Louis Thomas Detoro Lab 3_ Newton's Second Law of Motion

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Apr 3, 2024

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Title of the Experiment: Newton’s Second Law of Motion Student’s name: Louis Thomas Detoro Section SLN: PHY 122 - 14231 TA’s Name: Ayush Kumar Singh, Yash Patil Week of the experiment: 3 1
Objectives: (3 points) The objective of this lab is to prove that acceleration is directly proportional to the net force while being inversely proportional to the mass. While also attempting to validate Newton’s second law by measuring gravitational acceleration. Experimental Data (3 points): PART 1. Horizontal, frictionless track and a moving system of constant mass Mass of the cart, M = 250 grams or 0.250 kg Mass of the hanger, m h = 50 grams or 0.050 kg Total mass of the system, m system = 850 grams or 0.850 kg Table 1 Run Mass on the hanger Acceleration of the system (kg) (m/s^2) 1 0 0.572 2 0.010 0.686 3 0.020 0.801 4 0.030 0.916 5 0.040 0.984 6 0.050 1.145 Slope and its uncertainty from acceleration vs force graph: Slope = 1.076 Uncertainty = 0.05480 2
Figure 1. Net Force vs Acceleration Graph of 5 points PART 2. Two-way motion with friction on a horizontal track Mass of the cart, M = 250 g + 550 g = 800 g = 0.8 kg Mass of the hanger, m h = 50 g = 0.05 kg Table 2 Mean value of g: 22.94 standard deviation: 8.442 number of runs: 3 Run Mass on the hanger Acceleration 1 (system moves towards motion sensor) Acceleration 2 (system moves away from motion sensor) a aver (kg) (m/s^2) (m/s^2) (m/s^2) 1 0.020 1.379 0.2962 0.838 2 0.040 1.581 0.5217 1.05 3 0.070 1.867 0.8399 1.35 3
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Figure 2. Data Analysis (10 points): Be sure to include equations! PART 1. Horizontal, frictionless track and a moving system of constant mass ❖ Equation and 1 sample calculation of the force applied to the system that was calculated by Logger Pro (Fg = m hanging *g ) : Fg = m hanging *g Fg = 0.01 * 9.8 = 0.098 4
❖ Determine the experimental mass ( M sys ¿ of the moving system from the slope of the plot “acceleration vs. applied force”: M sys = 1 / slope M sys = 1 / 1.076 = 0.929 kg Compare the Newton’s second law equation to the linear equation (y=mx+b) we can find the mass of the system using the value of the slope as: slope = 1 M sys M sys = 1 slope ❖ Propagate an error of the experimentally determined mass of the system using the uncertainty in the slope of the graph “acceleration vs. applied force”: ∆ M sys = 1 slope 2 ∆slope ΔM sys = (1 / 1.076^2) * 0.05480 = + / - 0.047 kg ❖ The discrepancy between the experimentally determined mass of the system from the slope of the graph and its actual value ( m system ) is: %discrepancy = | M sys − m system | m system ∗ 100% %discrepancy = ( |0.929 - 0.850| ) / 0.850 * 100% = 9.29 % PART 2. Two-way motion with friction on a horizontal track ❖ Show one sample calculation of the gravitational acceleration for one of the runs, using equation (6): 5
g = a avg (M + m) / m g = 0.838 m/s^2 (0.850 kg + 0.20kg) / 0.70 kg g = 1.8 ❖ Calculate the discrepancy between the average value of the experimental and the theoretical value of gravitational acceleration (9.81m/s 2 ) is: Results (3 points) MASS OF SYSTEM (Part 1) GRAVITATIONAL ACCELERATION (Part 2) EXPERIMENTAL VALUE 0.929 kg 9.81 m/s^2 EXPECTED VALUE 0.850 kg 9.81 m/s^2 DISCREPANCY 9.29% Discussion and Conclusion (10 points): During these experiments the objectives were to prove whether or not acceleration is directly proportional to the net force and whether or not it was inversely proportional to the mass. The experiments also served as proof for Newton’s second law of motion by measuring the gravitational acceleration of the cart. In the first part of the lab, the cart had been weighed down by a hanger with various sized weights attached. The computed value for the moving mass was to be 0.850 kg, with an uncertainty of + / - 0.05480 kg. The discrepancy between the two values was calculated at 9.29%. During the second part of the experiment static and kinetic friction were added to the experiment. Through the data collected, the acceleration of the total run was used in order to compare it to acceleration due to gravity. 6
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In conclusion, every experiment conducted during the lab met the expected outcomes. During the first part of the experiment it could be seen that the acceleration of the cart was proportional to the amount of weight added to the hanger. 7

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