17-April-2017: Lab 13: Magnetic Potential Energy Lab

Lab 13: Magnetic Potential Energy Lab

Author: Tian Cih Jiao

Lab Partner: Weisheng Zhang, Kitarou

Date: April 17, 2017

Purpose of the lab: The purpose of this lab is to verify that conservation of energy applies to the system we set

up (cart-magnets system).

Theory/Introduction:

For this lab, we use the conservation of energy to find out the magnetic potential energy.

First, we used a track with different slope and get several data for the graph.

Apparatus/Experimental procedure:

Apparatus: cart, two strong magnets of the same polarity, air track glider, some books to change the slope, aluminum reflector installed on the cart for detection of motion, motion detector, Logger Pro.

Procedure: 

First, we need to find out the function for F(r). We change the slope to get a equilibrium position, where the magnetic repulsion force = the gravitational force component parallel to the track. This component is mgsin(x), where x is the angle of the raised track.We changed the slope so that we get enough data, then we can powerfit to find out the graph.

After we find the formula of F(r), we can now prove the validity of conservation of energy theorem is this setup. 

We turned air track power off, put the cart on the air track, close to the magnet. Run the motion detector. Determine the relationship between the distance the motion detector reads and the separation distance between the magnets.

After that, start the cart at the far end of the track. Start the detector and give the cart a gentle push. Record the data before, during and after the collision. Plot a graph showing PE, KE, and total energy of the system as a function of time.

Measured data:

The mass of the cart is measured to be 340 grams (0.34 kilograms).

To figure out the formula of F(r), five sets of data are collected.

x = 1.6 degrees r = 30.9 mm mgsin(x) = 0.34 * 9.8 * sin(1.6) = 0.093N

x = 3.8 degrees r = 22.3 mm mgsin(x) = 0.34 * 9.8 * sin(3.8) = 0.221N

x = 5.8 degrees r = 18.1 mm mgsin(x) = 0.34 * 9.8 * sin(5.8) = 0.337N

x = 7.5 degrees r = 16.1 mm mgsin(x) = 0.34 * 9.8 * sin(7.5) = 0.432N

x = 9.2 degrees r = 14.5 mm mgsin(x) = 0.34 * 9.8 * sin(9.2) = 0.533N

Kinetic Energy = 1/2 * m * velocity^2
The formula of Umag (magnetic potential energy) is derived from F(r), one of us calculated it on paper by hand.

Separated Distance =  0.342m = measured distance (which is 14 mm) + adjustment value

Graph for F(r) :

According to graph 1, F(r) = 159.3 * r^(-2.13). The integral is calculated to be -4.076. Therefore, U(r) = -(-4.076) = 4.076 J.

Analysis:

The sum of Umag, magnetic potential energy (in light green) and Kinetic Energy (KE) equals total energy (in blue).

According to graph 2, total energy (in blue) maintains a steady level in spite of the little zigzag (close to being a constant), which means that conservation of energy theorem applies to this setup reasonably enough.

Conclusion: According to our data (figure and graph), conservation of energy theorem applies to our setup as well (cart and magnets). 

Possible sources of error:

The phone we used to measure the angle of the incline is not calibrated (which may result in inaccurateness).

The assumption of zero friction on the air track (which leads to larger magnetic PE)