Hooke's Law Lab
Author: Tegan Durishin
Lab Partner: Anthony Farano
Date Completed: 28 February 2014
Lab Partner: Anthony Farano
Date Completed: 28 February 2014
Purpose
The purpose of this lab is to determine the spring constant of a metal tension spring. We will also see if the spring on the apparatus obeys Hooke's Law.
Theory
Hooke's law is a principle of physics that states that the force F needed to extend or compress a spring by some distance X is proportional to that distance. That is, where k is a constant factor characteristic of the spring, its stiffness. In other words, he discovered that elastic materials like coiled springs stretch proportionately with the force exerted upon them. That is, the more force, the more the spring stretches.
F∝x
The spring constant is the proportionality constant that relates force and stretch or compression and is represented as k with the unit N/m. Therefore, Hooke's Law can be expressed as:
F=-kx
The purpose of this lab is to determine the spring constant of a metal tension spring. We will also see if the spring on the apparatus obeys Hooke's Law.
Theory
Hooke's law is a principle of physics that states that the force F needed to extend or compress a spring by some distance X is proportional to that distance. That is, where k is a constant factor characteristic of the spring, its stiffness. In other words, he discovered that elastic materials like coiled springs stretch proportionately with the force exerted upon them. That is, the more force, the more the spring stretches.
F∝x
The spring constant is the proportionality constant that relates force and stretch or compression and is represented as k with the unit N/m. Therefore, Hooke's Law can be expressed as:
F=-kx
Experimental Technique
We will be determining the spring constant of the coiled wire. First, we must record the position, or how much it is stretched in length, of the spring at different masses. The tools needed for this lab are as followed: a spring apparatus, a mirror length scale, various amounts of masses, a mass hanger, and a spring.
Begin with assembling the spring apparatus to the right. Next, place enough mass on the plastic mass hanger so that all of the coils are separated. Hooke's law does not hold true when the coils are touching. Remember that the plastic mass hanger dangling from the spring weighs 5 grams (be sure to include this weight in data). Once this is done align the top of the blue mass hanger with the zero on the scale and begin documenting your data.
When measuring, one must use the mirror to measure length in order to eliminate parallax error. Parallax error occurs when the measurer is not eye level with the instrument. Determine the mass required to expand the spring to full scale so that you can find a proper interval for acquiring 10 or more data points. Finally, measure and report the mass and its complementary position for each point of data. With this information, create a Force (N) vs. Position (m) graph and determine the spring constant using the given trend line for the data. Once the trend line is applied, also show the slope equation of the line and the correlation coefficient. The closer the correlation coefficient (r) is to the number 1.0, the more accurate the line is.
We will be determining the spring constant of the coiled wire. First, we must record the position, or how much it is stretched in length, of the spring at different masses. The tools needed for this lab are as followed: a spring apparatus, a mirror length scale, various amounts of masses, a mass hanger, and a spring.
Begin with assembling the spring apparatus to the right. Next, place enough mass on the plastic mass hanger so that all of the coils are separated. Hooke's law does not hold true when the coils are touching. Remember that the plastic mass hanger dangling from the spring weighs 5 grams (be sure to include this weight in data). Once this is done align the top of the blue mass hanger with the zero on the scale and begin documenting your data.
When measuring, one must use the mirror to measure length in order to eliminate parallax error. Parallax error occurs when the measurer is not eye level with the instrument. Determine the mass required to expand the spring to full scale so that you can find a proper interval for acquiring 10 or more data points. Finally, measure and report the mass and its complementary position for each point of data. With this information, create a Force (N) vs. Position (m) graph and determine the spring constant using the given trend line for the data. Once the trend line is applied, also show the slope equation of the line and the correlation coefficient. The closer the correlation coefficient (r) is to the number 1.0, the more accurate the line is.
Data
Analysis
Calculation for determining force:
F = m * 9.8 / 1000 for which F is force and m is mass
Sample Calculation:
F = 49 * 9.8 / 1000
F = 480.2 / 1000
F = 0.4802 Newtons (N)
Calculation for determining force:
F = m * 9.8 / 1000 for which F is force and m is mass
Sample Calculation:
F = 49 * 9.8 / 1000
F = 480.2 / 1000
F = 0.4802 Newtons (N)
Conclusion
In this lab, we determined the spring constant of a metal coil spring. My spring specifically had a spring constant of 2.9 and a correlation coefficient of 0.99944, which is very accurate. We also needed to regulate whether or not the spring obeys Hooke's Law, and it found true here. I found two sources of error with the possibility to occur in the lab. First is the uncertainty error of the masses in which we diminished by using less numbers of masses at a time. For example, one 40g weight may have a percent uncertainty of 3%. If we then use two 40g weights to measure for 80g, then entire percent uncertainty is 6%. Instead, if we use one mass of 80g with a percent uncertainty of 4%, the amount of error is decreased. Another source of error in this lab is parallax error. Parallax error is described as the displacement of the apparent position of an object. The greater the angle of line of sight, the greater the error. Parallax error is exterminated by using a mirrored length scale in replacement of a regular ruler.
In this lab, we determined the spring constant of a metal coil spring. My spring specifically had a spring constant of 2.9 and a correlation coefficient of 0.99944, which is very accurate. We also needed to regulate whether or not the spring obeys Hooke's Law, and it found true here. I found two sources of error with the possibility to occur in the lab. First is the uncertainty error of the masses in which we diminished by using less numbers of masses at a time. For example, one 40g weight may have a percent uncertainty of 3%. If we then use two 40g weights to measure for 80g, then entire percent uncertainty is 6%. Instead, if we use one mass of 80g with a percent uncertainty of 4%, the amount of error is decreased. Another source of error in this lab is parallax error. Parallax error is described as the displacement of the apparent position of an object. The greater the angle of line of sight, the greater the error. Parallax error is exterminated by using a mirrored length scale in replacement of a regular ruler.
References
(n.d.). (n.d.). Retrieved from http://www.britannica.com/EBchecked/topic/271336/Hookes-law
Holzner, S. (n.d.). Retrieved from http://www.dummies.com/how-to/content/how-to-calculate-a-spring-constant-using-hookes-la.html
(n.d.). (n.d.). Retrieved from http://www.cyberphysics.co.uk/topics/forces/hooke.htm
(n.d.). (n.d.). Retrieved from http://www.britannica.com/EBchecked/topic/271336/Hookes-law
Holzner, S. (n.d.). Retrieved from http://www.dummies.com/how-to/content/how-to-calculate-a-spring-constant-using-hookes-la.html
(n.d.). (n.d.). Retrieved from http://www.cyberphysics.co.uk/topics/forces/hooke.htm