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.