Cambridge International Mathematics

Example 14 Self Tutor

Gravity is the force of attraction which exists between any

two objects in the universe. The force of attractionF

Newtons between two massesdcm apart is given in the

following table:

d(cm) 24 26 28 30 32 34 36 38 40

F(N) 237 202 174 152 133 118 105 95 85

a GraphFagainstdand show that a power model is reasonable.

b Obtain the power model which best fits the data.

c What factor confirms that the fit is excellent?

d Estimate the force of attraction between two spheres that are:

i 20 cm apart ii 29 cm apart iii 50 m apart.

a

b F¼138 000£d¡^2 :^00 ,soF¼

138 000

d^2

.

c r^2 ¼ 0 : 9999 is very close to 1 , so the fit is excellent.

diWhen d=20

F¼

138 000

202

ii When d=29

F¼

138 000

292

iii 50 m= 5000cm

when d= 5000

F=

138 000

50002

EXERCISE 30D

t 0 1 2 3 4 5

d 0 0 : 2 0 : 8 1 : 8 3 : 2 5 : 0

1 InExample 12with the small glass ball rolling down the

incline, we found that the model wasd=kt^2 withk=0: 2.

Use technology to check this result.

2 Use your graphics calculator to find the power model which best fits the following data:

a x^2358

y 3 : 25 0 : 96 0 : 20 0 : 05

b x^251225

M 35 : 4 22 : 3 14 : 4 10 : 1

3 Warm blooded animals maintain a remarkably constant body temperature by using most of the food

they consume to produce heat. The larger the animal, the more heat it needs to produce. The following

table gives the heat required (hJoules) for animals of various masses (mkg).

d

0

50

100

150

200

250

0 10203040

F(N)

d(cm)

The graph has both the and -axes as asymptotes

and it looks like an example of inverse variation.

A power model is therefore reasonable.

xy

) F¼ 345 N ) F¼ 164 N

) F¼ 0 :005 52N

620 Variation and power modelling (Chapter 30)

IGCSE01

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Y:\HAESE\IGCSE01\IG01_30\620IGCSE01_30.CDR Monday, 27 October 2008 2:58:09 PM PETER