# Introduction understand air resistance and consequently how fast

Introduction

This experiment proves that The concept of free-fall

provides underpinning knowledge in order to understand air resistance and

consequently how fast objects fall. Without proper knowledge of these concepts,

it wouldn’t be possible for people to use parachutes or go skydiving, for

instance.

The objective of the experiment was to neglect the drag

force caused by air resistance and try to calculate the acylation using suvat

equations. Comparing the results with the actual acceleration then gives

insight on how air resistance affects these bodies.

Theory

To understand the concept of free-fall, it is first necessary

to refer to Newton’s Second Law of Motion, which states and is commonly known by

the formula:

(1)

Where F is the force (N), m is the mass (kg) and a is

acceleraton (m/s²).

In the scenario of any given object falling freely within

the Earth’s gravitational field, its acceleration will always be the one due to

gravity, amounting to approximately 9.8 m/s². This acceleration is independent

of 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, known

as drag. In any body falling towards Earth, the acceleration will be directed

downwards and the drag upwards.

This drag force helps deaccelerate the body and is expressed

by the formula:

(2)

Where p is the density of the air, A is the area of the

object that is in contact with the air, Cd is the drag coefficient and v is the

velocity.

As the body starts to deaccelerate, it reaches one point

where equation 1 will be equal to equation two and at that point the velocity

will be constant.

This concept is crucial as it helps is predict how fast an

object will fall and what to do to reduce its landing speed.

On the other hand, there are cases where the drag force is

too small that it can be ignored and in these instances we can use SUVAT

equations to determine either the time, the acceleration of the distance of something

in free-fall.

Given the suvat equation :

(3)

Where s is the total distance, u0 is the initial velocity, t

is time a is acceleration.

If we wish to the acceleration, given that the initial

velocity is 0, we can rearrange formula 3 to get:

(4) or

(5)

Using equation 5 you can find out the acceleration, but

there’s also the possibility of plotting a graph of the time squared against

the distance, which would mean that the slope of the graph would be half the

amount of a, due to the fact that in the formula we’re using 2s.

Experimental method

In order to calculate the acceleration of the two balls, we

used a set of devices that when connected between each other could precisely

calculate the time between the ball dropped and it reached the floor.

A magnet drop box was placed at the top in a way that when

it was on, it would hold the balls (a small magnet was added to the plastic

balls so it could be held suspense). Once the timer was activated, the drop box

released the ball and when it reached the detector pad at the bottom, the smart

timer would give the total amount of time taken. This can see in more detail on

the 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. The

total distance was calculated used a measuring tape.

Figure 1: The system set up with one of the balls being held

by 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 smart

timer would have the total amount of time taken for the given distance.

After collecting the time measurements for different

distances for each ball, a plot of time squared against distance was done using

equation … and the gradient of that times 2 would give us the acceleration.

Alternatively, it was also possible to rearrange the formula

in 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 results

with the expected acceleration due to gravity.

Results

Looking at the graph, it is noticeable that both lines are close

to each other, but that their gradient, and consequently their acceleration, is

different.

The calulation of the gradient was done using equation … and then it was

multiplied by 2.

For the plastic ball the gradient was Mpb =9.12m/s2 and for

the steel ball it was Msb = 9.67 m/s2.

Using error progration fomulas on ….. we get that the error

for the plastic ball as … and the steel ball was …