Purpose
The purpose of this lab was to determine the spring constant in the spring used and then verify the law of conservation of energy.
Theory
The spring constant will be able to be measured when an amount of mass is added to the string and when the distance that the spring is compressed is measured.
The spring constant is: K=mx^2.
The spring constant is: K=mx^2.
Free body diagram of the cart and spring
Experimental Technique
Steps:
We first set up the cart and spring in to the proper testing position.
Added weight to the string at the end until the spring was fully compressed
Recorded the weight
Put a set weight on top of the cart
Released the cart and measured the velocity
Recorded data and found spring constant
We first set up the cart and spring in to the proper testing position.
Added weight to the string at the end until the spring was fully compressed
Recorded the weight
Put a set weight on top of the cart
Released the cart and measured the velocity
Recorded data and found spring constant
Data and Analysis
According to the data recorded in the table, it shows that there is a linear relationship between the mass and the velocity since as mass increases, the velocity decreases.
Percent Difference:
(.76m/s-.53m/s)/(.76m/s+.53m/s)/2 x 100
=2.3%
Spring Constant
1/2kx^2=mgh
k=2mgx^(1/2)
k=2(.550kg)(9.8m/s^2)(.0063)/.0063 ^(1/2)
k = 82.41N/m
(.76m/s-.53m/s)/(.76m/s+.53m/s)/2 x 100
=2.3%
Spring Constant
1/2kx^2=mgh
k=2mgx^(1/2)
k=2(.550kg)(9.8m/s^2)(.0063)/.0063 ^(1/2)
k = 82.41N/m
Conclusion
Overall, in this lab it was set out to find the velocity of the cart with different masses on it and record the amount of weight it took to compress the spring. This data could be then used to calculate percent difference and the spring constant. The spring constant was found to be 8.241 N/m and the percent difference was found to be 2.3%. Also, there was a linear relationship between the velocity and mass since as the mass increased, the velocity steadily decreased.
References:
Create A Graph. (n.d.). Retrieved 2016, from https://nces.ed.gov/nceskids/createagraph/default.aspx?ID=6348c869fd894b8fa9e1ba650747f157
Developing Mathematical Models of Translating Mechanical Systems. (n.d.). Retrieved December 21, 2015, from http://lpsa.swarthmore.edu/Systems/MechTranslating/TransMechSysModel.html
Energy Lab. (n.d.). Retrieved 2016, from http://lahsphysics.weebly.com/energy-lab.html
Developing Mathematical Models of Translating Mechanical Systems. (n.d.). Retrieved December 21, 2015, from http://lpsa.swarthmore.edu/Systems/MechTranslating/TransMechSysModel.html
Energy Lab. (n.d.). Retrieved 2016, from http://lahsphysics.weebly.com/energy-lab.html