Total Energy Lab
Objective:
Show that energy in a system is always conserved when one adds all forms of energy during each point in time and the sum stays consistent.
Set- up:
In this set up we used a mass of 600g attached to an end of a hanging spring (as seen in fig. 1a- 1b). Underneath the hanging spring we put a motion detector with its settings set to zero when the spring with the mass is at a relaxed position and its readings reversed so toward the sensor is positive.
Data Collection:
We set the weight at a height where the spring's length was the same as it was at a relaxed state without a weight attached to it. From there we recorded the data for position, velocity and acceleration for a trial of seconds. From there we used that information to numerically calculate different components of what we thought was what made up the system's energy. As a clsass we observed that there were 5 forms of energy in the system that is not negligible (as seen in fig 2.):
Kinetic Energy of the Mass (m): .5*m*v(mass)^2
Gravity Potential of the Mass (m): g*m*(position)
where mass (m)= .6 Kg
Elastic Potential of Spring: .5*k*(position- relaxed)^2
we calculated spring constant k to be :
F=k*(stretch) where stretch= x = 25 cm
Ms*g= k*x where Ms = .1 Kg
k= m*g = 23.52 spring constant
x
Kinetic Energy of Spring (Ms)= (Ms)*V^2
6
Gravity Potential of Spring (Ms) = Ms*g*position*(.5)
To prove that energy of this system is conserved, we add up all the forms of energy and we then see if the sum is consistent. Numerically it is apparently close and evidence of this can also be seen in fig 3. where each form of energy is graphed and the orange graph on the top is the sum.
Conclusion:
Energy is in fact conserved in this system. My level of uncertainty is around 3% seeing as not the entire spring was uniform, but behaved consistent enough during the trial to complete the objective.
 |
| Figure 1a. Our mass on the hanging spring |
We set the weight at a height where the spring's length was the same as it was at a relaxed state without a weight attached to it. From there we recorded the data for position, velocity and acceleration for a trial of seconds. From there we used that information to numerically calculate different components of what we thought was what made up the system's energy. As a clsass we observed that there were 5 forms of energy in the system that is not negligible (as seen in fig 2.):
Kinetic Energy of the Mass (m): .5*m*v(mass)^2
Gravity Potential of the Mass (m): g*m*(position)
where mass (m)= .6 Kg
Elastic Potential of Spring: .5*k*(position- relaxed)^2
we calculated spring constant k to be :
F=k*(stretch) where stretch= x = 25 cm
 |
| Figure 1b. Our motion sensor with appropriate settings placed directly under the hanging mass set up. |
k= m*g = 23.52 spring constant
x
Kinetic Energy of Spring (Ms)= (Ms)*V^2
6
Gravity Potential of Spring (Ms) = Ms*g*position*(.5)
To prove that energy of this system is conserved, we add up all the forms of energy and we then see if the sum is consistent. Numerically it is apparently close and evidence of this can also be seen in fig 3. where each form of energy is graphed and the orange graph on the top is the sum.
Conclusion:
Energy is in fact conserved in this system. My level of uncertainty is around 3% seeing as not the entire spring was uniform, but behaved consistent enough during the trial to complete the objective.
 |
| Figure 2. Each of our calculated values for different forms of energy found in the set up with an approximated sum of all the energy. |
 |
| Figure 3. Graphed values our our calculated energies with the sum of the energy values for each point in time graphed at the top in orange with consistency. |
No comments:
Post a Comment