### Energy Conservation (MBL) Pre-lab Assignment

Your name: _____________________

Please print this page, fill it in, and show it to your TF at the start of your lab session.

The interaction between the magnets in the Energy Conservation experiment is similar to what would happen with a spring. We'll examine a spring experiment to become familiar with the concepts.

The work done by a conservative force is equal to the negative of the change in the potential energy. In one dimension:

ΔU = - ∫ F dx

In other words, the change in potential energy is equal to the negative of the area under the curve of the force vs. distance graph.
For a spring, for instance, F = -kx and U = kx^{2}/2 are consistent with the equation above. The relationship is illustrated in the simulation below.

In the lab you'll spend some time rolling a cart, with magnets attached, down a small incline toward a second set of magnets. Throughout the process you'll 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 friction was acting on the cart, what would you get if you added the three curves?

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:

U_{g} = mg_______