PhysicsLab3

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(1 point) Title of the Experiment: Newton’s Second Law of Motion Student’s name: Section SLN: PHY 122 Professor’s Name: Darya Dolenko Week of the experiment: 3 1

Objectives: (3 points) The objective of this lab project is to collect data to validate Newtons Second Law of motion through a simulated cart being pulled by a weighted hanging mass. Physics principles will be used to determine the mass of the system, as well as measure the experimental gravitational acceleration. Using the data collected, the effects of changing force or mass on an object’s acceleration will be observed. 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 Graphs: 2

Part 2 Graphs: PART 1. Horizontal, frictionless track and a moving system of constant mass 3 State all values with appropriate units Mass of the cart, M = 250g Mass of the hanger, m h = 50g Total mass of the system m system = 850g

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Table 1 Run Mass on the hanger Acceleration of the system (units) (units) 1 50g 0.572m/s^2 2 60g 0.686m/s^2 3 70g 0.800m/s^2 4 80g 0.916m/s^2 5 90g 1.03m/s^2 Slope and its uncertainty from acceleration vs force graph: 1.168 +- 0.002039 PART 2. Two-way motion with friction on a horizontal track Mass of the cart, M = 250g Mass of the hanger, m h = 50g Table 2 Mean value of g: _9.806m/s^2__ standard deviation ___0.04_____number of runs_3_ 4

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: _____5.216 degrees_________ Experimental critical angle: ________Between 5.2 and 5.3 degrees______________ 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 ) : Equation: Fg = Mhangar * g Run 1: 0.05kg * 9.81m/s^2 = 0.4905N  Determine the experimental mass ( M sys ¿ of the moving system from the slope of the plot “acceleration vs. applied force”: a = F net M sys Slope: 1/1.168 = 0.8561kg 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: 5 Run Mass on the hanger Acceleration 1 (system moves towards motion sensor) Acceleration 2 (system moves away from motion sensor) a aver 1 20g 1.378m/s^2 0.2962m/s^2 0.8371m/s^2 2 40g 1.548m/s^2 0.5218m/s^2 1.035m/s^2 3 70g 1.815m/s^2 0.8394m/s^2 1.327m/s^2

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 1.168 + 0.002 = 1.170 1.168 – 0.002 = 1.166 1/1.170 = 0.8547kg 1/1.168 = 0.8561kg  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 = (|0.8561 – 0.850| / 0.850 ) * 100 = 0.72% 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): Run 1: 0.8371(0.750 + 0.07)/0.07 = 9.806m/s^2 = 9.81m/s^2  Calculate the discrepancy between the average value of the experimental and the theoreti- cal value of gravitational acceleration (9.81m/s 2 ) is: Run 1: |9.806 – 9.810|/9.81 * 100 = 4.07% PART 3. Cart on frictionless tilted track 6

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 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.  What acceleration would the system have as a result of 0.5 ° discrepancy in the tilt from the “critical” angle. 0.550 * 9.81 * sin(4.716) – 0.05 * 9.81 = -0.0468m/s^2 0.550 * 9.81 * sin(5.716) – 0.05 * 9.81 = 0.0468m/s^2 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) 7

EXPERIMENTAL VALUE 0.856 +- 0.002kg 9.806m +- .04m/s^2 5.2 ° < θ < 5.3 ° EXPECTED VALUE 0.850kg 9.81m/s^2 5.216 ° DISCREPANCY 0.71% 4.07% Discussion and Conclusion (10 points): The purpose of this lab was to demonstrate the proportional relationship between acceleration and applied force through a series of experiments, then use the values of acceleration and net force to calculate the experimental mass of the system. Using these results, the gravitational acceleration was calculated and used to validate Newton’s Second Law. In Part 1, there were 5 runs worth of data provided from the KET simulation in which a hangar with a specified mass was tied to a cart with added weights by a string along a frictionless track. The net force was obtained through the weight of the hangar and the known gravitational acceleration of 9.8m/s^2. With each progressive run of the simulation, weight was added to the hangar, and it was determined that the acceleration and in turn the net force of the cart increased with the added weight to the hangar. This proved that the acceleration is proportional to the force of the system. Additionally, Logger Pro was used to graph the acceleration vs. net force where the experimental mass was obtained through the inverse of the slope from the line of best fit. This value was determined to be 0.856+-0.002kg which was only 0.71% away from the expected theoretical value of 0.850kg. For Part 2 of the lab, there were three runs conducted and this time an element of friction was added to the track. The same 50g hangar was placed on the end and connected to the weighted car by the string and the weight was adjusted in the same manner as Part 1. Differing from Part 1, in Part 2 we gave the weighted cart a small push towards the distance sensor. The cart was then allowed to reverse its direction along the ramp due to the forces caused by the tension and the weight from the hanger. We then graphed this motion using Logger Pro (Graphs in the experimental data section). The direction of the cart could be determined by its velocity being either positive or negative. When the direction changed, the sign of the velocity would also change to reflect. The average 8

experimental acceleration value was obtained from the cart’s acceleration towards and away from the distance sensor and was calculated to be 9.806+-0.04m/s^2. In Part 3 of the lab, we were given specifications of a cart with a weight of 550g attached to a hanger with a weight of 50g. With the given information, I sketched a force diagram, and then used math to calculate the critical angle of the ramp that would hold the cart in place. This value was determined to be 5.216 °, but was not tested in KET due to the lack of a working simulation. Also calculated were a +0.5 and -0.5 degree change in the critical angle, which caused the cart to experience an acceleration of 0.0468m/s^2 and -0.0468m/s^2 respectively. Due to the nature of the experiment, there are opportunities for error and discrepancies to exist. One possible source of error is the resolution of the simulation, as the simulation can only be so accurate to real world situations. Additionally, since our experimental calculations were based on best-fit curves, it is likely that the curve is not an exact representation of the data. With these opportunities for error, we still only experienced a 0.71% discrepancy in Part 1, and a 4.07% discrepancy in Part 2, showing that our experimental values were accurate. Based on our experimental findings throughout the lab, it can be concluded that Newton’s Second Law held. This is because the acceleration of the system was directly proportional to the net force of the system. Additionally, the value of gravity that was obtained experimentally was within 5% of the theoretical value of gravity. 9

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