Elastic Energy
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Transcript of Elastic Energy
ELASTIC ENERGY
By: Thayne Bates, Allie Stricklan, and Brandon England
Summary
The purpose of this experiment was to find the spring constant of two different springs and determine the elastic energy between the two. We then had to use Newton’s Law to prove that a(t)=(-(k1 + k2)/m) x (t) is true and by using the equation ω²=(k1+k2)/m we get ω=-√((k1+k2)/m). After comparing our measured values with the calculated values, we could confirm that the equations are true.
Measured and Calculated Data can be found in the tables on the Data slide.
Introduction
In this experiment, we used 2 different springs and by adding weights, we found the spring constants. We built a device with an air slide to find the elastic energy in the springs.
Materials
2 Similar Springs Air Slider Weights of Different Masses Hooks and Rings to Support Springs A Video Camera
Procedure
1. Build a system with a spring hanging from some object and a weight hanger connected to the bottom of the spring.
2. Measure the mass of the weight hanger.3. Record the position of the weight
hanger.4. Place a weight on the hanger and
record the change in position.5. Calculate the k constant of the spring.6. Repeat for the second spring
Procedure (continued)
1. Build another device using an air slide and an air slide glider with a spring attached to each end.
2. Slightly tap one end of the glider and record the oscillation times for the glider with 3 different masses.
3. Use the given equations to determine ω.
Video
Math Model
Energy Balance
Spring Left Turning Point
Point of Equilibrium
Right Turning Point
Spring 1 1066.25 J 0 J 1066.25 J
Spring 2 981 J 0 J 981 J
Data found using the equation E=1/2(k1 + k2) A²
Left Turning Point
Point of Equilibrium
Right Turning Point
Glider 0 J 2047.25 J 0 J
Total Energy
Data found using the equation kE=1/2 mv²
Left Turning Point Point of Equilibrium
Right Turning Point
2047.25 J 2047.25 J 2047.25 J
E=1/2(k1 + k2) A²
DataSpring ∆y k=(ma)/∆y
Spring 1 .115 m 42.65
Spring 2 .125 m 39.24
Mass f=1/T ω
1 .110 kg .91715 Hz 5.76262
2 .210 kg .73674 Hz 4.62907
3 .310 kg .62630 Hz 3.93516
Mass f=1/T ω
1 .110 kg .88614 5.56776
2 .210 kg .64134 4.02965
3 .310 kg .52786 3.31662
Calculated
Measured
Conclusions
After measuring the displacement, we found the k constants to be roughly 39.24 and 42.65 .
The equations were proven to be true. The difference in the recorded ω and
the calculated ω can be seen in the table in the Data slide.
Acknowledgments
We would like to thank Mr. Walfred Raisanen for assigning this wonderful experiment.
We would also like to thank ourselves for being smart enough to complete the assignment.