Conservation of Energy

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Stony Brook University *

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133

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Mechanical Engineering

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Feb 20, 2024

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PHY 133 L07 Conservation of Energy Jeremiah Shawn Geotina Lab partner: Christopher Kim TA Loc, Ngo Experiment Date: 8 March 2023 Report Date: XX March 2023
Introduction This physics lab experiment will allow us to calculate Potential Energy (PE) and Kinetic Energy (KE) at certain times, use addition to get E total , and make a plot of total energy vs. time (while propagating for uncertainty). Under a set of assumptions, we will derive a formula for acceleration of the system and we will use this formula to generate a value for g. Procedure: Part I: Preliminary Setup and Measurements 1. (wait for TA to turn on the air) begin by leveling your air track. 2. Place cart in the middle of the track, making sure to keep it centered). (If it slides to the left or the right, turn the screw on the leg of the air track to level the air track.) 3. We need to scale for the photogate-measure D , the length of some number of black-clear segments, and divide by the number of segments to get d , the length of one segment. 4. Open “ConservationofEnergy” and properly connect your photogate. 5. Weigh your glider to get the mass M . 6. Identify the two masses m you’ll be hanging from the bottom of your string. Propagate for uncertainty in M based on the terminal decimal place of the measurements of your scale. 7. Hook a string from that drapes over the pulley and connects the glider to the hanging mass. Make sure that the cart has space to move before the hanging mass hits the floor. Part II: Using a 20g Mass 1. Hook a total mass of 20g to the bottom of the string and pull the cart to the opposite end of the track. 2. Press “Start Collection”, wait ~1sec, and release the mass. Catch the cart before it crashes, and press “Stop Collection.”
3. Highlight the region of the velocity vs. time plot, which is a straight line, and identify the data points that these values correspond to. 4. Looking at the data table, record the time, position, and velocity values for the first 10 data points of that region. Repeat the experiment if the region is not long enough. Part III: Using two 20g Masses 1. Repeat steps 1-4 in Part II, except now the hanging mass will have a total mass of 40g instead of 20g. PE and KE formulas: Uncertainty formulas:
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Results, Analysis and Discussion (include deriving conservation of energy and acceleration ) (include .xlxs file) .xlsx file - Copy of Conservation of Energy Data Sheet (1).xlsx Results:
Analysis: When analyzing the Total Energy vs. Time graphs of part II and III, we can see that the produced slope is very close to zero, both are less than 0.09 away from 0. In a perfect experiment we would expect a slope of 0, displaying the conservation of energy of the system. However, in real life we expect there to be some amount of friction that is preventing such a perfect value of 0 for the slope. Nonetheless, the fact that the value is less than 0.09 away from 0 tells us that some other factors, like friction, were involved in producing a slope that is non-zero. Assuming the pulley is massless and frictionless, we can derive a formula for acceleration using the tension of the string (T), gravity (g), and the masses of the glider and the hanging mass. You’ll get: a = (T – m2g)/2m. You can rearrange this to derive a formula for g: g = (T – m2a)/2m.