Purpose:
The purpose is to come up with
an expression for magnetic energy and use it to prove conservation of energy in
the glider-magnet system.
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| lab setup |
Experiment:
A glider with magnetic end has the
same magnetic polarity as the other one attached at the other end of an
air-track. The air-track is frictionless. As the glider is given a push (v0),
it moves toward the other magnet, they repulse, and the cart moves back. During
this whole time, we observe the change between KE and PE and vice versa. But
potential energy in this case is not GPE nor EPE. So we,
1. Come
up with an expression for Umagnetic from Force. We use FBD in order
to come up with sums of forces equation.
-We tilt the air track at several
various angles to ultimately get different separation distance, r, between
front of glider and the fixed magnet. We don't have to worry about height of the incline since we can just place phone on the air track and it will measure the angle with dθ= +/- 0.1°. We use a ruler, each time, to measure "r", when the glider doesn't want to slide down anymore (where repulsion fully occurs between the two magnets).
-Prediction
for the graph of F(magnetic) vs. “r”, and prediction for conservation of energy:
- where r = separation distance when the 2 magnets are at maximum repulsion.
- Attach an aluminum reflector to top of glider.
- Use a stand, and attach motion sensor at the top where it faces directly the aluminum reflector from the glider. Record the "fixed distance"as shown in setup below. This distance is from the front of the sensor to the front of the fixed magnet.
- With air vacuum turned off, place the cart on far end of the track. Set the motion sensor to record 30 measurements/ second.
- Turn on the air vacuum, click collect data on LoggerPro, and give the glider a gentle push.
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| The two magnets shown are covered in yellow tape |
- By the end of this part, LoggerPro will be able to give data of velocity, time. And we will utilize these below.
Data and Analysis:
1. Determining U(r):
- F(r)= mgsinθ; Therefore we use several of our angle measurement, plug it in to find F-magnetic for those several measurements.
-Two of the angles shown below give roughly the same r-distance. So we strike both of them out and use their forces average as one data instead.
- From power fit below, we get: F(r) = 0.001074(r)^(-1.44)
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| "B" in this case is "n" |
- error for "A" = (0.0003870 / 0.001074)100% ~36%
- error for "n" = (0.07286/1.440)100% ~5%
- Integrating this, we get
2. Verifying conservation of energy:
-Data: fixed distance = 0.426m; m(glider)= 0.34kg
-Under new calculated column, we add expressions for KE, U (magnetic), Separation distance, and E-total to LoggerPro in forms of:
Separation distance = r = "Position"-0.426
U(r)= 0.00244091("Separation")^(-0.44)
KE= (1/2)(0.34)("velocity")^2
Total Energy= KE + U(r)
- Then we get:
-Graph to see the relationships of (KE, Umagnetic, Esum) vs. time:
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| Time of interest is between the interval 2.83 to 4.86 second |
- The graph of U (magnetic) shows the peak significantly higher that the maximum of KE, which leads to the interpretation that our error of 36% (calculated above) plays parts of this.
-Ideally, total energy should align with the maximum of both KE and U-mag. So if we were to say that true value of max KE in this case is = 0.015J, then that's what the total energy graph should look like at any point in the interval of our time of interest (2.83 to 4.86 secs)
Conclusion:
Source of uncertainty for U-magnetic: dθ, dx in mass and distance measurements
Source of uncertainty for KE: flat surface is still at some angle (0.1-0.2 degree), uncertainty in mass and distance measurement.
Nonetheless, we verify that there is conservation of energy in this glider-magnet system.
