3) The total work done on a body by external forces is related to the object's displacement, which is the change in position. The total work is also related to the speed of the object which is called Kinetic Energy (KE). If gravity is the only force that acts up on an object during a free fall, then we call this work Gravitation Potential Energy (GPE). So if the total kinetic energy is equal to the total work done by gravity, then the total energy is equal to the change in kinetic energy plus the change in potential energy. This total energy is also called total mechanical energy of the system. Energy is conserved if only no other external force interacts with the object.
4) This is what we'll do in this experiment.
We will convert the cart's kinetic energy to potential energy and prove that energy is conserved. However, the cart will not be in free fall or experiencing gravitational potential energy during the test. We will use another similar approach which is magnetic potential energy. A friction-less cart with a strong magnet on one end approaches a fixed magnet of the same polarity. When the cart's position approaches to the fixed magnet, its' kinetic energy will be zero at that point while the energy is converted to magnetic potential energy. Then right after, the cart bounds back and magnetic energy is converted back to kinetic. We don't know the relationship in magnetic potential energy like we do in gravitational potential energy. So our job is to find an equation for it, and prove that the system is conserved. First we will find the distance, which we'll call r, of between the same polarity of the magnet. The distance the magnets are pushing each other will be the force. The relationship for work is force and distance. We will incline the ramp the cart is on with no friction, and let gravity do its work when the magnets repel each other. The higher or more inclined the ramp is, the closer r becomes.5) Here is the data we recorded while finding r using a caliper and the angle respect to the flat surface using an android application.
Using these data points, we punched these values in a graph and the result gave us the equation for force.
. Since the graph isn't a linear equation, we will have to integrate the equation to find the work done.
. So U(r) is the equation for the work done for magnetic potential energy.6) Now we will graph the results when the cart goes through the conservation of energy system.
7) We did experience technical difficulties during the experiment; however, we got the results we wanted. The first graph, which is Position vs time, shows the cart approaching to the motion sensor and then rebounds at the one second. The kinetic and magnetic potential energy vs time graph are equal but opposite to each other. This is what we wanted in our results.
8) In the velocity vs time graph, the object's speed begins to decline and reaches zero at one second. Since kinetic energy involves with speed, it makes sense the kinetic energy declines to zero to the 1 second interval. As the object gets closer to the origin at 1 second, the r value increases in the magnetic energy function and after the rebound r begins to increase. The reason why the object rebounds is because same polarity of two magnets repel. Since the graph looks symmetrical during the one second interval rebound, energy is conserved. If energy wasn't conserved, then the right end of the graph at the one second interval would be asymmetric.
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