The objective of this lab was to show that in an ideal system that conserves energy, the total energy at any given point (ei, the potential and kinetic energy) is a constant value.
The system in question was a mass attached to a spring, as shown in the diagram below. The weight of the mass was 600 grams, the spring was assumed to be massless and ideal (ei obeying hookes law). Below the mass spring system, we set up a motion sensor in order to measure position, from which we could calculate velcity and acceleration of the system.
We were not given a spring constant for the our spring, so we calculated it using newtons laws of motion.
Ma= net force
M(0)= Mg - k(x)
Mg=k(x)
k=Mg/x
In order to use this equation, we first measure the length of the spring without any weight on it, then the length of the spring once in equilibrium with the 600 gram weight hanging on it. The difference between our two distances (x) was observed to be 25 cm, or 0.25 meters. Plugging in our values, we obtained a spring constant value of 23.52.
0.6(9.8)/.25=23.52
In our model, we ignored the gravitational potential energy of the spring, leaving us with only elastic potential energy, gravitation potential energy of the mass, and kinetic energy of the mass. Which were calculated as follows:
GPE=mgh
EPE=1/2k(x)^2
KE=1/2m(v)^2
In order to collect data, we zeroed the motion sensor at the point where the mass and spring hung when at equilibrium. We then pulled the mass spring system down (stretching the spring, giving it an inital elastic potential energy while decreasing gravitational potential energy of the mass) and letting it go while having the motion sensor capture the movement of the system. We then used the position data to extrapolate velocity and acceleration, and in turn the various energies of the system at any given point. We then added all of these values (the energies) up in another row. The chart below shows our data collected.
Clearly, our value for total energy does fluctuate slightly around roughly 7.3 joules. This fluctuation is possibly due to several factors. Our model does not allow for the gravitational potential or kinetic energy of the spring, nor does it factor in the work done by friction from the air. It is also possible that the spring was not entierly consistent, and therefore does not perfectly adhere to Hookes law. However, with an uncertainty of 3 percent, our measurements are accurate enough to give strong evidence towards the confirmation of the concept of conservation of energy.
The system in question was a mass attached to a spring, as shown in the diagram below. The weight of the mass was 600 grams, the spring was assumed to be massless and ideal (ei obeying hookes law). Below the mass spring system, we set up a motion sensor in order to measure position, from which we could calculate velcity and acceleration of the system.
We were not given a spring constant for the our spring, so we calculated it using newtons laws of motion.
Ma= net force
M(0)= Mg - k(x)
Mg=k(x)
k=Mg/x
In order to use this equation, we first measure the length of the spring without any weight on it, then the length of the spring once in equilibrium with the 600 gram weight hanging on it. The difference between our two distances (x) was observed to be 25 cm, or 0.25 meters. Plugging in our values, we obtained a spring constant value of 23.52.
0.6(9.8)/.25=23.52
In our model, we ignored the gravitational potential energy of the spring, leaving us with only elastic potential energy, gravitation potential energy of the mass, and kinetic energy of the mass. Which were calculated as follows:
GPE=mgh
EPE=1/2k(x)^2
KE=1/2m(v)^2
In order to collect data, we zeroed the motion sensor at the point where the mass and spring hung when at equilibrium. We then pulled the mass spring system down (stretching the spring, giving it an inital elastic potential energy while decreasing gravitational potential energy of the mass) and letting it go while having the motion sensor capture the movement of the system. We then used the position data to extrapolate velocity and acceleration, and in turn the various energies of the system at any given point. We then added all of these values (the energies) up in another row. The chart below shows our data collected.
Clearly, our value for total energy does fluctuate slightly around roughly 7.3 joules. This fluctuation is possibly due to several factors. Our model does not allow for the gravitational potential or kinetic energy of the spring, nor does it factor in the work done by friction from the air. It is also possible that the spring was not entierly consistent, and therefore does not perfectly adhere to Hookes law. However, with an uncertainty of 3 percent, our measurements are accurate enough to give strong evidence towards the confirmation of the concept of conservation of energy.
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