How Height Affects Time Taken for A Falling Object to Reach Ground Level Essay Example for Free

How Height Affects cadence Taken for A Falling heading to Reach Ground Level EssayIntroduction In this investigation, how flower bequeath affect the prison term taken for a steel cluster pram to reach the fusee will be investigated.It is was Isaac Newton that first discovered gravity and wrote laws defining it. His Second Law of Motion states that the Resultant Force on an object (F) is personify to the Mass of the body (m) times its speedup (a), or .The weight (W) of a body is the force of gravity acting on it, which gives it acceleration (g) if it is falling freely close to the earths surface. If the body was to have a mass (m) Newtons 2nd Law of Motion could calculate its weight. Given that and Newtons Law becomes .In April of 2003, in a method standardized to that, which will be conducted in this investigation, the acceleration of gravity was concluded to be 9.81.Using the knowledge menti aned above, several equation of doing have been created. One particularly rel evant to this investigation is .In this equation S = Distance in meters (In this case height)u = Initial velocity in *t = Time Taken in secondsa = Acceleration in *** As the ball begins its fall from rest, its initial velocity, u, will be 0** As the ball is falling under acceleration due to gravity, = 9.81Plan In this investigation, since the means to calculate air resistance and friction are unavailable, they will be cut. Acceleration due to gravity and the method by which the investigation will be carried out are controlled variables. The height from which the ball is dropped is the in qualified variable, i.e. the variable that is changed and the dependent variable is the time taken for the ball to reach the ground.It is predicted that as the height from which the ball is dropped decreases, the time taken for the ball to reach the ground will too decrease. An actual set of predicted values can be predicted from the earlier mention Equations of Motion.This line of the equation ca n be related to the straight-line graph equation , (the gradient) and . When the ball is dropped from 0.00m, it takes 0.00seconds to reach the ground as this will mean that the graph will pass through the origin so .Alternatively .Using the above equations, the expect takingss for the investigation areHeight H, (m)Time t, (secs)Time squared t2, (secs2)1.00.4520.2040.90.4280.1830.80.4040.1630.70.3780.1430.60.3500.1230.50.3190.1020.40.2880.0820.30.2470.0610.20.2020.0410.10.1430.0200.00.0000.000This is what the expected graph of Height vs. time should look alike(p)Height (m)Time (secs)The chase page shows what the expected graph for Height vs. time2 should look like. It is a straight line passing through the origin, thus proving the prediction .The expected gradient, m, should be equal to 1/2 g, or, 4.905ms-2. It is actually 4.926ms-2, which is whole 0.021 ms-2 out or 0.428%. This is probably due to the rounding of decimal places when drawing the graph and human error in plotting t he points (i.e. not exactly accurate to 3 decimal places.)Apparatus DiagramSafety As there is a precise minimal risk in this investigation, no safety measures need to be taken.It is planned to drop the ball from a height of 1m and decrease in intervals of 0.1m. At each height 5 readings will be recorded and then the mean result will be calculated. This makes the results more reliable (and better for use in calculation like working out g or the mass of the steel ball.)The Results will be recorded in a table like thisHeight (cm)Time taken for ball to reach ground (seconds)Mean ResultMean Result21st2nd3rd4th5th10090807060504030201000It is hoped that a graph of height vs. the mean results squared will be produced similar to that on page 4. In the graph, it is hoped to prove that the time-taken-for-a-ball2 to fall is directly proportional to the height it is dropped from, i.e. .Obtaining EvidenceHeight (cm)Time taken for ball to reach ground (seconds)Mean ResultMean Result21st2nd3rd4th 5th1000.4560.4540.4580.4540.4540.4550.207900.4320.4310.4310.4320.4320.4320.186800.4060.4070.4060.4070.4060.4060.165700.3800.3820.3820.3830.3810.3820.146600.3530.3540.3540.3540.3540.3540.125500.3230.3230.3220.3220.3220.3220.104400.2890.2880.2930.2890.2870.2890.084300.2520.2510.2510.2500.2510.2510.063200.2080.2070.2060.2060.2060.2070.043100.1500.1500.1500.1500.1510.1500.023000.0000.0000.0000.0000.0000.0000.000Graphs In the following pages, the results recorded in the above table will be shown in the form of line graphs. This will make it easier to identify a trend in the results. It is also an appropriate method of recording the information and is useful for quick reference also if the time for the ball to fall is desired from a height other than the ones specified in the table, the value can be obtained from the graph.Conclusion The general trends from the graphs show, as predicted when the height from which the ball was dropped decreased, the time taken for the ball to reach the gro und also decreased.In the graph of Height vs. Time2,, it is shown that Height is directly proportional to Time2. The reason for this is derived from one of the Equations of Motion , from this equation below, it was shown that .The final line of the above equation can be related to the straight-line graph equation . , (the gradient) and . C can be ignored as the line in the graph passes the y-axis at the orgin.Fundamentally .H = S = The height in meters from which the ball was dropped.= The time in seconds that the ball took to land.a = g = The acceleration due to the gravitational pull of the earth.Note The factor that affected the acceleration was g, (which, on earth, is ) is the mass of the planet, for Earth this is constant.The results of the investigation are concordant with the prediction. The relationship of was proved in the similarity of the graphs on page 4 8, they had almost the exact same gradient, only 0.072ms-2 in difference (or 1.462%) it was also very similar to the mathematical prediction of the gradient (1/2g) again only 0.051 ms-2 out.Evaluation In this investigation, all results are held to be very reliable. When the data was being collected, train technology was used which measured time accurately and reliably to the nearest thousandth of a second. All recorded results were in very close proximity of each other, so that 0.006seconds was the maximum difference observed.There were no anomalies observed. All points on the graph on page 8 are not only close to the line of best fit, they are actually on it.The results in this investigation are believed to be very reliable as a result no changes need to be made to the procedure.