Conservation of energy within a system

Introduction:
According to the Law of Conservation of energy, the sum of all the energy within a system should always be constant. In this experiment, we examined this statement by observing the oscillating motion of a spring with hanging mass. We would determine the relationship of the kinetic energy, gravitational potential energy and the elastic potential energy within the system.

Apparatus:

We hang the spring on the force sensor, and with motion sensor under the spring. The force sensor would measure the magnitude of the elastic force, and the motion sensor would measure the position and velocity of the hanging mass on the spring.














Data and data analysis:
To find out the elastic potential energy, gravitational potential energy and kinetic energy, we will need to first measure the mass of the spring, the hanging mass, and the length of the un-stretched spring.
The mass of the spring=0.150g
The mass of the hanging mass=0.600kg
The length between the bottom of the mass when the spring was un-stretched and the floor=0.797m
The length between the bottom of the mass when the spring was stretched and the floor=0.560m
The total height of the apparatus= 1.48m
The following is the graph of the velocity, and position of the hanging mass and the elastic force of the oscillating motion:

With the measurements collected by the motion sensor and the force sensor, we were able to derive columns for kinetic energy, elastic potential energy, and gravitational potential energy.
KEm(J)=1/2*(hanging mass in kg)V^2
KEspr(J)=1/2*(mass of spring in kg/3)V^2
GPEm=MgHbottom
GPEspr=constant+(mass of spring in kg/2)*gHbottom
EPEspr=1/2k(stretched distance)^2
The following is the complete table with all the calculated columns:

The most right column of this table is the total energy within this oscillating spring system, which has magnitude between 4.3 to 4.4 J. This indicates that the total energy in this system is almost a constant value.
The following is the Energy(J) vs. Time(s) graphs:

We can see that total energy curve is almost a horizontal line.

Conclusion:
This experiment gives us a pretty good look at the relationship between different forms of energies within a system. We found the oscillation of the spring with hanging mass obeying the law of conservation of energy. The graph of energies versus time above shows that the potential energy decreases when the elastic energy and the kinetic energy increase, and vise versa. Through this experiment, we proved the statement of the law of conservation of energy to be true.