IntroductionThis experiment proves that The concept of free-fallprovides underpinning knowledge in order to understand air resistance andconsequently how fast objects fall.
Without proper knowledge of these concepts,it wouldn’t be possible for people to use parachutes or go skydiving, forinstance. The objective of the experiment was to neglect the dragforce caused by air resistance and try to calculate the acylation using suvatequations. Comparing the results with the actual acceleration then givesinsight on how air resistance affects these bodies.TheoryTo understand the concept of free-fall, it is first necessaryto refer to Newton’s Second Law of Motion, which states and is commonly known bythe formula: (1)Where F is the force (N), m is the mass (kg) and a isacceleraton (m/s²).In the scenario of any given object falling freely withinthe Earth’s gravitational field, its acceleration will always be the one due togravity, amounting to approximately 9.8 m/s².
This acceleration is independentof the mass of the object since gravity will act equally on each object.If there weren’t any other forces acting on the objects,then every object in free fall under the same conditions would fall at the time.However, this doesn’t happen due to an opposing Force exerted by the air, knownas drag. In any body falling towards Earth, the acceleration will be directeddownwards and the drag upwards.
This drag force helps deaccelerate the body and is expressedby the formula: (2)Where p is the density of the air, A is the area of theobject that is in contact with the air, Cd is the drag coefficient and v is thevelocity.As the body starts to deaccelerate, it reaches one pointwhere equation 1 will be equal to equation two and at that point the velocitywill be constant.This concept is crucial as it helps is predict how fast anobject will fall and what to do to reduce its landing speed.
On the other hand, there are cases where the drag force istoo small that it can be ignored and in these instances we can use SUVATequations to determine either the time, the acceleration of the distance of somethingin free-fall.Given the suvat equation : (3)Where s is the total distance, u0 is the initial velocity, tis time a is acceleration.If we wish to the acceleration, given that the initialvelocity is 0, we can rearrange formula 3 to get: (4) or (5) Using equation 5 you can find out the acceleration, butthere’s also the possibility of plotting a graph of the time squared againstthe distance, which would mean that the slope of the graph would be half theamount of a, due to the fact that in the formula we’re using 2s.Experimental methodIn order to calculate the acceleration of the two balls, weused a set of devices that when connected between each other could preciselycalculate the time between the ball dropped and it reached the floor.
A magnet drop box was placed at the top in a way that whenit was on, it would hold the balls (a small magnet was added to the plasticballs so it could be held suspense). Once the timer was activated, the drop boxreleased the ball and when it reached the detector pad at the bottom, the smarttimer would give the total amount of time taken. This can see in more detail onthe pictures below: The drop box was also set up in a way where its height was adjustable,and it was possible to try the experiment with several different heights. Thetotal distance was calculated used a measuring tape.
Figure 1: The system set up with one of the balls being heldby the drop box. Figure 2: One the time was pressed, the ball would instantly drop. Figure 3: One the ball reached the detector pad, the smarttimer would have the total amount of time taken for the given distance.After collecting the time measurements for differentdistances for each ball, a plot of time squared against distance was done usingequation … and the gradient of that times 2 would give us the acceleration.Alternatively, it was also possible to rearrange the formulain terms of a and get the acceleration from that. In this experiment, however,the first method was used for both balls.
With that data, it was then possible to compare the resultswith the expected acceleration due to gravity. Results Looking at the graph, it is noticeable that both lines are closeto each other, but that their gradient, and consequently their acceleration, isdifferent.The calulation of the gradient was done using equation … and then it wasmultiplied by 2. For the plastic ball the gradient was Mpb =9.
12m/s2 and forthe steel ball it was Msb = 9.67 m/s2.Using error progration fomulas on ….
. we get that the errorfor the plastic ball as … and the steel ball was …
