Lab#12: Conservation of Energy

Conservation of Energy

Samuel
Ellis
Mia
10-05-2016

Purpose:

  Find the force of the oscillating spring and determine whether the energy is conserved or not. In addition, find the relationship between oscillating force and the distances it traveled.

Theory:   

  According to Law of Conservation, we know that all energy must conserve; the initial energy will have to equal to final energy. If the final energy does not equivalent to initial energy, there must be other factor or force acting on it. Since Law of Conservation had been proven correctly,  then we should be able to calculate its final energy from initial energy.

Procedure:

1. Mount a table clamp with a vertical rod to the table. Mount a horizontal rod to the vertical rod. Put a Force sensor on the horizontal rod with the loop of the sensor pointing downward.

2. Calibrate the force sensor using zero mass and 1 kg weight.

3. Put a spring on the force sensor. Zero the force sensor.

4. Put a motion sensor on the floor facing up. Under the sensor setup select Reverse Direction.

5. Place a 50 grams the mass hanger so that it is vertical and spring is just un-stretched.

6. Start collecting data and slowly pull down on the 50 grams mass

7. Now do the same thing for real, collecting force vs. time data and stretch vs time data. Plot force vs stretch to get the equation that defines the force behavior of your spring.

8. Disconnect the force sensor from LabPro. Open up a new LoggerPro file with just the motion sensor attached.

9. Again, place a 50 grams the mass hanger, hang it on the spring, and then support it somewhat so that it is vertical and spring is just unstretch. collect data using the motion sensor and record the position of the bottom of the mass hanger.

10. Hang an additional 200 grams on your mass hanger. Record the position of the 200  grams using the motion detector.

11. Make a new calculated column. Call it 'unstretch'. Set up the formula so that it gives you the stretch of the spring from the unstretch position of the spring based on the position of the bottom of the hanging mass, as record by the motion sensor. 

Data(Graph & Explanation):

(Above graph is Energy vs position & Energy vs Time. The first graph have this back and fort kind of line, the reason why is due to osculating of the spring. Since spring kept on bouncing up and down, the position will have this back and fort line. For the second graph, the energy is conserved. It will just keep on repeating the same line.)

(Above is Position vs Time & Velocity vs Time graph. For the first one, as time increase; the spring goes up and down. For the second graph, velocity is constant with the same back and fort style.) 

(Above, we input some equation for Kinetic, Gravitational potential and elastic energy.)

(Above is kinetic vs position, kinetic vs velocity and GPE vs position. For the first one, it just back and fort line, which is accurate since the spring just keep on moving up and down. Third graph, since the height of the spring is the same, energy is increase when moving higher.) 

Conclusion:

We used gravitational potential energy to find kinetic energy and elastic potential energy. As result we can generate the graph of each individual energy. As you can see in elastic and total energy graph, there are slightly inconsistent line(getting lower and lower). The reason may due to the different gravity(instead of 9.8) or rusticity of the spring and maybe is due to not that accurate of the measuring tools. Those might be the reason why graphs are not consistent. However, its close enough for us to know what it will look like and how it relate to real life situation. Overall, it was a pretty good experimental result for law of Conservation.