DATA: Length of the Spring:Lo = 0.15m Real Constant: Kreal = 20 Table I: Hooke's Law. Trials 2 3 4 Mass 0.100 0.150 0.200 0.250 0.300 0.350 m(kg) Force on the 10.98 1.47 1.96 2.45 2.94 3.43 Spring Fs(N) Length 0.16 0.20 10.27 0.32 0.34 0.39 L(m) Increase in | 0.001 0.05 0.12 0.17 0.19 0.24 Length AL (m) 6 ANALYSIS: Part I: Hooke's Law: 1. Determine the spring's increase in length caused by the mass (41); AL = L - Lo = 0.100m - 0.160 = 0.50m 2. Calculate the force exerted by the spring on the mass (F), you will need to use the equilibrium principle: Fs = Fg = mg = 0.100kg . 9.8 -2 = 0.98N3. Using Logger Pro, create a graph of Force on the spring vs. change in g; Force and lenght I 3 Linear Fit for: Data Set | Force on the spring El F3 2 mx+b m (Slope): 10.4 N/m b (Y-Intercept): 0.854 N n 2 Correlation: 0.991 E, RMSE: 0.140 N 2 . o 2 E O {D U 5 [a LI. 1 0 0 0.05 0.1 0.15 0.2 [00214. 3-205} change in lenghl {ml 4. Describe y0ur relationship, what are the mathematical meaning of your slope and your y-intercept? - The force on the spring is directly proportional to the change in length, the relationship is linear. The y- intercept represents the force after seeing elongation of the spring. 0 Meaning of the slope: As the change in length increases 1m, the force 0n the spring increases by 10.4 Nlm - Y- intercept: When the change in length is ZERO, the force on the spring is 0.85 N 5. Write the mathematical equation showing the relationship between Force and elongation. F = kAx 6. Determine the spring constant from the slope of the best t line. The slope of the best t line = In: 10.4 me 7'. Determine the percentage error in the spring constant vs. its real value. real experimental %error = real N N 20 10.4 Vomar = LEEm = 48% 20?: Part II: Oscillation.. What g the meaning ofA, B. and C from the t data?I A is the amplitude, B is the angular frequency and C is the phase of the wave. 2. Determine the period of each oscillation: 3. Graph the period T (yaxis) vs. mass m (xaxis). Create a table of mass (kg) and Period squared (s?) Mass (kg) 0.100 0.150 0.200 0.250 0.300 0.350 Period squared 0.40 0.64 0.82 1.02 1.21 1.39 5. Calculate the spring constant from the slope of the line: k = - - = 18.45N/m slope 2.14 6. Determine your percentage error. real - experimental error = real Period and mass Linear Fit for: Data Set | Period T = mom+b m (Slope): 2.14 s/Kg b (Y-Intercept): 0.456 s Correlation: 0.991 RMSE: 0.0308 s Period (s ) 0.5 0.1 0.2 0.3 (0.1078, 0.602) Mass (Kg)10. 11. N N 20 13.455 %error = LN = 8% ZOE For Two of your save data les, determine the values of the velocity and the acceleration at the following times in the position vs. time graph for one complete oscillation (one complete sine): - Zero vertical displacement y = D 0 Maximum vertical displacement: y = A 0 Zero vertical displacement y = D 0 Minimum vertical displacement y = A Based on your results from the previous part answer the following questions: 0 Where along the path of the spring-mass system is the velocity maximum, zero, minimum? 0 Where along the path of the spring-mass system is the acceleration maximum, zero, minimum? For two different time within the same oscillation calculate the Kinetic energy of the mass, the elastic potential energy of the spring-mass system, and total mechanical energy of the system. (do not account for the gravitational potential energy} K = Emu2 and U9 = gkxz Where does the system Q the largest amount of elastic potential energy? Kinetic Energy? Why does the mass-spring system oscillate? When a mass is hung vertically from a spring, the spring stretches. The force on the mass due to the spring is proportional to the amount the spring is stretched. There is a point at which the spring force and the weight are equal in magnitude but the opposite direction. CONCLUSIONS: 1. Denitions: 0 Simple Harmonic Oscillation: motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law. 0 Period: Time required for one to complete cycle (back and forth). I Frequency: number of cycles per second - Restoring Force: force on the mass that acts in the direction of returning the mass to the equilibrium position. 0 Statement for Hooke Law: The amount of force applied to an elastic object is proportional to how far it stretches. II. Physical meaning of the slopes and the y-intercepts. Slope: spring constant y-intercept: Spring force at no elongation