am lab1

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San Francisco State University *

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243

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Mechanical Engineering

Date

Dec 6, 2023

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docx

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3

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LAB 1 - 1-D MOTION, FORCES, AND ENERGY Introduction In this experiment we will study the motion of a cart produced by a falling weight. The weight of the weight acts as a force accelerating the cart. Based on your knowledge of the weight of the weight, you should be able to predict the position and the velocity of the cart with time. For this lab, you will first perform the experiment and then apply your theoretical knowledge of Newtonian Mechanics to the data. First you will develop and apply a model for position and velocity as a function of time from Newton’s second law. Then you will develop and apply a model for velocity as a function of position from the Work-Energy Theorem. Experiment mass of cart = 250g mass of hanger = 50g mass A = 200g mass B = 100g mass C = 50g Data collection Trial 1 mass of cart = 400g mass of hanger = 250g Trial 2 mass of cart = 300g mass of hanger = 350g Trial 3 mass of cart = 250g mass of hanger = 400g Equations x(t) = 0.0049t 3 + 0.810t 2 - 0.737t + 0.0964
v(t) = 0.01491t 2 + 1.62t - 0.737 a(t) = 2.982t + 1.62 v(t) = 5.15t 2 + 6.49t + 0.0513 Trial 1 a 1 = 2.45/0.4 = 6.125ms -2 Trial 2 a 2 = 3.43/0.3 = 11.43333333ms -2 Trial 3 a 3 = 3.92/0.25 = 15.68ms -2 Results Discussion: How did your forces fit work out? How did the work-energy approach work out? The work energy approach worked because some of the work done by the forces is equal to the change in kinetic energy. Compare and contrast the dynamics approach with the work-energy approach: in terms of accuracy, ease of use, whatever else you deem valuable. the dynamics approach gave similar maganitudes to the data collected and it was easy because of the constant gravity acceleration. Experimental errors? Air resistances. Neglect of friction. conclusion
This experiment shows that as the work done on an object increases over the same distance, the the resulting kinetic energy on the object also increases hence proving newton's second law of motion since the only variables in this experiment are force of the work and the resulting velocity of the kinetic energy.
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