15-Oct-2016: Magnetic Potential Energy Lab

Apparatus: An air-track glider, an air track, a strong magnet, a motion detector, a telephone with an angle detector.

Purpose: Verify that conservation of energy applies to this system.

Model: Fmag=sinθmg, Fmag=Ax^B, and W=-∫Fmagdx=(A/(B+1))x^(B+1)
Fmag is the force existing on the magnet, θ is the angle of the track, m is the mass of the air-track glider, A and B is the constant of the magnet, x is the separation between the glider and the magnet, and W is the potential energy on the magnet.

Process: The air-track glider with a strong magnet on one end approaches a fixed magnet of the same polarity on the other end.  

    We raise one end of the air track which has the glider and record the angle θ. The glider slide will begin to slide down and stop at a position because of the force giving by magnet. Then, we determine the separation between the glider and the magnet x. 
    After six times changing the angle θ, we get:

                                         θ     3.7°        7.6°        10.3°        13.3°        15.1°        17.4°
                                         x     18.2        13.6       11.3          10.4          9.1           8..7
    
    By using the model Fmag=sinθmg, we get:
                                                 
                                         F    0.214      0.442     0.594        0.764        0.865       0.993

     We plot x as x-axis and F as y-axis into the LabPro, and we use the Curve Fit--Ax^B to get:

    According to the graph, we get:
                                                      Fmag=0.00003766x^-2.168

    Then, we place the the air track horizontally, and the motion detector is placed on the magnet side. We record the distant that the motion detector read L and the separation on that position l. We can use 
x=xread-(L-l) to get the actul separation.

    We creat a new columm about W by using W=-∫Fmagdx=(A/(B+1))x^(B+1)=0.000032243x^-1.168,
KE by using KE=(mv^2)/2, and Esum by using Esum=KE+W.
    We push the glider toword the motion detector, and we start use the computer to collect the data. Then we get:

    When we push the glider, we give the glider some kinetic energy. Without friction, the kinetic energy should be constant until getting close enough to the magnet. When the glider get close to the magnet, the kinetic energy decrease, and the potential energy increase. The kinetic energy transfer to potential energy. Then, after the kinetic energy reach the zero, the kinetic energy begin increasing, and the potential energy begin decreasing. The potential energy transfer to kinetic energy. 
    The sum of the eneegy should be constant and equal to the energy that we get the glider by pushing.