Lab #12: Magnetic Potential Energy

Purpose: To verify that conservarion of energy still applies for a system involving magnetic potential energy.

Set Up: Place an Air track on table and make sure to level it using something like notecards. Make sure there are magnets on the end supports of the air track and also on the glider. The vacuum will provide a force through the holes in the track and keep the glider afloat so we can oppose any drag due to the glider touching the track.



Procedure:
1) Because we have no set equation for magnetic potential energy we must build our own for it. We will use the relationship of potential energy being equal to the negative integral of force over distance.

2) If we raise one end of the air track the glider will slide and find an equilibrium point at which the magnetic repulsion is equal to the parallel gravitational component.



3) We stacked different heights of books underneath one end of the track and measured the distance between the glider and the opposing magnet and also recorded each new angle due to the raising of one end.



4) To plot this data in logger pro we first had to convert the angle measures into radians so that we could calculate each force using trig functions in logger pro.



5) Once we graphed each force vs the separation distance we used a power fit(Ar^B) to calculate a coefficient and exponent to be able to later integrate.



6) Now that logger pro has given us our A and B we can find the negative inegral of the force over distance to calculate an equation for magnetic potential energy.

Lab #11: Conservation of Energy - Mass-Spring System

Purpose: To explore the conservation and transfer of energy of a vertically-oscillating mass-spring system.

Procedure:

1) We need to identify all the different forms energy will take in this experiment. We know that th hanging mass will have both a kinetic energy and a potential energy. However, the mass itself is not the only thing interacting in this eperiment. The spring itself will also have its own KE and GPE, but because it is a spring it has a third energy form of elastic potential energy. Below are the equations we used for each:



2) We set up a column style apparatus with a force sensor attached to the top of our clamped bars, a spring with a hanging mass attached, and at the bottom we have a motion sensor reading upward. We then calibrated and oriented all the equipment as needed.



3) The only variable we will have to do extra work to find is the spring constant. To do this we slowly stretch the spring downward and plot the force vs distance stretched in logger pro. Once this is complete we simple have logger pro calculate a linear fit to the graph whereas our slope is equal to our spring constant.

4) Now we used our equations to set up calculated columns within logger pro and simply release the system from a sthertched position and have logger pro collect data for each seperate energy.



5) Observing each different energy oscilate we can see how the energy is trasfered from one type to another as they fluxuate in opposite paterns.

6) Our column and graph for the total energy stored in the system was reassuring that the energy is conserved.

Lab #10: Work-Kinetic Energy Theorem

Experiment 1: Work Done by a Nonconstant Spring Force

Purpose: To calculate the spring constant by using Hooke's Law



Procedure:
1) We first calibrated a force sensor by zeroing it with no mass hanging and then added 500grams setting the sensor to read 4.9N.

2) We set up a track on our table, a cart attached by a spring to the force sensor, which is held horizontally on one end of the track by a clamp and bar. On the other end we have a motion sensor to read the distance the cart will be pulled.

3) Using logger pro we collect data from both the force and motion sensors and plot them to create a graph of force vs distance.



4) Using a Linear fit we find the slope(spring constant) to be 5.724 N/m.

5) By measuring the area under the curve(integrating) we have now calculated the work done by the spring, .05 N*m

Experiment 2: Kinetic Energy and the Work-Kinetic Energy Principle

Procedure:
1) First we must create a new calculated column for kinetic energy of the cart, .5mv^2

2)Using the same set up as before we will now Release the cart from a stretched position and allow logger pro to graph both KE and Force against the distance.

Lab #9: Centripetal Force with a Motor

Purpose: To come up with a relationship between the angle that the hanging mass makes with the vertical and the angular speed of the apparatus.

The apparatus:
The motor mounted to the top of a tripod spins a pole with a two-meter stick with a hanging mass at one end. This apparatus is similar to a carnival "swing-merry-go-round".







Procedure:
1. Before turning the motor on we measure everything that will remain constant troughout the experiment: The height of the apparatus(H=2m), the radius where the hanging mass is attatched(R=.98m) and the length of the string for the hanging mass(L=1.645m).

2. We then drew force diagrams and symbolically solved for both the angle and time. (note* the height we will measure is from the ground to the rotating height of the mass denoted by the lowercase "h").

3. After deriving the formulas we used we came together as a class to observe the apparatus spin at different speeds. For each speed we timed ten rotations and divided that by ten to calculate the time for ohe rotaion. Each speed also provided us with a new height "h" that we measured by slowly raising a piece of paper on a ring-stand until the mass barely nipped it, pulled it aside and measured the height. We collected data for each of the six runs we had at increasingly greater speeds.

4. Once the experimental data was collected we went back to our equations and plugged in "h" and calculated our theoretical values of both the angle and time.

5. To compare our actual to our theoretical results we plotted them agains one another and had logger pro insert a line of best fit to show us how accurate our process was.

Lab #8: Centripetal Acceleration vs. Angular Frequency

Objective: To determine the relationship between centripetal acceleration and angular speed.

Apparatus: For this demonstration there was a wheel and an electric motor set up to spin a rotating platform. To measure the centripetal acceleration there was a accelerometer attatched to the top ot the platform facing inward toward the center and a photogate to measure the period of each rotation to find angular velocity.

Procedure:
1. We set the power supply to 4.8, 6.2, 7.8, 8.8, 10.9, and 12.6 volts and collected data and plotted acceleration vs. time for each setting.

2. Our data unfortunately shows acceleration to not be constant but instead bounce up and down, to remedy this we simply told logger pro to calculate the average acceleration for each setting.

3. Because our goal is to compare centripetal acceleration and angular frequency we used our equations of v=w/r and a=rw^2 to calculate two new colums in logger pro.

4. Finally we plotted Centripetal Acceleration vs W^2

5. To complete or comparison we asked logger pro to give us a linear fit, which had a correlation of .9999! The most important part was to notice that when we compare the acceleration to W^2, our slope is .1371 which is very close to the actual radius of the wheel (.138m).

Lab #7: Trajectories

Objective: To use our knowledge or projectile motion to calculate the "launch" velocity of a ball and use that to predict where the ball would impact a slanted board.

Procedure:
1. We first used our table, a ring stand, two "v-channel" rails, supports and tape to put together a slide for the metal ball to roll down and exit with only a horizontal velocity for the start of it's projectile path.

2. Because the launch point is above the floor, we had to make a plumb-bob with string and a mass to hang from the tip of the rail and find the location of our x-initial position. Using this we can better measure how far the ball travels for its x-componet. We also measured the height from the floor of the launch point to later use for our calculations.

3. We then had two test runs to see where the ball would hit the floor and taped a white paper to that area of the floor with a piece of carbon paper on top so that the impact would leave a mark so that we could measure how far it traveled horizontally.

4. Once everything was set up we ran 5 experimental trials and collected data on how far the ball had traveled along the horizontal.

5. Using our data, we broke down the ball's projectile motion into its x and y components. We made a chart of all the bits we knew for each component and used out kinematic equations to set up equations. Things that we had to keep in mind when doing this expariment was making sure the exit rail was level so that we would have no initial velocity for the y-component, understanding that there was no acceleration for the x-component and most importantly that the time used in both the x and y kinematic equations must be the same! We then used our y-component to solve for our time and plugged that into out x-kinematic equation to find our initial launch velocity for our ball.

6. Now we set up a slanted board to be flush with the exit rail and measure the angle between the board and the ground.

7. This time before our experimental runs we separate our information for each component and set up equations for each to predict where the ball should impact on the slanted board. These equations are more difficult to set up and solve than the previous ones because now we must include our angle and also understand the new distance traveled is along a diagonal and not only along one axis.

8. After predicting where the ball should impact we once again tape down a white paper with carbon paper onto the area where it should land and proceed with our five experimental runs.

9. Our calculations were right on the mark leavin us very close to our experimental values! However, because there is uncertainty in everything we do (for this experiment we have uncertainty in our measurements of both distance and the angle of the board) we must preform our propegated uncertainty calculations to make sure we are covered when reporting our results.

Our propegated uncertainty ended up giving us a range of 0.488 plus or minus .0315 meters for our distance which is more than enough for us to feel confident in our results when compared to our experimental values of the distance.