Template_Newton's Second Law-1

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Title of the Experiment: Newtons Second Law of Motion Student’s name: Jesus Gonzalez Section SLN: 74465 TA’s Name: Ayush Kumar Singh Week of the experiment: 3 1

Objectives: (3 points) Experimental Data (3 points): Insert experimental graphs and obtain from the graphs all the experimental data that will be used for further calculations in Data Analysis. PART 1. Horizontal, frictionless track and a moving system of constant mass Table 1 Run Mass on the hanger Acceleration of the system (units)kg (units)m/s 1 0kg .578 m/s 2 .010kg .686 m/s 3 .020kg .801 m/s 4 .030kg .916 m/s 5 .040kg 1.03 m/s Slope and its uncertainty from acceleration vs force graph: _______________________ PART 2. Two-way motion with friction on a horizontal track Mass of the cart, M = Mass of the hanger, m h = 2 State all values with appropriate units Mass of the cart, M = .250kg Mass of the hanger, m h = .050kg Total mass of the system m system = .850kg

Table 2 Mean value of g: ___________ standard deviation _________________number of runs_____ Note: The uncertainty in the experimental gravitational acceleration equals the standard devia - tion in the average g value as determined by Graphical Analysis. PART 3. Cart on frictionless tilted track Calculated critical angle: _______________________________ Experimental critical angle: ______________________________ 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 ) :  Determine the experimental mass ( M sys ¿ of the moving system from the slope of the plot “acceleration vs. applied force”: 3 Run Mass on the hanger Acceleration 1 (system moves towards motion sensor) Acceleration 2 (system moves away from motion sensor) a aver 1 .020kg 1.379 m/s .296 m/s 2 .040kg .7726 m/s .9593 m/s 3 .070 kg 1.123 m/s 1.233m/s

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a = F net M sys 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 uncer- tainty in the slope of the graph “acceleration vs. applied force”: ∆ M sys = 1 slope 2 ∆slope  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% 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):  Calculate the discrepancy between the average value of the experimental and the theoreti- cal value of gravitational acceleration (9.81m/s 2 ) is: PART 3. Cart on frictionless tilted track  Include the free body diagrams for the cart on the tilted track and the hanger, derive the equation for the “critical” angle at which the cart stays still on tilted track. Calculate its value. 4

 What acceleration would the system have as a result of 0.5 ° discrepancy in the tilt from the “critical” angle. Res u lts (3 points) State all values in the correct format with uncertainties and appropriate units! MASS OF SYSTEM (Part 1) GRAVITATIONAL ACCELERATION (Part 2) “CRITICAL ANGLE” (Part 3) EXPERIMENTAL VALUE EXPECTED VALUE DISCREPANCY Discussion and Conclusion (10 points): (Follow the general directions given in the Syllabus and describing how the Discussion and Conclusion section should be composed. In particular, explain the relationship you recorded between acceleration and force. Also, explain why the slope has slightly bigger value when the cart moves toward motion sensor when compared to when it moves away. Explain the nature of errors and reasons for discrepancies between your experimental and theoretical results. Include a paragraph that states whether Newton’s Second Law of Motion held based on your experimental data from both parts.) 5

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