1 Press ‘Ctrl-A’ © G Dear 2009 (Free to use. May not be sold) Year 12 - General

2 Direct Variation (1/3) Experiment Web Potential Energy varies directly with height. A 100 kg weight has PE of 5880 joules at a height of 6m. PE  H PE = k H Initial Conditions When H = 6m, PE = = k x 6 k = 5880 ÷ 6 k = 980 k = constant of variation What is the PE at 4m? PE = 980 x 4 PE = 3920 joules (Check using the Experiment) PE = k H

What is the weight on the moon of a person who weighs 78 kg on earth? 3 Direct Variation (2/3) Experiment Web A persons weight varies directly with gravity. A person weighing 100 kg on earth weighs 7.55 kg on the moon. W  G W = k G Initial Conditions When W = 7.55, G = = k x 100 k = k = constant of variation W = x 78 ≈ 5.89 kg (2 dec pl) (Check using the Experiment) W = k G k = 7.55 ÷ 100

What is the volume of the earth whose radius is km ? 4 Direct Variation (3/3) The volume of a sphere varies directly with the cube of the radius. A sphere of radius 10cm has a volume of about 4200 cm 3. V  R 3 V = k R 3 Initial Conditions When R = 10, V = = k x 10 3 k = 4.2 k = constant of variation = 4.2 x ≈ km 3 V = k R 3 k = 4200 ÷ 10 3 ≈ 1. 1 trillion km 3