Conservation of Energy Lab
Author: Jacob Hoffner
Lab Partners: Andrea Schafer and Connor Frey
Date: December 2015
Lab Partners: Andrea Schafer and Connor Frey
Date: December 2015
Purpose
The Purpose of this lab is to verify the Law of Conservation of Energy by investigating the compression of a spring.
Theory
When an object is compressed a certain distance, it gains elastic energy. In this case, that object is a spring. When compressing a spring a certain distance from its original position, x, a certain amount of elastic energy is accumulated within the spring.
Hooke's law was discovered in 1660 by English scientist Robert Hooke. Hooke's law states that , for relatively small deformations in an object, the displacement in the size of the deformity is directly proportional to the force or load that causes that deformation. Hooke's Law therefore states that Force equals the k constant of an object multiplied by the displacement of the deformity in the object. In other words, F=kx. Using a cart on a track propelled by a spring (elastic energy) and emitting kinetic energy, we will find a measured velocity. The calculated velocity to compare to the measured velocity will be found using the derived velocity equation below: To the right, the derived equation to find the calculated velocity is shown to be derived from the Kinetic and Elastic Energies. By comparing the velocities, we will observe how close in value the Elastic Energy gathered behind the cart is to the Kinetic Energy that propels the cart in Part 2. By setting the two energies equal to each other, we can discover how velocity can be calculated; this calculated velocity will be compared with the measured velocity. This comparison will exhibit the Law of Conservation of Mass. We will discover how the velocities created from the Elastic Energy is similar to the velocities created from the Kinetic Energy.
The Law of Conservation of Mass states that the amount of mass in a system that is closed will persist to be constant over time, indicating that matter cannot be created nor destroyed. |
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Experimental Technique
In order to find the elastic coefficient in each of our springs, we each added weight to a pulley system to indicate how much mass each of our springs could take. This was done by pushing a wheeled vehicle against the spring by applying masses suspended on a pulley to the end of the vehicle pushing against the spring. The vehicle pushes the spring into a screwed-in stopper; the displacement of the spring's deformation determines the x-value, or position, in meters. This distance is measured using the ruler attached to the side of the track the wheeled vehicle sits on. The Force of the spring is determined by the mass exerted on the spring multiplied by gravity, g. This data could now be put into a graphical form in order to find the spring constant by observing the slope of the graph's line.
After finding the spring constant, we launched the wheeled vehicle with the spring to see how fast the vehicle's velocity is when the spring is at different compressions. First, we leveled the plane the vehicle was launched on. Second, the vehicle was supplied with different masses and a "picket fence" to test velocity. A rotary motion sensor was placed above the vehicle to measure its velocity. The spring was compressed behind the vehicle and held in place by a pin behind two screwed-in stoppers. The pin was released by a string to begin the vehicle launch.
We launched the vehicle six times in order to get a set of data for velocity. Through these six runs, we varied the amount of mass the wheeled vehicle held, along with different spring compressions. Using the derived velocity equation summarized in the Theory section, we will calculate velocity in order to compare it with the measured velocities found by launching the wheeled vehicle. This comparison will be done using percent difference. The data collected in this lab will be used to verify the Law of Conservation of Mass due to the compression of the spring.
After finding the spring constant, we launched the wheeled vehicle with the spring to see how fast the vehicle's velocity is when the spring is at different compressions. First, we leveled the plane the vehicle was launched on. Second, the vehicle was supplied with different masses and a "picket fence" to test velocity. A rotary motion sensor was placed above the vehicle to measure its velocity. The spring was compressed behind the vehicle and held in place by a pin behind two screwed-in stoppers. The pin was released by a string to begin the vehicle launch.
We launched the vehicle six times in order to get a set of data for velocity. Through these six runs, we varied the amount of mass the wheeled vehicle held, along with different spring compressions. Using the derived velocity equation summarized in the Theory section, we will calculate velocity in order to compare it with the measured velocities found by launching the wheeled vehicle. This comparison will be done using percent difference. The data collected in this lab will be used to verify the Law of Conservation of Mass due to the compression of the spring.
Data
Below is the chart displaying the data that was used to find our spring constant:
The graph below resembles the data in the chart above. The slope of the line below is the spring constant, k. Therefore, k=127.4 N/m.
Analysis
Below are the sample calculations for the Calculated Velocity and the Percent Difference between the Measured Velocity and the Calculated Velocity. These sample calculations below just so happen to be from Run #3 of Part 2 of the lab.
Conclusion
Through the data collected in this lab, the ending percent differences were not too far high, indicating that the calculated velocities came close to the measured velocities. Some factors that may have caused the difference between the two velocities could be the Friction between the wheels of the wheeled vehicle and the track it traveled upon, which led to the build-up of Thermal Energy. The loss of some energy is due to Thermal Energy, one reason the calculated velocity would be higher than the measured velocity. Human error could have occurred when releasing the wheeled vehicle from the spring; the rotary motion sensor could have been placed too close to the wheeled vehicle to prevent the wheeled vehicle from arriving at its maximum speed before passing the sensor. Parallax error could have been a problem due to the viewing distance between the spring and the measuring tape used to measure it; the measuring tape was a couple inches away, and could have caused minuscule inaccuracy in measuring. Air resistance is not included in the calculated velocity, so this could have posed as a problem when finding the measured velocity. Error could have been produced by placing the rotary motion sensor at a different location, and by using another form of accurate measuring when finding the lengths of the compressed spring. By using F=kx, we were able to derive Elastic and Kinetic Energies to find the calculated velocities. While there are considerable percent differences found, the Law of Conservation of Mass was verified by comparing the calculated and measured velocities.
References
Marie, A. (2015, November 30). What Is the Law of Conservation of Mass? Retrieved January 06, 2016, from http://chemistry.about.com/od/chemistryglossary/a/conservmassdef.htm
Hooke's law | physics. (2016). Retrieved January 6, 2016, from http://www.britannica.com/science/Hookes-law
Giancoli, D. (1998). Chapter 6: Kinematics in Two Dimensions; Vectors. InPhysics: Principles with applications (5th ed., p. 1096). Upper Saddle River, N.J., New Jersey: Prentice Hall.
Bowman, D. (2015, October 1). Chapter 6: Work and Energy. Lecture presented at Physics, Lehighton.
Bowman, D. (n.d.). Lahs Physics. Retrieved October 1, 2015, from http://lahsphysics.weebly.com/
Hooke's law | physics. (2016). Retrieved January 6, 2016, from http://www.britannica.com/science/Hookes-law
Giancoli, D. (1998). Chapter 6: Kinematics in Two Dimensions; Vectors. InPhysics: Principles with applications (5th ed., p. 1096). Upper Saddle River, N.J., New Jersey: Prentice Hall.
Bowman, D. (2015, October 1). Chapter 6: Work and Energy. Lecture presented at Physics, Lehighton.
Bowman, D. (n.d.). Lahs Physics. Retrieved October 1, 2015, from http://lahsphysics.weebly.com/