our track wasn't as frictionless as we thought it was. Most of the errors in our graphs have to do with our track not being frictionless. The equation for our potential energy did a good job of giving us the graph that we were looking for. 

Overall we were able to get an equation for the our potential energy but we were not able to prove that the total energy is conserved because our graphs were not able to show this. The line for our total energy should have been a straight line that was equal to the initial kinetic energy of our cart. 

Work-Kinetic Energy Theorem Activity

Lab #11
Ana Leyva, Ricardo Gonzalez, Chris Garcia
4/19/17

For the different experiments in this lab we are trying to prove that the change in kinetic energy is equal to the work done by the object. In order to do this we did different experiments graphs that would help us prove this theory.

EXPT 1. Work done by a constant force

To do this experiment we first had to set up a track, a pulley at the end of the table and a motion detector on the opposite side of the track. We then tied a piece of string that was long enough to our cart on top of the pulley and attached 50 g to the other side of the string that was hanging over the table. Finally we ran the motion sensor and gave our cart a push so that it would move at a constant speed. This gave us a force vs position graph and a kinetic energy vs position graph that we used to see if the kinetic energy would be equal to the work done.

10. Integral value = 0.1011 N*m        KE value = 0.098 J
- The value of the integral gives the area under the Force vs. Position graph which is equal to the work done. Therefore the integral equals the work done.
-Ideally, integral should be equal to the kinetic energy therefore integral - kinetic energy = 0
           0.1011-0.098= .0031 which is not equal to zero  however it is a relatively very small number and we can still conclude that the integral = kinetic energy.    

11. integral value/ work = 0.2290      KE= .204

         work - KE = 0.2290-0.204 = .026  Although it does once again not equal 0 we can still assume that the work done = KE. The reason why it does not equal zero is probably because of an error with motion detector or an error when we calibrated our force or motion sensor. 

EXPT 2 Work Done by a Nonconstant Spring Force

For this experiment we used the same setup as last time but we made a few changes we connected the force sensor to a rod at the end of the table. Then we connected the spring to the cart and to the force sensor. After this we pulled the cart towards the motion sensor until the string was stretched for about .60 m. We tried to pull the cart at a constant rate. We then got the force vs position graph and got the spring constant from this. 

6.

In order to get the spring constant I used the following equation:

the integral gave us the work done. 

- work = 1/2 k x^2 

0.7068 N*m = 1/2 k (.5m)^2

k= 5.6544

EXPT 3:Kinetic Energy and The Work - Kinetic Energy Principle

I will have to redo this one because I forgot to find the KE at different positions.

EXPT 4: Work- KE theorem

For this experiment we have to watch a video, create a Force vs. Position graph , find the work that was done, and then find the kinetic energy and compare it to the work that was done. 

The work that we calculated should be equal to the kinetic energy however in this case they are not. This might be due to the fact that our graph wasn't completely accurate it was just a rough estimate. I believe this is the major reason why our work isn't equal to the kinetic energy.

Work and Power Activity

Ana Leyva, Andrew, Jonathan
4/5/17
lab #10

With this experiment we are trying to calculate our power output while we do various activities.
In order to calculate our power output we are using the equation power= mgh/t. In order to calculate our mass we estimated how much we weigh the height was calculated by measuring the distance from the floor to the top step of the stairs we were going up and we calculated our time using a stopwatch. We then used these measurement to calculate our power output.
To start this experiment we had to complete various tasks. My lab group started off by pulling a 5kg backpack a height of 4.342 m. We timed ourselves to see how long it would take us to do this. Then we timed each other to see how long it took us to walk and run up the stairs. We calculated the height by measuring one step and multiplying how many steps there are. After gathering this data we started calculating our power output.

1. Power pulling up a mass a certain height.

2. Power output walking up the stairs.

3. Power output running up the stairs.

4. A. 

Power output of 1 and 2 including KE.

In order to do this we first had to calculate the vertical distance traveled when going up the stairs. Then we calculated the velocity which allowed us to solve for the KE.

Including the KE shows us that it does not make a big difference which is why it is negligible. For walking up the stairs the difference was of 0.316. For running up the stairs was the difference was of 2.235. 

4B. 

Number of stairs we would have to climb to to equal the power output of the microwave.

4C. 

Number of steps we would have to climb to equal the amount of time it takes to rum a microwave for 6 minutes.

D 1-3.

Finding a relationship between theta and omega

Ana Leyva, Jonathan, Andrew
4/5/17
lab #9

For this experiment we are trying to find a relationship between theta and omega. We will try to accomplish this by using the free body diagram of our hanging mass and a few calculated values.

In order to find a relationship between theta and omega we first had to come up with a freebody diagram whose equations would allow us to find a relationship between theta and omega. We then had to come up with other equations that would allow us to calculate theta. However, before being able to calculate theta we have to find the measurements of a few object in order to be able to calculate theta.

Our apparatus was an electric motor that was attached to a tripod. We had this motor spin at different rates in order to find different values of omega and theta.

To start this experiment we measured the height (H) of the apparatus, the length of the horizontal bar(R), and the length of the string(L). Then by creating a right triangle with L being the hypotenuse and the H-h being the adjacent side of theta. We then let theta = arccos ((H-h)/L). After this, we created a freebody diagram of the hanging mass in order to try to find a relationship between theta and omega. Then by manipulation the equations we were able to get an equation for omega where the radius(r)= R+Lsin(theta). Finally, in order to test this out we started measuring how long it would take the apparatus to make a certain number of rotations and what the height of the mass was during those rotations. We then calculated omega using that data, and then we calculated it again using the equation that we had came up with.  

Observed data

Calculated data

After plotting a graph of my observed values of omega and calculated values of omega I observed that there was a correlation of 0.9553. Although this is not that great a correlation if it pretty good considering that all of our observed values aren't as accurate as we would want them to be. However, we can still conclude that the equation for omega that we came up with does an adequate job of giving you a value for omega.

Centripetal Acceleration Vs Angular Frequency

Lab 8
3/29/17
Ana Leyva , Jonathan, Andrew

For this experiment we are trying to find a relationship between centripetal force and angular speed (omega w).
What we are trying to see in this experiment is how and if there is a relationship between the centripetal force and angular speed. In order to see if there is a relationship we will use our equation F=mrw^2 to plot a force vs mass, force vs radius, and force vs w^2 graph to see if there is any relationship between these graphs.

apparatus used for this experiment

For this experiment we used this pre constructed apparatus to help us collect the period and force data. We did this for different masses, radii, and power supply. Then with all the information that we gathered from this, we started to create our graphs. 

An excel sheet of all our recorded data

Force vs Mass 

Force vs Radius

Force vs w^2

For our three graphs the graph which was the closest to our calculated value was our Force vs. w^2 graph. We believe that this is that graph that gives us an answer closest to our actual graph because for this one it was easier to make sure that our mass and radius were the same for our 4 trials. Keeping w and the force constant was harder to achieve. In the Force vs w^2 graph we are taking this into consideration which is why it makes our calculated and graph value so much closer than the other two. 

Although the our third graph gave us values that were way similar to our calculated values it still wasn't perfect. This is due to our experiment not being completely error proof. Our apparatus didn't perform perfect which means that the values that we got weren't 100% accurate. The power source of our apparatus is also a source of error this is because the power source isn't always the same it fluctuates which results in us not getting data that will be the same every time the experiment is done. 

Modeling Friction Forces (Lab #7)

Ana Leyva, Andrew, Jonathan
3/22/17
The goal for this experiment was to be able to model static and kinetic friction by conducting different experiments. This will be done by using free body diagrams and applying Newton's laws.

1.) Static Friction
In order to find the static friction for this experiment we had to find out how much mass it would take to get a certain object to move. In order to set up for this experiment we first set a white piece of wood on the table that would provide us with a smooth surface. Then we put a pulley on the end of the table. We then attached a string to a block and to a hook that would allow us to place weight on top of it. We then set the block to a designated place on the table and started adding weight to the hook until we got the block to move. We then repeated this process three more times. Each time we added 100g to the block. After doing this we plotted a F_static vs. N graph that would allow us to get a coefficient of static friction. By using the free body diagram you can see that the weight that forces the block to move will be the static friction and the weight of the block will represent the normal force. We then graphed these values and got the following graph with gave us a coefficient of static friction = .3935

2. Kinetic Friction

For this part of the experiment we used a force sensor to find the average force that it takes for an object to keep on moving. We did this for all of the four different masses. Once we got the means for each run we made a F-kinetic vs Normal force graph. For this one we used the mean for each of the four graphs to represent F_kinetic and the mass of the block to represent the Normal force.

According to both of these graph the coefficient of kinetic friction is equal to 0.234

3. Static friction from a sloped surface

In order to find the static friction from a sloped surface we first lifted the board until the board started to slip. For this we got theta= 20.05 degrees. We then used the free body diagram to help us find what the coefficient of static friction would be. After solving for this we got coefficient of static friction = 0.365

4. Kinetic Friction From Sliding a Block Down An Incline

 For this experiment we set the board at a certain angle. We then put a block down on the board and let it slip down. Using a motion detector we calculated the acceleration of the block. By getting the value of the acceleration and the angle at which the block slipped we were then able to calculate the coefficient of kinetic friction. In this case the coefficient of static friction was 0.298.

5. Predicting the Acceleration of a Two-mass System
In order to predict the acceleration of a two-mass system we first had to go back to drawing a free body diagram. We then solved for A and plugged in all of our values.

 This was a very interesting experiment that allowed me to have a better understanding on how to solve for various thing. It also allowed be to see a correlation between everything.