Lab Report 3

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School

Northeastern University *

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1141

Subject

Mechanical Engineering

Date

Apr 3, 2024

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docx

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5

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Report for Experiment #5 Uniform Circular Motion Abstract In this experiment, we used it the equipment to find the centripetal acceleration of an object. In this experiment, we found the acceleration, velocity and period by means of timing and calculations. These data were obtained to find their role in the centripetal force. In the experiment, by using a rubber band and a spring to generate centripetal force, we investigated how different tensions affect centripetal acceleration and the force of rotation around the apparatus. Introduction The main heading of this experiment is rotational motion. The most important thing in this is the centripetal force. Centripetal force is the force that causes an object moving in a circle to change its direction constantly but to move steadily around the circle as a whole. However, the constant change of direction means that the object moving in a circle always receives a force towards the center. According to Newton's second law, a centripetal force is needed and always a centripetal acceleration is needed. The magnitude of this centripetal force can be calculated using the following equation F = m v 2 r The main objects of this were 1. to understand the velocity of an object in uniform circular motion, and acceleration in uniform circular motion 2. to measure the force on an object in uniform circular motion 3. to apply Newton’s second law to
an object in uniform circular motion. In investigation1, we measured the rotational velocity and centripetal force of the iron block by using the equipment. For this experiment, the centripetal force was tension, since it was perpendicular to the velocity. The following equation can be used to express the centripetal force: F ( t )= mg Through several experiments, we can calculate the period based on the data obtained and the following formula. T = 2 π ω in this equation, ω is the angular speed which could be calculated by the times of rotation over how long did these rotation take. Once the period is calculated, we can calculate the speed by using the following equation: V = 2 π r T After completing all the tests, we inserted the compiled data into an Excel sheet and plotted scatter plots of force vs. velocity and force vs. v². Investigation 1 In investigation 1, the equipment that we used were Rubber bands, Assorted springs, Stopwatch or timer program, Plastic pail, washers, String, paper clips, Ruler, and Digital scale. The way how they were assembled is showed in the graph on the right. By unscrewing the screws on the top of the column, we could adjust the front and rear position of the horizontal arm of the instrument until the bob is directly above the pointer. String was used to provide different values of centripetal force to the bob. The amount of centripetal force was determined by the mass of the bucket and washer. The bucket was attached to the other end of the rocker by a string across the pulley, then the washer was added to the bucket until the rocker is realigned with the pointer, and the weight of the washer and bucket are recorded in the data sheet. However, after the bucket was removed, the speed and period were calculated by artificially providing the bob with a rotational force and then using the phone to record the time and number of revolutions. The following two tables were the data that we collected. Since the 17 column table was too big to implement in one table, I divided them into two pieces.
Table : Time Trials, Mass, Force, revolutions, period, velocity, and their errors Trials M (kg) Error M (kg) Centripet al Force (N) Error (N) Revolution s t1 t2 t3 Averag e Time (s) 1 0.13 0.009 1.274 0.088 2 2 2.79 2.97 2.91 2.89 2 0.133 0.018 1.3034 0.176 4 2 2.72 2.77 2.72 2.75 3 0.568 0.032 5.5664 0.313 6 5 4.08 3.59 3.86 3.84 4 0.482 0.034 4.7236 0.333 2 5 3.43 4.08 3.61 3.707 5 0.214 0.014 2.0972 0.137 2 5 5.9 5.95 6.15 6 6 0.947 0.039 9.2806 0.382 2 5 3.17 2.84 2.91 2.973 7 0.637 0.039 6.2426 0.382 2 5 4.18 3.91 3.68 3.923 Error t (s) Period T Error T (s) v (cm/s) Error v v^2 (cm/s) Error v^2 0.09165 1.445 0.0458 80.877 2.565 6541.09 103.73 0.02887 1.375 0.0144 84.994 0.893 7223.98 37.97 0.2454 0.769 0.0491 151.973 9.701 23095.79 737.12 0.3356 0.741 0.0671 157.716 14.287 24874.33 1126.61 0.1323 1.2 0.0265 97.389 2.148 9484.62 104.59 0.1739 0.595 0.0348 196.526 11.487 38622.47 1128.72 0.2503 0.785 0.0501 148.939 9.497 22182.83 707.24 m of bob (kg) 0.434kg ± 0.00005 kg radius (cm) 18.6cm ± 0.01cm
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