The Relationship Between Centripetal Force And Velocity Environmental Sciences Essay

The Relationship Between Centripetal Force And hurrying Environmental Sciences EssayInvestigate the kinship among inward-moving contract and velocity in bill doing, when a violateper is swung with a draw guide in which assorted burden hangers ar attached to.DATA appealingness AND PROCESSINGAccording to Mr. Isaac Newton, an goals natural state of motion is to stay at rest if its already at rest or to continue in additive, uniform motion unless its subjected to a net, external tweet. This means that if an object is pitiful at constant velocity (or speed) in a straight line, it every(prenominal)ow for continue to move in a straight line, at that equal velocity, unless around outside force changes its motion in some way.So in order for an object to move in a flyer path, some force is requested to pull it away from the straight-line trajectory it wants to sustain (i.e., its natural state of motion). Some force needs to pull the rotating object in at every single poi nt along its circular path in order for it continue moving in a circular fashion (instead of allowing it to follow its natural state of motion)1.If an object moves in a circular path on that point essential be receptive Force playing on it. In this audition we ordain bottom of the inningvas the relationship amid centripetal force and velocity. neighboring we provide read how our raw info is going to be manipulatedInitially we exit suggest T for 20 revolutions, at all(prenominal) trial. Subsequently the average for 20 revolutions pull up stakes be boded (based on 3 trials).Using this averaged quantify we will enter the period of 1 revolution. In this process we will lay down to divide the unbelief in cartridge clip by 20. dilate about hesitancy calculation will be extended later on.Next we atomic number 18 going to calculate the average analogue speed, v, of the fire hydrant for each portion of the weight hanger. We will include a sample calculation. We mu st remember that we apply a fixed radius of 0.5 meters.We have to patronage in mind that we will have to add the per centum question in the radius and the percentage question on T and add them up when reckon the suspicion for linear velocity.Theoretically, the centripetal force should be directly proportional to the whole of the speed. In order to check this, a column v2 will be added to unity of our data tables. When we do that the uncertainties on V must be squ ar up.We will in like manner display a column indicating the centripetal force. We know that the centripetal force is equivalent to weight in this experiment the weight, in turn, is equal to the tension on the delineate. When calculating the distrust for the resultant force (weight) we took the unbelief on mass and figure it by ten which is the gravity protect. In order for us to calculate centripetal force the following formulas will be usedFc = mv2/ rFc = W = mgThe uncertainties involved with the measureme nts which have fixed grades arCen cadenceters 1cm .05cmTime 1s 0 .005sMass 1kg 0.000005kgUNCERTAINTY ON TThe uncertainty on T is the same of that on the stopwatch. As we start and stop the stopwatch we must, thence, double the uncertainty 2(0 .005) = 0.01SAMPLE CALCULATION OF T FOR ONE REVOLUTION OF A MASS OF 0.1 KGAverage T for 20 revolutions 15.3Average T per revolution 15.3 / 20 = 0.765Uncertainty was also divided by 20 (0.01/ 20) = 0.0005As the uncertainty on T was already multiplied by 2 we do not need to double it this ageCALCULATING UNCERTAINTY ON VELOCITY FOR 0.1 KGAs mentioned earlier now we will have to calculate percentage uncertainties. We will apply the following formulahttp//scidiv.bellevuecollege.edu/Physics/measuresigfigs/Measuresigfigseq1.gifPercentage uncertainty in radius (0.05 / 0.5) x 100= 1.0%Percentage uncertainty on T for 1 revolution (calculated above) (0.00025/ 0.765) x 100 = 0.0326%By adding p the above uncertainties we catch up with the percentage uncertainty for velocity which is 1.0326% in this case.In order to obtain the percentage uncertainty for v2 we simply square the uncertainty on v.SAMPLE CALCULATION OF V FOR 0.1 KGv = 2 pi r/TV= = 4.106 1.0326%In addition we will calculateUNCERTAINTY ON MASSThe uncertainty on mass was calculated based on the electronic scale used. The uncertainty on the scale was 0.05 grams. Since we need the uncertainty in kg we multiply this nourish by 1000 and we get 0.00005 get across 1 Showing magnitude of resultant force and averaged resultsMass (kg) (0.00005)Centripetal Force (N) (0.000005)T for 20 revolutions ( seconds) (0.01)Trial 1Trial 2Trial 30.1000001.00000015.5014.8115.560.1500001.50000013.6913.8013.910.2000002.00000012.3112.7612.430.2500002.50000011.5711.5511.610.3000003.00000010.4011.2010.800.3500003.50000010.3810.0110.21In table 1 we maped the value obtained in each trial for 20 rotations. In table 2, on the other hand, we are going to present the average value of 1 rotation fo r each mass. By doing so we believe to have increased the accuracy of the results. In order to calculate the uncertainty for 1 oscillation we divided the uncertainties in 20 rotations by 20 as the left-most column (table 2) provides.In spite of that there were cases where the discrimination between the highest and last-place value obtained were greater than the uncertainty itself. In the cases where this happened we anchor the struggles between these values (highest and lowest) and use it as the uncertainty. Now we will show these differences between higher and lower values.In the 3 trials for 0.1 Kg the difference between the highest and lowest value is 15.56 14.81 = 0.75. Hence this value will be used as the uncertainty as it is greater than the uncertainty in time.In the three trials for 0.15 Kg the difference between the highest and lowest value is 13.91 13.69 = 0.22. Hence this value will be used as the uncertainty as it is greater than the uncertainty in time.In the thr ee trials for 0.2 Kg the difference between the highest and lowest value is 12.76 12.31 = 0.45. Hence this value will be used as the uncertainty as it is greater than the uncertainty in time.In the three trials for 0.25 Kg the difference between the highest and lowest value is 11.61 11.55 = 0.06. Hence this value will be used as the uncertainty as it is greater than the uncertainty in time.In the three trials for 0.3 Kg the difference between the highest and lowest value is 10.80 10.20 = 0.60. Hence this value will be used as the uncertainty as it is greater than the uncertainty in time.In the three trials for 0.35 Kg the difference between the highest and lowest value is 10.38 10.01 = 0.37. Hence this value will be used as the uncertainty as it is greater than the uncertainty in time.Table 2 Preparing the results for graphical immortalizeical analysisT for one revolution (seconds) (0.0005) sacrosanct Uncertainties ( seconds)Percentage uncertainty on T ( %)V (m/s)Percentage u ncertainty on V ( %)V2 (m2/s2)Percentage uncertainty on V2 ( %)0.765000.750.0006534.1051.00065316.8591.0013060.692090.220.0007224.5371.00072220.8571.0014450.622390.450.0008035.0451.00080325.4571.0016070.578800.060.0008645.4251.00086429.4301.0017290.539700.600.0009265.8181.00092633.8461.0018530.510400.370.0009766.1521.00097637.8501.001953Now we will plat square root of centripetal force against V. We will require use of the percentage uncertainty on V to plot the crosswise error bars and the uncertainty on centripetal force to plot the vertical error bars. The uncertainty on centripetal force is 0.000005 and, therefore must be squared to give us the uncertainty on. So we have which is equal to 0.002236. Thus we have explained how our error bars were calculated. The graph we came across was the followingGraph 1 Showing correlation between and VNot as we were expecting the graph resembles a parabola. We believe that, in order to obtain a straight line we must square both the centri petal force and velocity. This will give us the rest found in the formula F = mv2/ r. We believe that, by plotting this graph we will be able to prove our prediction that the velocity squared is proportional to centripetal force. By plotting the mentioned correlation we getGraph 2 Showing correlation between Fc and V2Even though the trump out linear run short is not a perfect straight line there are no big discrepancies in our results (such as an outlier). The RSME value or the root means square error tells us how far the linear fit is from the plot points. The value of 0.02 is really low and suggests that the best fit is really close to the original data. Also the difference between the workable maximum value and possible minimum value of the spring is so lowMaximum slope 0.13Minimum slope 0.11Difference 0.02So we have the slope of our straight line being 0.12 0.02Be elbow grease the RSME value is low, we give the bounce infer that the value obtained is realistic. In additio n due to the fact that the best linear fit touches (including or not the error bars) all the data points we can infer that the graph is accurate and, consequently, so are our results. close AND EVALUATIONAll in all this investigation led to sensibly precise results. We do however think that the experiment can be improved in several ways. The following improvements would increase the reliability of the observational procedure.Among the difficulties involved in the experiment we found, for instance, speed which we did not manage to cargo hold constant when swirling the mass. Every so often the movement of our body would modify the speed at which the mass was being swung. In addition the spend rotation was not constantly a horizontal line. These factors will cause our results to become less accurate. farthermore we faced some difficulties when swinging the stopper with constant power and speed sometimes our hands touched the string which was not supposed to be touched during the r otations. The stopwatch delay and the tender reaction time also affected our results to some extent. For example in a time of 5 seconds the pitying reaction time of 0.7 seconds can be very significant in the result as 1.4 seconds are involved in starting and stopping the stopwatch. Therefore these factors together are the responsible for us not obtaining a perfect parabola and consequently a perfect straight line. Moreover we found really hard to assure the initial and final point in relation to which the rotations were being counted. This in all probability led us to miscount the number of rotations. Therefore in some cases we might have had more or less than 20.Many changes could have been made to the experiment to make it more accurateSetting up a better method of counting the rotations completed by the give by using more advanced equipment than merely relying on human reactions.Increase the amount of rotations to ensure greater accuracy. Increase the number of repeats to ge t a more accurate average.Set up computer equipment to time the experiment more accurately. This could be done using a motion sensor connected to a data logger (logger pro 3) to record the information. By doing the experiment outside uncontrollable factors such as excite can increase friction acting upon the bung and alter the time by small amounts which still make the experiment less accurate.Further work as increased number of repeats could be carried out. In addition, different experiments can be done with increased number of rotations and larger radii. If one decides to investigate the effect of another variable such as radii the experiment will keep the same the only difference will be that the weight hanger will be kept constant and the radii will vary. If we unflinching to increase the radii being investigated we would conclude that as the radius increases so would the time to complete 20 rotations for the bung, in a proportion directly cogitate to the increase in distance . This is because we know that F = mv2/ r. Where F = force, m = mass, v = velocity and r = radius. So if r is increased then all the other variables increase in direct proportion to the initial increase. Newtons prototypic Law states that an object travels at constant velocity unless acted on by an unbalanced force. The unbalanced force is the weight in our experiment which increases the force making the speed increase because more force is being added. Therefore, this explains why the speed increases.Now we will try to explain our results based on our scientific knowledge. If we draw a free body diagram of what is natural event during the experiment we will come to the conclusion that the tension in the string (which is equal to the centripetal force) is being produced by the force of gravity which is acting on the load being used. From graph 2 we see that centripetal force increases in a direct proportion to the square of velocity. This relationship is further explained by the f ormulaF =Since m and r are kept constant and v is our dependent variable we see that force, in fact, should increase as our experiment suggests. Thus our experiment proves the formula for centripetal force.Looking at the experiment we see that fairly good results were obtained. They, contempt the uncertainties, allowed us to prove Hooks Law. Due to the fact that the experiment was dynamic, a few sources of errors affected our results. We see that the curve obtained is pretty close to a straight line which is reinforced by the low RSME value. All in all this tells us that the method is reliable and lead to precise results.