Investigating the Effect of Different Sports Balls on Rolling Speed

1. CBA 1-Investigation By Rafia Nauman

2. Slide 3- Sub-title slide: A-Define a Problem Slide 4- Question/problem Slide 5- Mathematical Areas of Interest Slide 6- Assumptions Slide 7- Sub-title slide:B-Develop a strategy to help with solving the problem Slide 8- Considerations Slide 9- Considerations Slide 10- Formulas Slide 11- Resources needed for the investigation Slide 12- Variables Slide 13- Plan:Step 1 Slide 14- Plan:Step 2 Slide 15- Plan:Step 3 Slide 16- Plan:Step 4 Slide 17- Plan:Step 5 Slide 18- Diagrams Slide 19- Sub-title slide: C-Implementation Slide 20- Predictions Slide 22- Material of the balls Slide 23- Circumference of the balls Slide 25- Radius and surface area of the balls Slide 27- Mass of the balls Slide 30- Time averages for 2m distance Slide 31- Time averages for 3m distance Slide 34- Speeds for 2m distance Slide 35- Speeds for 3m distance Slide 37- Slope of the ramp Slide 38-42- Distance time graphs of balls Slide 43- Comparing speeds bar chart Slide 46- Sub-title slide: D-Reflect, evaluate and report your findings Slide 47-50- Solving the problem itself Slide 51- Conclusion Slide 52- Do the answers make sense? Slide 53- Was there anything surprising in my results Slide 54- Did I learn something new? Slide 55- Has the question I have asked been solved Slide 56- Is the solution useful in real life? Slide 57- Could I have tried a different strategy to solve the problem Slide 58- What worked well? Slide 59- What would I change If I was to do this again? Index

3. A-Define a problem

4. Problem I would like to answer: “Would a different type of sports ball affect how fast it rolls?”

5. Mathematical areas of interest ● Natural numbers ● Speed, distance, time and real life graphs ● Coordinate geometry ● Statistics

6. Assumptions ● The ramp is smooth and a constant texture ● The last distance out of the two distances will have a similar trend amongst all of the balls

7. B-Develop a strategy to help with solving the problem

8. Considerations -things I need to research ● ● ● ● What are the sports balls made of? What’s the circumference? What’s the mass? What’s the surface area (requires radius measurement)? What’s the slope of the ramp? How long does it take a ‘x’ ball to reach ‘x’ distance? ● ●

9. Considerations-why do I need to research these things? ● I will need to know all the information about the balls so I can determine whether the different balls affect the speed.

10. Formulas Surface Area = C2/? ○ Used to find the surface area of the balls Radius = C/2? ○ Used to find the radius of the balls Speed = Distance/time ○ Used to find the speed of the balls Rise over run ○ Defines the slope of the ramp Average = (a1+a2+...+ax)/x ○ Used to find the average time of the balls reaching a distance ● ● ● ● ●

11. Resources needed for the investigation: ● ● Smooth ramp - to roll the balls down Football, tennis ball, basketball, volleyball, rugby ball - I will need a diverse set of balls so I can figure out whether the different types of balls affect the speed and find more accurate results Piece of string - to measure the circumference of the balls Mass balance - to measure the ball’s mass Tape - to measure the distance travelled by the balls (I will mark two distances on the ground) Measuring tape - to measure the distance necessary iPad - to time the balls as they roll to certain distances ● ● ● ● ●

12. Variables ● Variable = type of sports ball ● Variable = speed of the ball ● Constant = slope of the ramp ● Constant = the two distances at which the ball must roll to, will stay the same

13. Plan - Step 1: Research and find the material, mass, circumference, and surface area of each of the balls - we will need this information to compare them at the end and decide whether the different types of balls affect how fast they roll

14. Step 2 - This isn’t relevant at all but the ramps name is Solenya which means ‘pickle’ in Russian Prepare a smooth ramp for the balls to roll down, I will be using this same ramp throughout the experiment.

15. Step 3 - ● One by one roll the sports balls down the ramp and time how long it takes for them to reach a certain distance ● I will do this three times to get an average time thus making it more accurate than if I was to do it once - I am timing and measuring the distance so I can calculate the speed later

16. ● I will roll them one by one down the ramp again but this time with a larger distance than previously (Again, repeating three times to get an average)- this is so I can see whether the speed of the balls will stay constant, slow down, speed up, or if it will curve due to deceleration This will help to clarify whether it will have a similar trend amongst the balls Step 4- ●

17. Step 5 - ● After I have recorded all the data I will review and convey it onto graphs and tables to compare my results ● This will help to determine whether a different type of sports ball affects how fast it rolls.

18. Diagrams ● Bar Chart ● Trend Graph ● Table

19. C-Implementation

20. Before I start the experiment a few predictions I have are: 1.The heavier more denser balls will roll faster 2.The rugby ball will be slower rolling due to its awkward shape 3.A dense ball like a tennis ball that doesn’t need to be inflated with air will roll faster

21. First I’ll research and find all the information I need on the balls: material circumference, mass, surface area, radius.

22. Football Usually made from leather,rubber, and synthetics Tennis ball Mainly made of felt, nylon, and rubber Basketball Mainly made from leather, synthetic, and rubber Volleyball Usually made of synthetic and/or leather Rugby ball Mainly made from rubber or polyester Material of the balls

23. Football 67.5cm Circumference of the balls Tennis ball 21.5cm Basketball 70cm Calculated by wrapping a piece of string around the balls and measuring the length of the string Volleyball 66cm Rugby ball(circumfe rence from long side) 58cm

24. ● Now I need to figure out the surface area and radius of the balls, since I have the circumference I can use that to figure out the surface area and radius ● The formula to get the surface area using the circumference is A = C2/? ○ eg. A = 67.5/?= 1450 ● Using the circumference I can also figure out the radius, the formula is r = C/2? ○ eg. r = 67.5/2?= 10.7

25. Type of ball 1.Calculat ion for surface area (cm) 1.Surface area (cm) 2.Calculat ion for radius (cm) 2.Radius (cm) What’s the 1. Surface area and 2. Radius of the balls Football 1450 10.70 67.52/? 67.5/2? Tennis ball 147 3.42 21.52/? 21.5/2? Basketball 1560 11.10 702/? 70/2? Volleyball 1390 10.50 662/? 66/2?

26. ● The rugby ball calculations for circumference, radius, and surface area were left out due to it’s awkward shape ● If I was to use the surface area, radius, and circumference calculations for the ball I do not believe it would work out as it is not a perfect sphere ● Instead of performing the calculation I searched for the surface area 1256.64sq.cm

27. Mass of the balls Football 426g Tennis ball 57.3g I got the mass of the balls by using a mass balance Basketball 624g Volleyball 264.7g Rugby ball 413.6g

28. ● Now, I will start the experiment part of the investigation, as explained in the steps section ● I will be rolling the balls down a ramp and timing how long it takes to reach 2m ● I will repeat that 3 times with each ball and then do all that again with a distance of 3m

29. ● To figure out the time of each ball accurately I recorded 3 different times with each ball,I'll then find the average of three times.To find average = (x + y + z)÷3 = a/3 = b, ● An example being : 1.60 + 1.93 + 1.72 = 5.25 ÷ 3 = 1.75 ○ In this calculation x = 1.60, y = 1.93, z = 1.72, a = 5.25, b = 1.75

30. The 3 time and calculations to find the average. The average time is the time it took the balls to travel 2m Type of ball Time (seconds) Calculations Average time (seconds) Football 1.60, 1.93, 1.72 1.60+1.93+1.72= 5.25÷3 1.75 Tennis ball 1.35, 1.45, 1.69 1.35+1.45+ 1.69= 4.49÷3 1.50 Basketball 1.35, 1.52, 1.55 1.35+1.52+ 1.55= 4.25÷3 1.47 Volleyball 1.42,1.47,1.57 1.42+1.47+1.57= 4.46÷3 1.49 Rugby ball 1.72, 1.58, 1.86 1.72+1.58+1.86= 5.16÷3 1.72

31. Type of ball Times (seconds) Calculations Average time (seconds) Time it took each ball to travel 3m Football 1.85, 1.98, 1.81 1.85+1.98+1.81= 5.64÷3 1.88 Tennis ball 2.14, 2.09, 1.90 2.14+2.09+1.90= 6.13÷3 2.04 Basketball 1.67, 2.09, 1.88 1.67+2.09+1.88= 5.64÷3 1.88 Volleyball 1.98, 1.82, 1.97 1.98+1.82+1.97= 5.77÷3 1.92 Rugby ball 2.22, 2.22, 2.51 2.22+2.22+2.51= 6.95÷3 2.32

32. ● Now that I have all the information I need, I can begin figuring out the speed of each ball and comparing the speeds. ● Using the formula for speed = distance/time.

33. Speeds for the 2m distance Type of ball Calculations Speed (m/s) Football 2m/1.75s 1.14 Tennis ball 2m/1.5s 1.30 Basketball 2m/1.47s 1.36 Volleyball 2m/1.49 1.34 Rugby ball 2m/1.72 1.16

34. Speeds for the 3m distance Type of ball Calculations Speed (m/s) Football 3m/1.88 1.60 Tennis ball 3m/2.04 1.47 Basketball 3m/1.88 1.60 Volleyball 3m/1.92 1.56 Rugby ball 3m/2.32 1.29

35. Now that I have the speeds of each the balls for both the distances I’ll find the slope of the ramp then convey the data in bar charts and trend graphs

36. 53cm 94cm To find the slope of the ramp I’ll use the rise over run formula, the height of the ramp was 53cm and the length of the ramp was 94cm. Slope = 53/94= 0.564

37. Football distance time graph, for each of the trend graphs I rounded up to the nearest tenth.

38. Tennis ball distance time graph

39. Basketball distance time graph

40. Volleyball distance time graph

41. Rugby ball distance time graph

42. By looking at the trend graphs it’s much easier for me to understand what has happened to each of the balls as they rolled. Now, I’ll compare the speed of each of the balls with both the three-metre and two-metre distances so I can further understand each of the ball's behaviour

43. Bar chart comparing the speeds of each ball, the 2m distance is in a lighter green while the 3m distance is a dark green, the numbers along the side and on the bars is the speed of the ball.

44. By looking at the graph I can tell that each ball accelerated its speed, The speed for the 3m distance is always more than the speed of the 2m distance this means that the speed is not constant,if I had done this experiment with a greater distance then perhaps it would have accelerated further. The fact that the speed is not constant is a similar trend amongst all the balls.

45. **because of the fact that the speeds are all different and changing means that I can’t write a maths rule that would apply to all the balls The overall highest speed from the balls at the 2m distance is the basketball at a speed of 1.36m/s; however, the football then accelerates to the speed of 1.6m/s to match the speed of the basketball at the 3m distance. I wonder if this is because the material used to make the balls are more or less the same?

46. D-Reflect, evaluate, and report your findings

47. I am now going to interpret my findings in the context of the original problem, the problem was “would a different type of sports ball affect how far it rolls?”. To figure out this problem I set up an experiment where I would roll balls down a ramp to find their speeds. Now that I have their speeds and information about each type of ball I am going to compare each ball with each other while keeping their mass, material, and measurements in mind. This way I can figure out whether the different types of sports ball does or does not affect how fast it rolls.

48. First I’ll look at the slowest ball and the fastest and compare the materials and mass: The fastest ball overall was the basketball and the slowest was the rugby ball, the basketball is made mainly from leather, synthetic, and rubber which also **this is the same bar chart from before I just changed the colours for important aesthetic reasons happens to be the same materials as the football which is the second-fastest ball, the rugby ball is made from rubber or polyester. Now I’ll look at the material of the volleyball as it came in as third-fastest, it is mainly made from leather and synthetic which is nearly the same as the football and basketball. What is also interesting is the fact that the ball with the most mass(basketball) has the most speed and the football has the second most mass and speed.

49. I tried to figure out what exactly is the factor that mainly affects how fast the balls roll. I looked at all the information I had gotten on the speed and surface area, material and radius and discovered that there is two patterns that I can see with two factors. 1. Radius - I saw that the order of balls with the highest to lowest speeds match the order of the highest to lowest radius. The basketball has the highest radius with 11.1cm which also happens to have the highest speed, the football has the second highest radius with 10.7cm which happens to be the ball with the second highest speed and so on with the rest of the balls.

50. 2. Material - it seems that the balls that are mainly made from synthetic, leather and rubber are faster eg.the basketball and the football both have synthetics,leather and rubber. The volleyball is made from just leather and synthetics so perhaps the absence of rubber affects the speed, however when it comes down to the materials I do not know how much of each material there is in the balls so maybe balls with more leather are faster and more synthetics slower and vice versa.