Investigation of the Factors Affecting the Rate at Which an Object Falls

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All objects, when no force is acting upon them, shall remain at the same steady speed, without accelerating or decelerating; so if an object is still, it shall not move and if it is moving then it shall continue moving so long as no force is acting upon them. This was explained by Newton's first law. However it must also be noted that the meaning of "no force" may also be understood as "all forces acting upon a certain object balances each other out" so the object is in equilibrium.

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Liquids and gases are known as fluids. If an object passes through either of these two mediums there shall be a force acting in the opposite direction known as "friction". One very important type of fluid friction is air resistance.

If there was no force acting upon two falling objects (both having a different mass), other than gravity, they shall both fall with the same rate of acceleration regardless of their mass.

This is explained by Newton's second law which states FORCE = MASS X ACCELERATION, so acceleration is equal to force/mass. Because the force (of gravity) is dependant upon the mass, all objects will have the same rate of acceleration. Consider the following:

means "the force of gravity".

This was further proved by the hammer and feather experiment on the moon where air resistance is scarce and the only force acting upon the two objects would be gravity (from the moon).

However on earth objects of different masses will fall very differently.

As an object falls, it continues to accelerate (because the force of gravity will be stronger than that of air resistance) until the force of air resistance is equal to the force of gravity (at this point acceleration will stop because f/m will equal one). This is call "terminal velocity". When an object reaches terminal velocity it stops accelerating. The magnitude of terminal velocity depends on the weight of the falling object. For a heavy object, the terminal velocity is generally greater than a light object. This is because air resistance is proportional to the falling object's velocity squared. For an object to experience terminal velocity, air resistance must balance weight. An example that shows this phenomenon was the classic illustration of a rock and a feather being dropped simultaneously. In a vacuum with zero air resistance, these two objects will experience the same acceleration. But on the earth this is not true. Air resistance will equal weight more quickly for the feather than it would for the rock. Thus the rock would accelerate longer and experience a terminal velocity greater than the feather.

In the early 1600s Galileo started to come up with new ideas about the link between force and motion. In a series of experiments, he rolled balls down slopes and deduced that that all falling objects light or heavy, should gain speed at the same steady rate.

It is said Galileo investigated the laws of motion by dropping cannon balls from the top of Pisa's famous tower. This is almost certainly not true. However Galileo was born in Pisa, Italy (in 1564) and lectured there.

Factors which affect the rate at which an object takes to fall to the ground:

* Weight of the object. A heavier object will fall quicker. This is because the force of gravity will be greater on a heavier object and thus its terminal velocity will also be greater (as mentioned in the latter paragraph).

* Surface area of the object. An object with a larger surface area will fall slower. This is because air resistance will act more strongly on an object which has more surfaces exposed; the reason being that the air particles will be able to intersect more areas of the object. This can be seen from the preliminary experiments 4 and 5 (shown below) where the surface area, when lessened, fell a lot quicker.

* Height at which the object is dropped. An object dropped from a higher height will have a higher speed (in accordance to speed = distance/time). This is because there would be more chance of an object reaching terminal velocity when it is dropped from a higher height.

Preliminary Experiments:

1. Method: A one penny coin is dropped from the same height as a one pound coin, at the same time.

Results: They fall (as far as the eyes could tell) at the same speed and fall to the ground at the same time.

2. Method: A tennis ball is dropped from the same height as a cricket ball, at the same time.

Results: They fall (as far as the eyes could tell) at the same speed and fall to the ground at the same time.

3. Method: A flat paper is dropped from the same height as a one penny coin, at the same time.

Results: The penny fell quicker.

4. Method: 2 flat papers are dropped from the same, at the same time.

Results: They fall at the same speed and fall to the ground at the same time.

5. Method: A flat paper is dropped from the same height as a crumpled paper (of the same weight), at the same time.

Results: The crumple piece of paper fell quicker.

Diagram showing how terminal velocity occurs:

4. 9.

In these diagrams, it is shown how a falling object will continuously fall until the force of air resistance is the same as the force of gravity (this point is called terminal velocity). The object (the man) in diagram 9 will continue to fall at this very speed without accelerating or decelerating.

Plan

Aim: to observe how the rate at which paper cups fall to the ground is affected by changing the number of paper cups and the height from which they are dropped.

Apparatus:

1. Paper cups: used as the object

2. Stopwatch: to time how long the fall takes

3. Metre ruler: to measure the height from which the paper cups are dropped

4. 3 people:

* person no.1: hold the rulers

* person no.2: hold and release the paper cup

* person no.3: time and record the results

Diagrams:

Paper cup(s)

metre ruler(s)

Method:

1. One person stands and holds a metre ruler, whilst a second holds a single paper cup to the height of 1 metre (the top of the ruler).

2. The latter drops the paper cup and a third who is watching starts the timer as soon as the paper cup is released and stops the timer when the paper cup reaches the ground.

3. The one who times fills in the table of results.

4. The previous 3 steps are repeated two more times.

5. The previous 4 steps are repeated 5 more times but with varying numbers of paper cups (rather than "a single paper cup" as in procedure no. 1): 2,3,4,5 and 6 respectively.

6. The previous 5 steps are repeated but rather than dropping the paper cup(s) from 1 metre (as in procedure no. 1), is dropped from 1.5 metres firstly and then 2 metres.

Safety:

Safety isn't really an issue in this investigation. However precaution should be taken when dealing with paper, ruler and electrical equipment (i.e. the stopwatch). The paper cups, accidentally may cause paper cuts. The ruler(s) may fall, if misused, and hurt someone. The stopwatch, if precautions aren't taken, could harm someone slightly by giving them a small electric shock.

In reality, these safety matters are very logical and would only occur very rarely or if done deliberately.

Fair testing:

All factors (mentioned in the Background Knowledge) must remain equal during the experiment except for the variable, so the following must be done to assure fairness in the experiment:

* All paper cups used must be the same ones in all experiments

* All paper cups should be almost identical (i.e. equal in weight, surface area and shape)

Other means to assure fairness are:

* The person timing is always the same person because people have different:

i. ability in eyesight

ii. speed of reaction

* The other two people should also be consistent in their respective duties as there may be slight or even major variances between them, which could affect the results.

Prediction:

How the factors of weight and height affect the rate at which an abject falls has been explained in the background knowledge: the heavier and higher the object is, the longer it shall take to reach the ground. Concluding from this information, we can deduce that paper cups dropped from 1.5 metre shall take longer to reach the ground than the same quantity of paper cups dropped from 1 metre high and a lesser time than when they are dropped from a height of 2 metres.

The higher an object is dropped, the more time it has to accelerate. An object shall continue to accelerate as long as it falls until it reaches terminal velocity in which case it shall not accelerate or decelerate but remain at a constant speed. Therefore insufficient information is known to give a verdict on how much longer paper cups dropped from 2 metre will take to fall to the ground than from 1 metre, because the terminal velocity is unknown. However what is known is that an object dropped from higher up would be more likely to reach terminal velocity, just as an object which is lighter will be more likely to reach terminal velocity. I predict that paper cups ranging from 1 to 3 (including 3) shall only reach terminal velocity if it is dropped from 2 metres because they are lighter and are dropped from quite high whereas the other experiments would be either too heavy or dropped from too low. The experiments cannot prove this latter prediction.

In conclusion, I predict that the results shall show me that:

* A heavier object takes a shorter time to reach the ground and has a greater speed - it can reach terminal velocity a lot quicker because the force of gravity is greater, causing the air resistance to also be greater.

* An object dropped from a higher height shall take longer to reach the ground, but will have a higher speed because it will have more time to reach terminal velocity.

Obtaining Evidence

TABLES:

Paper cups dropped from 1 metre

Number of cups

Experiment

0.75

0.62

0.34

0.41

0.34

0.22

0.75

0.51

0.43

0.32

0.31

0.34

0.66

0.56

0.44

0.4

0.31

0.28

Average time (secs)

0.72

0.56

0.4

0.38

0.32

0.28

Average speed (m/s)

1.39

1.79

2.5

2.63

3.13

3.57

Paper cups dropped from 1.5 metres

Number of cups

Experiment

1.12

0.94

0.78

0.68

0.65

0.56

1.18

0.85

0.75

0.66

0.69

0.62

1.19

0.87

0.75

0.66

0.63

Average time (secs)

1.16

0.89

0.76

0.67

0.66

0.6

Average speed (m/s)

1.29

1.69

1.97

2.24

2.27

2.5

Paper cups dropped from 2 metres

Number of cups

Experiment

1.53

1.12

1.01

0.9

0.78

0.81

1.5

1.34

0.97

1.03

0.84

0.75

1.75

1.22

0.88

0.84

0.78

Average time (secs)

1.59

1.27

0.99

0.94

0.82

0.78

Average speed (m/s)

1.26

1.57

2.02

2.13

2.44

2.56

GRAPHS

Paper cups dropped from 1 metre

Paper cups dropped from 1.5 metres

Paper cups dropped from 2 metres

Analysis

The graphs made from the results portray distinctly the patterns found in the results. All the time graphs have a similar trend as do the speed graphs. It seems as though if the graphs had continued, the curve would almost flatten out. This opposes my theory that the weightier an object, the quicker it'll fall. However there could be many reasons for this, the main one being that the heights were too small, thus to mark accurate results would be very difficult in such a low height. Therefore, because the time for some objects (especially the heavier ones) was really short and difficult to time using a stopwatch, heavier objects would be even more difficult to time, so they would seem similar whereas in reality they are not. In conclusion, the heavier an object the quicker it falls.

The speed graphs correspond directly with the time graphs. The average speed shall also be greater at higher heights the object will be at terminal velocity (if reached) for longer. An average speed/time graph would look like this:

The speed neither increases nor decreases after a certain amount of time. This means that the quicker an object reaches terminal velocity the greater its average speed shall be (i.e. the speed would be at terminal velocity for longer). This is why when the paper cups were dropped from higher heights they tended to have greater speeds.

Increasing the height, causes the object to have more time to accelerate, so the final speed shall be more, as seen by the results.

The conclusions to these experiments are as my prediction stated that:

* An object dropped from a higher height shall take longer to reach the ground, but will have a higher speed because it will have more time to reach terminal velocity.

Evaluation

I am pleased with my results. The results showed accuracy and the variances in the figures were minute. However I believe some minor errors may have occurred during the practical which affected the results slightly.

Firstly, the person who held the ruler could have held it bent. In addition the ruler may have moved slightly throughout the experiments so the test wasn't completely accurate. To remove this in further experiments which are similar, the ruler could be held leaning straight (at its full height) on a wall; a mark could be placed at the heights of 1 metre, 1.5 metres and 2 metres so as to assure all objects fall from exactly the same height. Read the paper helicopter physics

Another error which may have occurred is the accuracy in timing. The heights were too small, thus to time accurately would be very difficult in such a low height (because the time is so less that it would be difficult to time using a stopwatch). To aid this problem more repetitions should be made (more than 3) so that a more accurate average could be calculated.

In addition the paper cups may not have all been exactly the same in weight. To reduce this error the paper cups should be weighed and those paper cups which are not the same as the majority should be removed.

To improve this experiment, light gates could be used. This is a tool which starts timing as soon as an object passes a certain point and stops when it reaches the ground.

Further experiment may include:

* Increasing the weight (the number of paper cups).

* Increasing the heights (e.g. 2.5 metres, 3 metres, 3.5 metres etc.)

* Experiment on surface area (e.g. by folding the paper cups or flattening them out.

Almost all the results in the practical fell within the curve of best fit. From the 18 different results only 2 of them were slightly out of the curve in the time graphs. They were as follows:

* When 3 paper cups were dropped from 1 metre.

* When 3 paper cups were dropped from 2 metres.

As regards to my final results and findings, I am pleased by its accuracy and recommend this procedural method of executing further experiments of a similar nature.