Analyzing Uniform Circular Motion
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Lab Report: Analysing Uniform Circular Motion Name: Adam Purpose In places where the velocity of an object is difficult to find, it is reliable to attain the frequency of an object. This is the most-favourable method used when dealing with circular motion. Frequency, as we know, is indirectly proportional to the period of a motion, or more precisely. We can determine the relationship between a spinning objects mass, the radius of its circular motion (if attached to a thread) and the hanging mass in a circular horizontal motion by applying a formula we already know. The following steps will describe the derivation of a formula which will be beneficial for this experiment; Newton's Second Law states: Fnet = msa However; acceleration of a circular motion is given by; But Thus; Substituting back to Newton's second law, Fnet= ms ( But since there is a hanging mass which is hanging down from the thread; the tension in the thread is equal to the weight of the hanging mass. And the only force applied during the motion is by the tension in the thread, thus T = Fnet and T = mhg; therefore Fnet = mhg. Putting it back in the original formula we get; mhg = ms ( where; mh = the mass of the hanging object ms = the mass of the spinning object r = the length of the radius of the horizontal motion. To measure the relationship between frequency and Isolate for the three independent variables; we must isolate for each variable. Isolating for the three manipulating variables in the y = mx + b form we get: ; Where ; Where ; Where These are the manipulated equations which will be utilised throughout the lab report. Materials and Procedure - Refer back to the Lab Sheet provided by the instructor. Variables Although un-noticeable, there are three different experiments being held in this one lab.
2.08 0.006 This equation was derived from the previous equation provided, and helps us determine the relationship between Ms and frequency in a linear manner. A further graphical explanation will be provided in the Graphical Analysis part. Data Table # 8: Frequency for Manipulating Hanging Mass (Mh) Hanging Mass (+/-0.00001kg) Frequency (Hz) Uncertainty (±) 0.013 1.05 0.0011 1.04 0.0011 0.027 1.16 0.0013 1.11 0.0012 0.038 1.27 0.0016 1.31 0.0017 0.051 1.58 0.0025 1.61 0.0026 0.065 1.69 0.0029 1.64 0.0027 Data Table # 9: Frequency2 for Manipulating Hanging Mass (Mh) This equation has also been derived from the original equation provided. It provides a linear relationship between the hanging mass and f^2 which will be further discussed in the graphical analysis section. Hanging Mass (+/-0.00001kg) Frequency ^2 (Hz^2) Uncertainty (±) 0.013 1.11 0.0023 1.08 0.0022 0.027 1.34 0.0031 1.24 0.0028 0.038 1.61 0.0041 1.73 0.0045 0.051 2.51 0.0080 2.58 0.0083 0.065 2.86 0.0097 2.68 0.0088 Graphical Analysis (Notice that due to the precision of the data and its closeness, an average of the trials was taken by the graphing program. By visualizing the data, we see that it is very precise, and its accuracy will be measured later on in this section of graphical analysis. The scatter plot is an average of the two trials which leads to more precise and accurate answers, and eliminates any random errors.) 1. Manipulating Radius This section describes the basic relation between Frequency and radius, as well as the manipulated relation between Frequency2 and 1/r, which is attained from the formula provided. As visible from the graph of Frequency vs. Radius, an indirectly proportional relationship is visible and thus the line of best fit provided for that graph is a rational function. As radius increases, frequency decreases. This is due to the fact that when the radius of a circle motion increases, if the mass of an object and the hanging mass are kept constant, the object must travel a longer distance around the circle, since increasing the radius means increasing the circumference of the circular path taken.
This is because a change in reaction time may occur. Reaction time is neglected throughout this experiment, and assumed to be perfect. This is why only the manufacturer's uncertainty was taken for the stopwatch. Since it is a digital device, the smallest unit is the uncertainty. However, reaction time was a major factor and the idea of a bad reaction time could not be eliminated by taking more trials. Although, an attempt to keep it unimportant was made by having the same person and their frame of reference decide, when to start and when to stop. Some non-major sources of error could be those such as air resistance. Although, not much air was there, but the air molecules do interfere with the radius going down at an angle, and more human force being required for the system compared to the force originally caused by the Hanging mass. These errors lead to a systematic error, and the y-intercepts in each manipulated equation reflects that. The experiment could be made better in a sense that, more trials are taken for each different sub-experiment. The person revolving can also make sure that they put enough force behind it to overcome the force of resistance. Also a constant speed would be required for more accurate results. The manipulated graphs could have also had a line of best fit, which touched 0 in order to get a more accurate slope, since there were no y intercepts in the original equation. But if the data was accurate, then the line would have automatically touched 0. All in all, the percent error can be high due to the fact that we deal with quite small numbers. This experiment does consist of some systematic errors which can be improved on. Instruction # 4 Finding the mass of a rubber stopper Radius = 0.53 (+/- 0.0005m) Frequency = 1.22 (+/- 0.001 Hz) Hanging mass = 0.03237±0.00001 kg The original spinning mass of the stopper is 0.013 kg. This means that the error is really low, and that this value is valid.
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