Purpose: Verify that conservation of energy applies to a magnetic system.
Procedure: Unlike with Gravitational and Elastic potential energy, we were never given an equation for Magnetic potential energy. So we set up a lab where energy from a frictionless moving cart transfers its kinetic energy completely into a magnetic field as magnetic potential energy and rebounds back, where theoretically all the energy should be conserved. Using this experiment, we want to first find an equation for magnetic potential energy in order to verify that conservation of energy in the system. The lab apparatus consisted of a frictionless cart with a strong magnet on one end placed onto a track with a fixed magnet of the same polarity placed on one end.
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Lab apparatus, air holes on the track to make cart glide over track.
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Any system with a non-constant PE, the PE (U) is caused by an interaction force F. The relationship between the two is U(r) = the negative integral of F(r)dr from -infinite to r, where r is the separation distance. So we have to solve for F(r). (assume F=0 when r=infinite).
Raising one end of the track to a height h makes the cart reach an equilibrium position with the magnetic field, where the magnetic repulsion force between the two magnets equals the gravitational component on the cart parallel to the track. Then we tilted the track at various angles so that we could plot a relationship between the magnetic force F and the separation distance r. Next we plot the graph of F vs. r and assumed that the relationship takes the form of a power law: F = Ar^n. We are able to to solve for F by drawing a free body diagram of the cart at its equilibrium and inputing the corresponding theta and r with a meter stick.
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| data of theta and corresponding r and F |
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| graph of F vs. r |
Using a curve fit for F(r) = Ar^n, we got A = .0001092 and n = -2.003. By integrating the function, we get a function for magnetic potential energy.
%2Bto%2BU(r).JPG) |
| calculation for derivation of magnetic potential energy |
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| Data set for all energies in system |
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| graph of KE, PE, and TE vs. time |
Results: Total energy should have been a constant line, our results showed that energy was fairly conserved within the system but not exact.
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