# Marked Report 2

# Design Practical using plasticene

#### Research question

This practical is an investigation into an object dropped over a uniform plasticene cube. A book is dropped over the plasticene and gets smashed, then the surface area under the cube increases. I decided to investigate the relationship between the different heights from where the object is dropped and the expanded area after the cube is smashed. Therefore my research question is:

__How does the expansion of the bottom face area of a plasticene cube depend upon the height from where an object is dropped over it?__

#### Variables

__Independent Variable__: The height of release

__Dependant variable__: The expanded area of the bottom face of the cube

__Controlled Variables:__

- Mass of the object being dropped
- Volume of the plasticene cube
- Initial surface area of the bottom face of the cube
- The height where object being drop

#### Method

The apparatus I am going to use to develop this practical are listed below:

plasticene

Four rulers

A flat surface (table)

A stand

A heavy uniform object (thick book)

Squared sheets

In order to keep the under surface constant in all the trials I placed two rulers perpendicular to each other placed in a fixed position over the table in order to create a corner. I placed the plasticene and then used another ruler to compress it until get a cube shape. I draw two perpendicular lines next to the cubes sides; hence each time I would compress the plasticene until make it feet into the lines and therefore keep the same volume.

The following picture will help to give a better understanding of what has been done:

In addition, in order to make sure the under surface was kept constant, I placed the cube over the squared paper, draw the contour of it over the paper and then measure the area by counting the number of squares in it.

To measure the height from where the uniform object was going to be dropped I attached a ruler in vertical position to a stand. All measurements were made from the bottom of the object since by doing this I could make a straight line and therefore it was easier to measure the height with the ruler. The object I used was a book because it presented uniform sides and a flat faces, this was helpful for making the straight line. (And also for making sure the smash was done uniformly over the cube surface). To reduce parallel errors the measurements were done placing my head in line with the bottom of the object. I used always the same book and the same ruler to keep these variables constant.

After I dropped the book sometimes over the plasticene I found that if the cube was too big the under surface won’t experiment any considerable change. Therefore I used a smaller volume; using the process mentioned before. (*The area I tried to get was 3.5 cm ^{2})*

In order to measure the expansion of the under surface area I placed the smashed cube over the squared paper, drown the contour and measure the area by counting the number of squares into it.

I choose 5 different heights and I repeated the process, at least, 5 times for each height. I choose a range from 30 cm. to 100 cm. make a fair difference in height

#### Results

The values taken from the experiments are displayed in the following table. The uncertainty in height was considered to be half of the smallest division of the ruler (0,1 cm). The uncertainty in area has been found by subtracting the min. area value from the max. area value and then dividing the result by 2.

Since occasionally some obvious wrong value was taken, it was ignored. A new trial was done in that case.

#### Conclusion and Evaluation

The graph seems to follow a proportional relationship between the height dropped and the area expanded since it passes through all the error bars. In addition, if we measure the change in area, we would have to subtract 3.5 cm^{2} from each area and the y-axes intercept will reduce by 3.5 as well. By doing this the line is very close to the origin (0,0)

Maximum and minimum error lines were not plotted since the purpose of finding this value will be added to the result of the slope. However, there is no equation that be used in this case and therefore they were not plotted.

The error bars values could be reduced if taking wider range of heights. However air resistance might affect the process since the book has a big flat area. A heavier object could be use in this case.

The error bars look big but reasonable since the difficult to measure an accurate area. I tried to make a uniform cube for every trial, it was close to be uniform in all trials but there was always some difference. Some improvements which could be done are creating a different method to keep the area always exactly the same, making a mold for instance; then we will always have a shape closer to a perfect cube.

#### Improvements

A problem I experienced in the first trial was that I loss some mass of the plasticene, since I had placed it over the squared sheet of paper. It was really stack and some pieces stayed in the paper when pulling it up. Afterwards I found a surface which did not create the same effect; however when I had to pull it up sometimes it got a bit stack and therefore I pressed it a bit with my fingers, this may have vary the result a bit(no mass was lost though). Since we always will have to use pressure to pull the cube up, we should measure the area before doing this. We could place the cube over a plastic sheet, which will be over a squared paper; draw the contour with a marker over the plastic and then pulling it up.

Another improvement could be done for measuring the area. It was very hard to measure due to the inconsistent and non-uniform shape the plasticene after being smashed, in addition the size of the squares in the paper sheet were quite big. We could get sheets with smaller squares or take a picture of the contour and then use a computer program to measure the area inside it.