Spring Constant Report julia

Carleton University Laboratory Report Course #: Experiment #:3 PHYS1007L10 Spring constant JULIA MATAR 101100731 Date Performed: 2023-10-18 Date Submitted: 2023-10-31 Lab Period: 8:30-11:30 Partner: no partner Station #: 24 TA: Matt

Purpose The purpose of the Spring Constant Lab is to work with Hooke’s Law to determine unknown spring constant and learn how to linearize equations using the static method and dynamic method. Static Method: Fig 1: Results of the Static Method 𝑘? , 𝜎𝑘? and the Y-intercept (b). Table 1: : Results of the Static Method 𝑘? , 𝜎𝑘? and the Y-intercept. Slope Y-intercept m σ m b σ b Value 31.38 1.089 0.4157 0.08944 Units N/m N

Fg=Mg ( k s ±σ k s ) = ( 31.38 ± 1.089 ) N/m t-test= σ √ ( ¿¿ b 2 + σ b ) 2 = ¿ bp − b ¿ KsX=MGx Wheree X is the extension Gx= KsX M = 31.38 ( 0.144 ) 0.4 = 11.3N Dynamic Method Calculations 𝑘 d = 1 m = 1 0.03318 =30.138 kg/s 2 𝜎kd= σ m m 2 = 0.0002608 ( 0.03318 ) 2 =0.235894 kg/s 2 Now to convert it to N/m kg s 2 N = k gm s 2 kg / s 2 m = kg s 2 so k gm s 2 = kg s 2 therefore the two units are equivalent So, ( k d ±σ k d ) = ( 30.138 ± 0.235894 ) N/m

3 ω = √ σ k d M = √ 0.310820496 0.55 = 0.75234( side calc) ω av = ω 1 + ω 2 + ω 3 + ω 4 + ω 5 + ω 6 + ω 7 + ω 8 + ω 9 + ω 10 + ω 11 11 = 6.930 rad / s ( side calculation) 1 ω 2 = 1 Kd M + 1 Kd ( M Kd + Mh ) = 1 ω 2 = 1 Kd M + 1 Kd ( b ) 1 ω 2 = 1 30.138 0.03318 + 1 30.138 ( 0.002607 ) = 0.0001187437 rad/s 2 Approx.” 0.00012 rad/s 2 σ 1 / ω 2 = 1 σ k d σ m + 1 σ k d ( σ m σ k d + Mh ) = 1 σ k d σ m + 1 σ k d ( σ b ) = 1 0.235894 + 1 0.235894 ( 0.0001437 ) = 0.0001714753 rad/s 2 Approx.:0.0018 rad/s 2 ( 1 / ω 2 ±σ 1 / ω 2 ) ¿ ( 0.0001187437 ± 0.0001714753 ) N/m Discussion Using the values in Table 1 and 2 the spring constant found through the static method was calculated based on graph to be 31.38 ±1.089 N/m . the calculated result of the y-intercept, the answer was less than 2, making the data consistent. In the dynamic method, by linearizing the equation and finding the slope of the graph, the spring constant was calculated to be ( ( 30.138 ± 0.235894 ) N/m

object object to carry the masses was more straight and less crooked both the results for the dynamic and static method would be more accurate and I will have different recorded results. Improvements In terms of improvements for more certain results and calculations I would suggest to have the object that carried the weights and is placed on the spring, to be a straight vertical object and not a crooked one like the one I had to work with for this lab,I can also say that if there is a stable force to control how the spring is being pushed/ pulled down instead of us pulling it down, it would for sure create more accurate results.