15-Oct-2016: Conservation of Energy-- Mass-Spring-System

Apparatus: Two clamps, a metal rod, a motion detector, a spring, and some masses.

Purpose: Find out the relationship about the energy in a vertically-oscillating mass-spring system.

Model: KEhanging=(mhanging*v^2)/2, KEspring=(mspring*v^2)/3, GPEhanging=mhanginggh, GPEspring=mspringgh/2, Elastic PE=x^2k/2, x=H-h. KEtotal=KEhanging+KEspring, and GPEtotal=GPEhanging+GPEspring.
    KEhanging is the kinetic erengy of hanging mass, KEspring is the kinetic energy of spring, GPEhanging is the gravitational potential energy of hanging mass, GPEspring is the gravitational potential energy of spring, Elastic PE is elastic potential energy of the spring, mspring is the mass of the spring, mhanging is the mass of the hanging mass, v is the velocity of the hanging mass, h is the heigh of the mass, x is the length of the spring, and H is the heigh of the top of the spring.

Process: First, we determine the mass of spring and the mass of the masses. We use the clamps and the meter rod to hang a spring vertically. In the bottem of the spring, we hang some masses. We place a motion detector directly below the mass and the spring. Then, we measure the heigh of the top of the spring H.
    The apparatus set up as:

    Then, we pull the masses down, stretch the spring, and let it go. click the strat buttom to begin collecting data such velocity v. the heigh of the masses h.
    We add the calculate column of KEhanging, KEspring, GPEhanging, GPEspring, Elastic PE, KEtotal, GPEtotal by using the equation KEhanging=(mhanging*v^2)/2, KEspring=(mspring*v^2)/3, GPEhanging=mhanginggh, GPEspring=mspringgh/2, Elastic PE=x^2k/2, x=H-h. KEtotal=KEhanging+KEspring, and GPEtotal=GPEhanging+GPEspring.
    We get the graph and data:

 



    We plot KEtoyal, GPEtotal, Elastic PEtotal and Esum vs. position on one graph. We get:

    The sum of the energy is the sum of the kinetic erengy of hanging mass, the kinetic energy of spring, the gravitational potential energy of hanging mass, the gravitational potential energy of spring, and elastic potential energy of the spring. The sum of the energy should be a constant number. This constant number should due to the length that the spring be stretched. It is the initial energy that the entire system has.
    However, in our experiment, the sum of the energy is not constant. This error may cause by the spring constant of the spring that we measure in last experiment or the heigh of the top of the spring that we measure.