# Investigation into how the speed of a falling cone is affected by its mass

Planning

Apparatus list:

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* Sugar paper

* 1 meter ruler

* Stop watch

* Scales

* selotape

* plastercine

* Compass

* Ruler

* Protractor

The cone will look some thing like this:

I will drop the cone from a height of 2.5 meters

I did a preliminary experiment to test different heights, these are my results:

Height (Meters)

Time (Seconds)

1m

0.72s

1.5m

1.22s

2m

1.47s

2.5m

1.78s

I chose the height of 2.5m because I thought that this would be the best height to do my experiment and I thought that it would give me a clear set of results. To show me if any of me result reach terminal velocity or not it would also show me which one had the fastest speed and which one had the fastest time.

I will time how long it takes the cone to fall from my chosen height (2.5m) to the ground.

I will repeat the experiment 3 times. I did a preliminary experiment to decide how many repeats are necessary these are my results:

Height (Meters)

Time (Seconds)

2.5m

1.78

2.5m

1.75

2.5m

1.72

I chose to repeat my experiment 3 times because if I do my experiment once the results might be wrong so if I do it 3 times it will make sure that my results are right and it will also show me if my results are accurate.

The ranges of values that I will investigate are 8g-24g. I chose this range because I think it will give me a clear indication to see if it falls faster or slower and if there is a pattern. I have not chosen to do any weight over 24g because it would drop like a stone ( drop really fast) and it would also be too hard for me to time it would also not show a clear set of results.

To make my investigation fair I will control the following factors:

* Keep the same height

* Hold the cone in the same way

* Drop the cone from the same place

* Not drop the cone from outside because the wind might affect the way that the cone falls.

* Keep the surface area of the cone the same. (The air resistance will be the same)

* The same cone will be used.

Prediction

I think that the 24g cone will fall the most quickly and the 8g cone will fall most slowly. I think this is because the weight of the 24g cone will be more than the weight of the 8g cone, the weight of the 24g cone will be 0.24 and the weight of the 8g cone is 0.08 (the weight of the cone is worked out by multiplying the mass in kilograms by the gravitational field strength, the gravitational field strength on earth is 10N/kg) this show that the weight of the 24g cone is higher so it will fall much faster and it will also reach its terminal velocity much faster, I also predict that the higher the mass is the quicker the cone will reach its terminal velocity. for it to reach its terminal velocity there would have to be a resultant force this is when both or all of the forces acting on the cone falling are equal this is called a resultant force this means that the cone would be travelling at a steady speed. The frictional force (drag force) on all of the cones that I test will be the same this is because it will always have the same surface area (the cone will always be the same).

Results Table

Mass (Grams)

Test 1 (Seconds)

Test 2 (Seconds)

Test 3 (Seconds)

Average (Seconds)

Speed (M/S)

8g

1.75s

1.72s

1.71s

1.72s

1.4m/s

10g

1.40s

1.56s

1.50s

1.48s

1.6m/s

12g

1.38s

1.31s

1.39s

1.36s

1.8m/s

14g

1.22s

1.28s

1.25s

1.25s

2m/s

16g

1.13s

1.09s

1.19s

1.13s

2.2m/s

18g

1.10s

1.19s

1.00s

1.09s

2.2,/s

20g

0.97s

1.12s

0.97s

1.02s

2.4m/s

22g

1.00s

1.09s

1.00s

1.03s

2.4m/s

24g

0.94s

0.94s

0.94s

0.94s

2.6m/s

Analysis

I found out that if there’s more mass the time of the cone falling decreases, this is shown by the graph and by the results table. I also found out that as there’s more mass in the cone the cone also accelerates faster.

My graph shows that as the mass of the cone raises the time decreases, the graph also shows negative correlation. The pattern of the graph is that as the time decreases the mass gets higher. The graph starts of high and then start to drop rapidly and then it slows down slowly and then start to level of a bit. (I think that this may be showing terminal velocity).

The 14g cone fell the fastest this happened because there was a bigger resultant force pulling it down so it fell down to the ground faster, on the 8g cone there was a resultant force but it wasn’t as big as the resultant force on the 24g cone this is why the 24g cone fell to the ground quicker it also fell to the ground quicker because it was travelling faster than the 8g cone this can be seen in the table, I also worked out the speed of the cones on my table by dividing the distance by the time I did this so I could see which one travelled the fastest, the more mass that there was in the cone the bigger the resultant force there was ( there is more weight pushing the cone down) .

I think that some of the masses that I tried might of reach terminal velocity (16g, 18g, 20g, and 22g) I think that this is because on my results table the speed of these four results is the same this means that some of them may have reached terminal velocity. This is shown on my graph because most of the lines start of high and then start to drop rapidly and then they start to level of a bit I think this is showing the terminal velocity but this is not shown clearly because the graph does not carry on long enough to see if this is right or if it wrong to make this clear I would have to use a higher range of masses to see if they did reach terminal velocity or if they didn’t.

The air resistance on my cone was always the same this is because I didn’t change the cone I only changes the weight of the cone, the shape of the cone could have made a difference on the air resistance. The air resistance on my cone could have been affected this could have been affected if the cone was dropped at a different angle or if there was a little breeze in the room or if there was a window open this could have made a difference in my results.

The gravitational force was always the same (10N/kg) the gravitational force would only be different if we were on another planet or if we were in space the gravitational force could not have affected my results.

I found that my prediction was right in my prediction I said that the 24g cone will fall the fastest because its weight and its mass was higher then the 8 g cone and this was right it did fall faster it fell faster in its time to reach the ground and in its speed. In my prediction I also said that the 8g cone will fall slower because its weight was less then the 24g cone this was also right it was slower in the time that it reached the ground and in its speed. I think that my prediction about the terminal velocity was right (the higher the mass is the quicker the cone will reach its terminal velocity)but I cant be sure about this to make sure of this I would have to do some further work( I would have to use a higher range of values).

Evaluation

From looking at my results table, I saw that two of my repeats look out of place, on the 20g test 1 and test 3 look out of place this is because they fall faster then the 22g (there time is less) but test 2 looks ok. I think that they are out of place because the experiment might have been done wrong or it was because they weren’t timed properly.

I think that most of my results are reliable this is because I repeated each experiment three times, my repeats were close except for the two that look out of place. I think that I could have improved my experiment by using more advanced equipment such as the speedometer.

I think that I don’t have enough evidence to certainly say that any of my results did reach terminal velocity but there is a little indication, to see if any of them did reach terminal velocity I would have to do some further work.

If I did this experiment again I would use a higher height, I would also think about using a higher rang of masses I think using a higher height or a higher range of masses might have gave me a better set of results because it might of gave me a clear indication if any of my tests reached terminal velocity or not.

I found it difficult to time the cones falling this was because I hade to start and stop the stop watch at exactly the right moment and if I did this wrong I would also get a wrong set of results to make it easier to time the cone falling I could use more advanced equipment e.g. speedometer.

I could do some further work if I did this I would use a different height to see if any of my masses reach terminal velocity that way or I could use the same height but I could use a higher range of masses this would show me if my results did start to reach terminal velocity and it would also have proved my prediction right about the terminal velocity and the mass. In my further work I would also use more advanced equipment like the ones listed above e.g. speedometer.