2019 Year 12 IB Extended Essays

THE PHYSICS OF THE ROLLER COASTER

Maximum trendline M= ∆ ∆ =

Equation Y=mx +c M =

Minimum trendline M= ∆ ∆ =

5.2−0.8 36−10 = 4.4 26 = 0.17

4.8−2 30−12 = 2.8 18 = 0.156

∆ ∆ = 2− 1 2− 1

C = 0.16

C = 0.16

C = y-intercept

 Y= 0.17x -1.5

 Y= 0.156x +0.16

Average trendline M= ∆ ∆ =

7.2−0.8 46−6 = 6.4 40 = 0.16

Final trendline ∆ = ±0.007 ∆ = ± .67  Y= (0.16±0.007)x – 0.6±0.67

Error:

C = 0.16

 Y= 0.16x -0.6

Graph with curved line showing the relationship between the height of release and the maximum radius the ball can circulate

GRAPH 1.2: HEIGHT OF RELEASE VS RADIUS

12

11

10

10

8

8

6

6

4.5

4

RADIUS OF THE LOOP/CM

2

0

0

10

20

30

40

50

60

70

80

HEIGHT OF THE RELASE/CM

P a g e | 16

IB Diploma