The objective of this lab is to prove that magnetic energy is conserved in a frictionless cart system.
In the system in question, there are 3 forms of energy to consider. Gravitational potential energy of the cart, kinetic energy of the cart, and magnetic potential energy from the magnetic field between the two magnets. The first two can be determined by the usual formulas ( PE=mgh and KE=1/2mv^2 respectivly). Magnetic potential, however, had to be derived. We suspected that magnetic force followed a power rule (ei A(x)^B, where A and B are constants and x is the distance between the two magnets). In order to determine A and B, we measured the distance between the cart and the end of the track at various levels of tilts of the track. By doing so, we increased the sin(theta)mg value in the equation
mgsin(theta) = Magnetic force
We then plotted the forces against distance in logger-pro and applied a curve fit to the resulting graph, giving us the result for A and B as shown
giving us an equation of F=0.0002133(x)^-1.903
which we integrate since PE= -integral(F)dx
which gives us PE= (0.0002133/0.903)(x)^-0.903
To verify the accuracy of this value, we ran an experement where we let the cart go at a random angle and meausing kinetic energy and our theoretical magnetic potential energy on the same graph, which is below.
As we can see, at the point where kinetic energy reaches zero, magnetic potential reaches its maximum. Which is what we would expect if our equation for magnetic potential energy is accurate. However, our value for total energy is not constant, And in fact increases. Which means that there was some large error in our model.
I suspect that this error is due to the fact that gravitational potential energy was ignored in our model, which would explain why initial total energy is so low, since gravitation potential energy would be at its maximum at this point.
In the system in question, there are 3 forms of energy to consider. Gravitational potential energy of the cart, kinetic energy of the cart, and magnetic potential energy from the magnetic field between the two magnets. The first two can be determined by the usual formulas ( PE=mgh and KE=1/2mv^2 respectivly). Magnetic potential, however, had to be derived. We suspected that magnetic force followed a power rule (ei A(x)^B, where A and B are constants and x is the distance between the two magnets). In order to determine A and B, we measured the distance between the cart and the end of the track at various levels of tilts of the track. By doing so, we increased the sin(theta)mg value in the equation
mgsin(theta) = Magnetic force
We then plotted the forces against distance in logger-pro and applied a curve fit to the resulting graph, giving us the result for A and B as shown
giving us an equation of F=0.0002133(x)^-1.903
which we integrate since PE= -integral(F)dx
which gives us PE= (0.0002133/0.903)(x)^-0.903
To verify the accuracy of this value, we ran an experement where we let the cart go at a random angle and meausing kinetic energy and our theoretical magnetic potential energy on the same graph, which is below.
I suspect that this error is due to the fact that gravitational potential energy was ignored in our model, which would explain why initial total energy is so low, since gravitation potential energy would be at its maximum at this point.
No comments:
Post a Comment