Lab 13: Magnetic Potential Energy Lab

Magnetic Potential Energy Lab 

I-Shou Lin, Kirk Paderes, Jorge Avalos 

4/ 17/17

The experiment is to verify that the principle of conservation of energy applies to all types of systems, and to find an equation that describes the magnetic potential energy.

Energy is present in the universe at a fixed constant. According to the principle of conservation of energy, energy can't be destroyed or created, only transferred from one form to another. In this lab, the two energies of interest are the kinetic energy of the cart and the magnetic potential energy in the magnetic field. When the cart slides one a friction-less surface with a magnet attached to one end and another magnet with the same polarity at the end of the track, the cart's kinetic energy is transformed into magnetic potential energy as the cart is momentarily at rest. Then, the magnetic potential energy is transformed back into kinetic energy as the cart speeds up. However, the magnetic potential energy isn't constant, but varies with the separation distance. Thus, in order to find the magnetic force, another force must be set equal to the magnetic force. This way, we could derive an equation for the magnetic force and the potential energy based on the other force. 

We first begin with the setup of a friction-less glider on an air track with a magnet attached to one end and another magnet of the same polarity at the end of the track. Then, we set the motion detector at the end of the air track and raise the track at various angles to determine the separation distance between the cart and track when the cart is in equilibrium. At this point, the magnetic force is equal to the gravitational force in the x-component parallel to the track. We do this for several angles and get several distances until we have enough data to plot force versus separation distance. The equation of the curve of that graph is the magnetic force. In order to verify conservation of energy, we attach an aluminum reflector to the cart, and then mass the cart. Since the motion detector isn't at the same position as the magnet at the end of the air track, a determination of the separation distance between the magnets and the distance the motion detector reads is necessary. We then push the cart from the far end of the track and record the data. Afterwards, we make a single graph of the kinetic and magnetic potential energy of the system as a function of time.



Measured Data

Separation distance (m)	Angle of Elevation	Mass of Cart ( kg)
0.0352	0.7	0.347
0.029	2.5	0347
0.0236	3.8	0.347
0.02	5.50	0.347
0.0182	6.8	0.347
0.0165	7.9	0.347
0.0152	9.0	0.347

Calculated Results 

F= A*r^n= 0.0001761*r^(-1.920 +/-0.08972)

F= mg*sine θ= 0.347 kg * 9.81 m/s^2 * sine ( 0.7)= 0.04159 newtons

Separation distance= distance motion detector reads - extra distance 

kinetic energy= 0.5 * mass*velocity ^2

kinetic energy= 0.5* 0.347 kg * (0.152 m/s )^2= 0.004 joules 

U(r)= ( A^(r+1)) /r+1

U(r)= ((0.001761 +/-6.409*10^-5)^ (0.02+1)/ 0.02+1= 0.00152 joules 

The first graph shows the inverse relationship between the separation distance and the repulsion magnetic force exerted by the two magnets on each other. Since there's no standard force equation for the force of magnetism, we have to derive the function. By plotting a graph of force vs separation distance and then finding a curve fit equation, a function for the unknown magnetic force arises. The second pair of graphs show the relationship between kinetic, potential, and total energy versus time and position. What verifies the principle of conservation of energy is the graph of kinetic, potential, and total energy as a function of time. That graph is in very close agreement with the theoretical graph that we did before the experiment.Just by visual inspection, we see that as the kinetic energy decreases, potential energy increases by the same amount, and so the total energy in the system is constant.

This magnetic conservation of energy lab turned out to be a very insightful and informative lab. It validated the universal principle of conservation of energy The graph of the various energies versus time depict almost perfectly that total mechanical energy in a system is conserved if external forces such as friction and air resistance can be ignored. What's most uncertain in the derivation of the magnetic potential energy function and also the force function is the uncertainty in the values of the constants A & n. These propagated uncertainty could have a significant effect on the value of the magnetic potential energy function because it's the integral of the force function. Overall, the results from the graphs show a successful demonstration of conservation of energy.