Physics Lab Report Centripetal Acceleration PDF

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professor Olugbenga Adeyemi Olunloyo ...

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Physics 2221 Section 009 Olugbenga Adeyemi Olunloyo Experiment Performed: 19 September 2017 Report Handed In: 26 September 2017 The Force Table Introduction The purpose of this lab was to study centripetal acceleration, to study centripetal force, to measure centripetal force on a mass, and to verify the equations for centripetal force and acceleration. Centripetal force is found by multiplying the mass of the object by the centripetal acceleration. The centripetal acceleration equals velocity squared divided by the radius of the circle. This then allows the equation Fc=m(v2/r) to be used for calculations in this lab. The period is calculated by dividing the time by the number of revolutions. Circumference is found by multiplying the radius by two pi. The velocity is then the circumference divided by the period. Fc is the symbol for centripetal force. The symbol for velocity is v, T stands for the period and d is the circumference. Procedure The equipment used in this lab was the centripetal force apparatus, a timer, and the standard masses and weight hangers. A radius was chosen, the spring from the apparatus was attached and the apparatus was then spun and timed for 50 revolutions. This information helped calculate the period, circumference, the speed, the centripetal acceleration and the centripetal force (Fc). Then, weights were hung from the rotated mass to align the mass with the chosen radius. This measurement then allowed for the calculations of centripetal force (Ww) and percent difference. The centripetal force (Fc) and the centripetal force (Ww) differ due to the latter being the mass times the gravitational force, instead of an experimentally-determined value like Fc. Data See attached. Analysis The period for one revolution was calculated as follows for trial 1: T= t/N = 61.621s/53 = 1.163s The circumference of the circle that the mass moves in was calculated for trial 1 as follows: d = 2pi*r = 2(3.14)(0.18m) = 1.13m The speed of the mass was calculated for trial 1: v=d/t = 1.13m/1.163s = 0.97m/s The centripetal acceleration for the mass was calculated as follows for trial 1: 2 2 2 ac =  v /r = (0.97m/s) /0.18m = 5.25 m/s The centripetal force required for the mass to achieve the centripetal acceleration was calculated as follows:

Fc= mv2 /r = (0.365kg)(0.97m/s)2 /0.18m = 1.91N The percent difference values for each trial are shown below. Trial Number

Percent Difference

1

-48.38%

2

-38.67%

3

-37.21%

Average

-41.42%

Table I: Percent Error Sample Calculation: percent differencetrial 3 = [(calculated-measured)/calculated] x 100% = |(8.47N-13.49N)/13.49N| x 100% = -37.21% This experiment demonstrates that centripetal force can be experimentally determined based on the mass of a rotating object and the time it takes for that object to make a certain number of rotations. This centripetal force can then be compared to the force (i.e. weight) to pull the mass to the same radius using a pulley system. The experimental centripetal force (Fc ) can be compared to the actual centripetal force (Ww) using the percent difference formula. The percent difference values shown in table 1 above indicate that it is difficult to measure and calculate centripetal force exactly, particularly when it involves maintaining an exact radius of rotation by hand. Therefore, the average of 41.42% difference indicates a source of random human error that cannot be avoided. However, since the percent difference values were not extremely large, our results support the theory of centripetal force. The results of this experiment also indicate that a larger centripetal acceleration corresponds with a larger centripetal force, both for the calculated force and for the force measured from the hanging weights. This makes sense, as force is directly proportional to acceleration. A smaller period (T) was also associated with a larger centripetal acceleration. Again, this makes sense, as a shorter time for a revolution would mean the object was moving at a greater speed, and acceleration is directly proportional to the square of the velocity. Furthermore, since the formula for centripetal force is Fc = mv2 /r, the expectation is that centripetal force will increase as velocity increases. This was the case across all three trials, playing a more significant role than an increase or decrease in radius, since the velocity value is squared. Conclusions The prediction that a larger velocity will correspond to a greater centripetal force was supported by this experiment. Additionally, a smaller period was associated with a larger centripetal acceleration and a larger centripetal force. The experiment was successful in reiterating the concepts and equations of centripetal acceleration and centripetal force. The set-up of the instrument physically showed how an object that moves in a circular orbit more quickly has greater centripetal force and acceleration. The results are significant in that they support the equations of centripetal force and acceleration, while simultaneously indicating the presence of human error in maintaining constant speed through the larger percent difference values. To improve this experiment, it would be useful to have a machine that could

ensure that a constant speed was maintained by the apparatus, keeping the hanging weight at the correct radius. If this is too advanced, a simple piece of paper that could stick up at the correct radius value so the weight would hit it during each rotation would be useful. Questions 4.) The calculated centripetal force from measurement is more likely to be in error. This is because the calculation was based off a velocity that is assumed to be constant. However, since the apparatus was being spun by a human rather than a programmed machine, it is likely very inaccurate. The apparatus would often begin to slow down, only to have to be spun again. This resulted in an uneven velocity that lead to an inaccurate centripetal force calculation, which is based on a constant velocity maintained at a constant radius, which was difficult to achieve....