### Magnetic Forces and Potential Energy (MBL) Pre-lab Assignment

We're doing the MBL (Microcomputer-Based Lab) version of the Magnetic Forces and Potential Energy experiment. The interaction between the magnets in the experiment is similar to what would happen with a spring. We'll examine a spring experiment to become familiar with the concepts.

In general, in one dimension, the connection between a conservative force and the potential energy associated with it is:
 [Equation 1] F = -dU/dx or [Equation 2] U = - òF dx
Starting with F = -kx for an ideal spring, use Equation 2 to obtain the expression for the spring's potential energy. Take the lower limit on the integral to be where the potential energy is zero.

In the first part of the experiment you will obtain the equation giving force as a function of distance between repelling magnets, and then use Equation 2 to obtain the corresponding potential energy. One way to verify the potential energy relationship is to roll a cart, with magnets attached, down a small incline toward a second set of magnets and keep track of all the different kinds of energy.

The simulation shows a similar experiment using a spring. Three curves are shown in the graph below the simulation. Identify each. The graphs are plotted versus position, not time. x = 0 is at the bottom of the ramp.

 The red curve is the: gravitational potential energy spring potential energy kinetic energy The blue curve is the: gravitational potential energy spring potential energy kinetic energy The green curve is the: gravitational potential energy spring potential energy kinetic energy

Assume there is no friction acting. If you added the three curves, what would you get?
 a horizontal line a line that decreases as the object travels down the slope a line that increases as the object travels down the slope

If the object's position is X, measured from the bottom of the ramp along the incline, express the gravitational potential energy in terms of X and the angle of the incline:
Ug = mg_______