Annex A - Group Research Proposal

Group Project Proposal (Science)
SCHOOL OF SCIENCE AND TECHNOLOGY, SINGAPORE
INVESTIGATIVE SKILLS IN SCIENCE
Names: Benjamin Koh (9) ,Darie Chan (12) ,Ho Jia Wei (14), Kenneth Kiang (18)
Class: S2-09
Group Reference: F

1.    Indicate the type of research that you are adopting:

[    ] Test a hypothesis: Hypothesis-driven research
e.g. Investigation of the anti-bacteria effect of chrysanthemum

[    ] Measure a value: Experimental research (I)
e.g. Determination of the mass of Jupiter using planetary photography

[ X ] Measure a function or relationship: Experimental research (II)
e.g. Investigation of the effect of temperature on the growth of crystals

[    ] Construct a model: Theoretical sciences and applied mathematics
e.g. Modeling of the cooling curve of naphthalene

[    ] Observational and exploratory research
e.g. Investigation of the soil quality in School of Science and Technology, Singapore  

[    ] Improve a product or process: Industrial and applied research
e.g. Development of a SMART and GREEN energy system for households  


2.    Write a research proposal of your interested topic in the following format:

Investigation of how the initial velocity of the cue ball affects the final velocity of the coloured balls

A.    Question being addressed

i) The problem is when people play Pool,  there is too many factors that can affect the pool balls so it is hard to hit the ball to where he or she wants.



ii) After research, we found out the factors that affects the accuracy of the ball. They are, height of the cue from the ball, area of the ball hit, the incident angle of the cue ball when striking the the pool ball, the weight of the ball, the density of the ball, size of the ball, amount of friction the Pool table fabric used has, the cue stick used, the cue bridge used, distance from the cue to the ball, initial velocity of the cue ball, distance from cue ball to pool ball, speed of wind.
iii) We plan to study only on 1 factor which is the initial velocity of the cue ball, leaving the other factors constant. So we would measure the initial velocity of the cue ball and measure the final velocity of the coloured ball. We would then try to find out how the initial velocity of the cue ball affects the final velocity of the coloured balls

The independent variables are:
(a) The initial velocity of the cue ball

The dependent variable are:

(a)  The final velocity of the coloured ball

The constants are:
(a)  The balls used
(b)  The Pool table used
(c)  The cue stick used
(d)  The cue bridge used
(e)  Distance and height from the cue to the ball
(f)   Amount of force used to hit the ball
(g)  Distance from cue ball to pool ball
(h)  Wind speed
(i)   Area of the ball hit.
(j)   The incident angle of the cue ball when striking the the pool ball

B.    Hypothesis

If there is a constant relationship between the initial velocity of the cue ball and the final velocity of the coloured ball when they hit straight on, then it is possible to derive a formula to predict the speed of the coloured ball.



C.    Description in detail of method or procedures (The following are important and key items that should be included when formulating ANY AND ALL research plans.)


Equipment list:
- 1 x Pool table, length 122 cm x width 61 cm x height 24.5 cm
- 1 x Cue stick, length 107 cm
- 1 x Cue ball, diameter 4 cm
- 1 x Coloured ball, diameter 4 cm
- 1 x Compact digital camera (Has flat body, no overly protruding parts like flashes, can record at least 720p videos, has a focal length of at most 25 mm and is lightweight). Example “Fujifilm Finepix JX200”
- 2 x Sheets of A3 size corrugated board
- 8 x Aluminum profiles, length 76 cm, base 2 cm by 2 cm
- 1 x Aluminium profile, length 134 cm, base 2 cm by 2 cm
- 12 x 90 degrees triangular connector Gussets, 2 cm x 2 cm
- 24 x Fasteners, size M4 x 8
- 1 x Allen key, screw size no. 6, socket size 0.278 cm
- 1 x Masking tape
- 1 x One meter ruler
- 1 x Pencil
- 1 x Eraser (optional)
- 1 x Blue tack (optional)
- 1 x Geometry compass
- 1 x Scissors
- 1 x Super glue
- 4 x A4 Rough paper



Procedures: Detail all procedures and experimental design to be used for data collection

Camera holder:
  1. Measure the length of the camera (Measurement 1).
  2. Measure the width of the camera (Measurement 2).
  3. Measure the diameter of your lens (Measurement 3).
  4. Measure the distances between the lens and the 2 lengths of the camera (Measurement 4).
  5. Measure the distances between the lens and the 2 widths of the camera
  6. (Measurement 5).
  7. Measure the height/thickness of the camera (Measurement 6).
  8. Referring to Measurements 1 and 2, draw them on the corrugated board using a pencil, adding an extra 2 cm for each of them.
  9. Referring to Measurements of 3, 4 and 5, and minusing the added 2 cm to the measurements 1 and 2,  locate the position of the lens on the rectangle drawn on the corrugated board in the previous step and draw the circle at the position.
  10. Using Measurement 6, multiply it by 2, add the length of the thickness of the aluminium profile and add an extra 2 cm (Measurement 7).
  11. Referring to the 2 widths of the rectangle, continue them by drawing the length of Measurement 7 on both sides of each line.
  12. Connect the ends of the 2 lines that was a product of the previous step on each sides by drawing the length of Measurement 2. (Lines 1)
  13. In each of the two lines of “Lines 1”, mark a point where the distance between it and one of the the lines in “Lines 1” is 2 cm.
  14. Take one bar of the aluminium profile and place one side of the bar at the point. Shift the bar so that the side is parallel to the side of the board.
  15. Shift it from right to left until it i estimated to be in the middle of the 2 sides


  1. Trace out the base of the bar on the corrugated board at that position
  2. Repeat on the other side.
  3. Cut out the outer shape or everything drawn.
  4. Cut out the circle
  5. Cut out the shape of the base of the bar.
  6. Slice the 2 lines in the middle of the rectangle, only slicing half the thickness of the corrugated board. It is okay to slice the back or the front part of the board.
  7. Bend the sliced part until it is 90°
  8. Tape it together on the outside and inside. Do not tape the holes.

Aluminium profile:
  1. Connect three 76 cm aluminium profiles together using 2 connectors and 4 fasteners. Make it so that it is the shape of a rectangle with one side open.
  2. Repeat once
  3. Face the 2 open sides to get to form a rectangle.
  4. Use two 134 cm aluminium profiles to connect the two shapes together. Using 4 connectors and 8 fasteners
  5. Use a 76 cm aluminium profile to connect the two 134cm aluminium profiles. Adjust the profile so that it is underneath the pool table. Using 2 connectors which are to be fastened with 4 fasteners underneath the profile.
  6. Skip step 5 if there is no gap underneath the pool table
  7. Take a 76 cm aluminium profile and slide the camera holder in.
  8. Use the 76 cm aluminium profile with the camera holder to connect the two 134 cm aluminium profile at their tip. Using 2 connectors and 4 fasteners.





Cue bridge:
  1. Draw out a rectangle with the width 13 cm and length 17.5 cm on the corrugated board. The width and length just has to be more than 4 cm.
  2. Using the Geometry compass, draw a circle of diameter 2 cm, inside the rectangle, 1 cm away from the side that you are planning to rest on the table and in the middle of the same side.

  1. Repeat Steps 1 and 2, 4 times. Which means that you have 4 rectangles with a circular hole
  2. Cut the rectangles and circles out
  3. Find a flat surface and cover it up using the A4 paper.
  4. Connect the 4 layers by adding super glue carefully. Do not glue the holes.


























Set up of the experiment:


  1. Properly set the pool table at a safe and open space. At least 2 m spacing from the perimeter
  2. Place the ruler such that it is in the middle and perpendicular to that of the head rail.
  3. Measure 12.5 cm away from the head rail and mark the point using a strip of masking tape.
  4. Label the strip of masking tape as “Point 1”


  1. Measure 13.5 cm away from point 1 and mark the new point with a new strip of masking tape
  2. Label the new strip of masking tape as “Point 2”.
  3. Place the white cue ball on Point 1
  4. Place 1 coloured ball on Point 2
  5. Place the cue bridge on the wooden part and not on the fabric part
  6. Adjust it from left to right so that the hole is facing straight at the 2 balls.
  7. Tape it tightly down using masking tape. You can add blue tack underneath for extra support.
  8. Make sure that there are no other objects on the table other than those stated.
  9. Place the aluminium profile at place where you can see clearly, at least half the table. Take pictures using the camera to check.
  10. Slot the cue stick into the hole in the cue bridge.
  11. Place the camera into the holder
  12. Use the cue stick to hit the cue ball in the midpoint so that it hits the mid point of the coloured ball.
  13. Place the camera into the holder and record all the shots.
  14. Keep repeating steps 14 and 15 until you have enough data (Recommended at least 60 times)

• Risk and Safety: Identify any potential risks and safety precautions to be taken.
  • As this experiment involves pushing solid heavy objects, avoid getting hit by them or breaking them.
  • When placing the camera, you need to be careful as you might need to stand on a chair.


Data Analysis: Describe the procedures you will use to analyze the data/results that answer research questions or hypotheses


We gathered our data by recording the motion of the balls using a camera. We had many tries, all taken in two videos, with a flat, two dimensional view of the table.
After that, we use a program called Tracker. We set the axes to measure the displacement from the origin and the scale by comparing with the 1 metre rule on the table.

Then, we define the data that is to be gathered from the experiment.

Displacement = x (using the x axis that was set)
Velocity = Displacement/t
Acceleration = Velocity/t (which was then useless as it was inaccurate)

Next, by using the auto-tracking system of the software, we gathered the data and then listed them out on a spreadsheet.

Through the spreadsheet, we found the average Velocity of black ballVelocity of cue ball of all the data gathered.

D. Bibliography: List at least five (5) major references (e.g. science journal articles, books, internet sites) from your literature review. If you plan to use vertebrate animals, one of these references must be an animal care reference. Choose the APA format and use it consistently to reference the literature used in the research plan. List your entries in alphabetical order.

Alciatore, D. (2008). Pool and Billiards Physics Principles by Coriolis and Others. Retrieved Aug 13, 2014, from
http://billiards.colostate.edu/physics/Alciatore_pool_physics_article.pdf




Billiard World (n.d.). Glossary of Billiard terms.
Retrieved Aug 14, 2014 from
http://www.billiardworld.com/glossary.htm

Hamlin, K. (N.D.). The Physics of pool: A “Break” from the Ordinary. Retrieved Aug 12 2014 from http://www.unc.edu/~tidol/Physics%20project%20vectors%20page.htm
Normani, F. (N.D.). The Physics of Billiards. Retrieved Aug 12, 2014, from http://www.real-world-physics-problems.com/physics-of-billiards.html

NEWTON Ask a Scientist! (n.d.). Sliding Versus Rolling on Friction Free Incline. Retrieved Aug 13, 2014, from
http://www.newton.dep.anl.gov/askasci/phy05/phy05139.htm

NCSA Math Projects. (2003). The Math and Physics of Billiards.
Retrieved Aug 13, 2014, from
http://archive.ncsa.illinois.edu/Classes/MATH198/townsend/math.html

Meador, J. (n.d). Do you really need sidespin to shoot well?
Retrieved Aug 14, 2014, from
http://www.billiardworld.com/sidespin.html

Shepard, R. (1997). Amateur Physics for the Amateur Pool Player. Retrieved Aug 12, 2014, from http://billiards.colostate.edu/physics/Shepard_apapp.pdf

Walker, J. (1983). The physics of the follow, the draw and the massé (in billiards and pool). Retrieved Aug 12, 2014, from
http://billiards.colostate.edu/physics/walker.pdf


Wikipedia (2014) Pool (Cue Sports)
Retrieved Aug 14, 2014
http://en.wikipedia.org/wiki/Pool_(cue_sports)

Wikipedia (2014) Billiard Ball
Retrieved Aug 27, 2014
http://en.wikipedia.org/wiki/Billiard_ball

Reflection

22/7/14

Kenneth Kiang - We created the markings and made the preparations to set up the camera and table for the experiments.

Darie - Me and Benjamin already set up the tables already before coming to the lab and opened and set up the pool table already so most of the equipments are there already Benjamin had made 3D model of the cue bridge already on google sketch up so i drew the markings with the 3D model as a guide.we went upstairs and asked Mr Tan for the aluminium profile and broughtt it downstairs.

Jiawei - Today, we started to set up the experiment. I had a theory in mind before coming so I went to tested it out today and the theory was true. It was about whether it is possible to spin the coloured ball and it isn’t. Even if you hit it at the side it will still not spin but just roll straight into the other direction. We had some problems setting up the aluminium “tripod” to position where it can look directly down. It was very hard to set it up.

Benjamin - Me and Darie had set up the table already the day before. I went to make a 3d model of the cue bridge. We then went up to ask Mr Tan about the aluminum profiles. He then gave it to us and we brought it down.

23/7/14

Darie - Today i went to go find the alan key for the aluminium profile I went to the research lab, Admt lab and Bio lab but the alan key could not be found anywhere. I asked Mr Tan and he said i should go out and buy the alan key first then giving him the receipt Benjamin and I are going to either find or buy a allen key thats compatible with the aluminum profile. We recalculate the markings on the bridge and we need to find some time to drill the hole.

Kenneth Kiang - Today, I went to try and find someone who could help us drill a hole in the wooden plank, for the creation of the cue bridge. In the end, we didn’t manage to get it immediately.

Jiawei - Today, we continued to set up the “tripod” we still had a lot of problems. In the meanwhile, I went to the ADMT studio to seek help for drilling a hole in a plank of wood which is going to be used for a cue bridge. However, we were told that there would be a common date that everyone can do all the drilling and cutting etc. We started brainstorming a better way to position the camera because the tripod is too hard to assemble. Since it was a foldable table, I thought of lowering the table down by bending the legs. So a normal tripod could be used to look directly down onto the table.

Benjamin-We tried fixing the aluminum profile, in which we didn’t have the required allen key to fix it, i also remarked the wooden board after noticing the mark for the hole was to high.

24/7/14

Darie - Me and Benjamin borrowed the correct alan key from home and we were finally able to build the aluminium profile. It was easier than expected to build it when we have the alan key. After that, Me and benjamin ran up stairs and checked the camera. After that we ran out of time.

Kenneth Kiang - We built the set up for the camera to get the top view of the pool table, so we can observe the motions of the pool ball at a 2D view.

Jia Wei - We finally managed to finish the camera frame and did part of the camera holder. It still does not have the hole for the lens nor the hole to slide through the camera frame.

Benjamin-We finished the camera frame and part of the camera holder.

25/7/14

Darie - I then built the camera holder, I had to measure all the lengths of the camera and made sure it fitted properly. I had to work in the research lab as the biotech lab do not have a cutting board. After i finished cutting i went downstairs and we ran out of time.

Kenneth Kiang - We constructed the camera holder by carrying out all the necessary
measurements and cutting and taping them together.

Jiawei - We went to borrow and test out the highspeed camera. We also went to borrow some tools to help with constructing the full camera holder. We measured the circumference of the lens and me used a pen knife to cut a circle for the lens. We then went to measure the thickness of the poles of the camera frame and made two holes.

Benjamin-We finished most of the camera holder and tested the camera.

29/7/14
Darie - We reinforced the aluminum foil got the camera in place already We checked and done everything except for the cue bridge. Mr Tan told us while we were returning the leftover aluminium profile that we can do the cue bridge on thursday. Once we done the cue bridge, we are ready to start recording our project

Kenneth Kiang - we fixed the camera holder through the poles and got our camera to fit in there by cutting some flaps. We also know that we will be drilling the cue bridge this Thursday.

Jia Wei - We fixed the camera holder onto the camera stand. We went to borrow the camera and do not plan on returning it until the end of ISS. We then went to position the camera accurately and took some test shots.

Benjamin:We added two more rods to the frame of the camera holder and tested the camera whether the view was okay, now we are just waiting for Mr Tan to let us drill the hole for the cue bridge.

30/7/14

Ho Jia Wei: We went to try the application tracker out and we prepared as much things as we could for the next time we come back.

Darie Chan:We tried out the tracker.Me and Benjamin shot the pool ball and recorded and then kiang recorded it. Since we already finished, we are still waiting for cue bridge so we prepared everything we could.
Kenneth Kiang: Today, I prepared for next week’s experiment by studying tracker and experiencing the errors before the real experiment begins. We don’t have much time as
the drilling is occurring rather late, so we have to make as much preparations as we can so that we will be able to finish the experiment as soon as possible.

Benjamin:We tried using tracker where me and darie shot some pool balls while kiang reviewed the video. Most of the project is finished, but we need to drill the cue bridge.
31/7/14
Ho Jia Wei: We discussed with Mr Tan about the project and he said that he would order a drill to drill a hole in the plank of wood for the cue bridge. We have to add an extra part so that we can use it to clamp the cue bridge down. However we were short of the joints for the aluminium profile. The extra part can be also used for stabilisation.

Darie Chan:We asked Mr Tan about the drilling with Kiang,Benjamin and I but he told us it was not time yet though.We must also buy extra aluminium profile to make the camera stable so it will not shake when we film and record the experiment.

Kenneth Kiang: We realised we needed more of the aluminium bars to stabilise our set up. We also couldn't drill the wooden blocks too, so we had to go outside to get someone to drill.

Benjamin: Today we went to look for Mr Tan where he said the drill bit was being delivered and he said he would have to get more aluminum profiles to firm up the frame.

8/1/14
Kenneth Kiang: For today, we just focused on typing out the report, mainly consisting of the history, mechanics and fundamentals of pool.

Ho Jia Wei: Today we couldn’t do anything so we just focused on writing our abstract and introduction.

Benjamin : Today we started typing the report, focusing on the abstract and the introduction.

Darie Chan:we did the report today as we couldn’t do anything else. So the whole group just sat down and we research on anything we could write like the history of pool, What are the parts of the cue or how is the ball made.

8/5/14
Kenneth Kiang: We didn’t have our drill yet so we just completed our abstract and report.

Ho Jia Wei: We tried shortening the abstract. We also decided on how can we get a cue bridge as soon as possible.

Benjamin :We continued on the report as our equipment havent arrived yet.

Darie Chan: Our abstract was too long so we shortened it as we expand more on our report. We also waited until we could do the cue bridge.


8/7/14
Kenneth Kiang: We plan to use corrugated board instead of drilling a hole into the wooden plank. We figured that it would be much more efficient than waiting for the drill any longer. We will be stacking up 6 layers of the board for stability and then cutting a circle in each board for the cue stick to go through.

Ho Jia Wei: We gave up on drilling a hole into the wooden plank and decided to use corrugated board, layer them and cut a hole into it. We cut out 6 layers. The rest was brought back home to finish by Darie.  

Benjamin :We tried to look for replacement for the cue bridge, and in the end we used corrugated board.

Darie Chan:We decided not to wait for the drill anymore and we use the corrugated cardboard to make our cue bridge.the corrugated cardboard is strong and can also be easily cut so we could finish it quickly. I decided to bring it back home and finish up the cue bridge myself.

8/15/14
Ho Jia Wei: We went to the lab to complete final set up of the experiment so that we can do it the next time. Like tape the points for the ball, take test footage, put the cue bridge in place and wanted to change the camera holder with a new one. However, we found out that the old camera holder could fit the camera.

Darie Chan:We went to lab this time to set up the experiment. Benjamin, Jia Wei and I went to there to set it up. What we did was to test out the the camera, make sure we can see everything and taping everything in place. We also decided where to place our cue bridge and balls.

Benjamin: We wanted to go down to the lab to start the project as we finished making the cue bridge, but there was no staff in the lab so we have to go after school.

Kenneth Kiang: We completed our set up and tested everything so we can finally start our project the next time.

8/19/14
Ho Jia Wei: I was not able to make it in the afternoon due to remedial.

Darie Chan: We recorded 90 shots. I was the one who was shooting the ball with the cue stick. Kenneth helped me with filming it and rearranging the ball back so I can keep shooting without stopping to rearranging the ball. We managed to collect everything quickly and finished soon after.

Kenneth Kiang: We recorded 90 shots, but only plan to gather results from 60 of them as not all of them will be reliable. We started out with a very weak shot, then we gradually increased in the amount of power used until it managed to bounce off the 2 edges of the table in one go.

Benjamin: During normal lesson we went to finalise the report, but after school due to remedial me and Jia Wei were not able to come and help.

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