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1 Energy transfers Speifiation referenes: Maths skills 1a, 1b, 2a, 2h, 3a, 3b, 3, 3d Aims In this worksheet you will learn how to alulate kineti energy, gravitational, and elasti potential energy. You will also rearrange equations to alulate unknowns and arry out alulations involving indies. Learning outomes After ompleting this worksheet, you should be able to: alulate the amount of energy assoiated with a moving objet alulate the amount of elasti potential energy stored in a strethed spring alulate the amount of gravitational potential energy gained by an objet raised above the ground. Worked example An Olympi arher applies a fore of 100 N in pulling bak her bow by 0.5 m. How muh energy is stored in the bow? The arrow she shoots has a mass of 0.05 kg. What is its maximum speed if there are no losses due to frition? Firstly you need to determine the work done in strething the elasti string for the bow, whih equals fore (F) distane (d). So: Elasti PE Joules We assume that all of the elasti potential energy is onverted to kineti energy of the arrow so EP Ek. You know that the kineti energy of a moving objet an be alulated using the equation: Ek 1 2 mv2 Rearranging the equation to give v on its own you get: v 2 E k 1 2 m or v E k 1 2 m This resoure sheet may have been hanged from the original. 1

2 You know that kineti energy Ek 50 J and mass m 0.01 kg, and want to know speed v; its units will be m/s. Substituting the values you know into the equation 50 v v 100 m/s The arrow flies at a speed of 100 m/s. Questions 1 Calulate the kineti energy of the following objets. a A ar that travels at a speed of 20 m/s and has a mass of 1200 kg. b A pupil with a mass of 55 kg swinging bak on a hair and falling off at a speed of 0.6 m/s. The earth with a mass of kg moving at a veloity of 461 m/s. d A tennis ball travelling at a speed of 46 m/s with a mass of 58 g. e A plane at a speed of 255 m/s with a mass of kg. This resoure sheet may have been hanged from the original. 2

3 2 Calulate the veloity of: a A bus travelling through town, with a mass of 5040 kg and kineti energy of J. b A lift travelling up to the top floor of the Empire State building with a mass of 4200 kg and a kineti energy of 4116 J. A bird flying towards its nest with a mass of 0.25 kg and a kineti energy of 40.5 J. d A hot air balloon with a kineti energy of J and a mass of 1890 kg. 3 Calulate the mass of: a An automati door losing at 0.2 m/s with a kineti energy of 1.6 J. b A wind turbine blade with a kineti energy of 1 MJ turning at 6 m/s. An aeroplane travelling at 75 m/s with a kineti energy of 843 kj. This resoure sheet may have been hanged from the original. 3

4 d A anoe moving down the river with a kineti energy of 5 J and a speed of 0.5 m/s. e A hild riding a bike at a speed of 0.6 m/s with a total kineti energy of 12.4 J. If the mass of the hild is 30 kg, what is the mass of the bike? 4 A ar moves at a onstant veloity of 30 m/s and has J of kineti energy. The driver applies the brakes and the ar stops in 95 m. a Calulate the fore needed to stop the vehile. b Calulate the mass of the vehile. 5 A pendulum of mass 200 g is pulled horizontally sideways by 30 m. The length of the pendulum string is 50 m. a Calulate the potential energy of the pendulum in this position. Assume g 9.8 N/kg This resoure sheet may have been hanged from the original. 4

5 b Calulate the maximum veloity that the pendulum falls with from this position. This resoure sheet may have been hanged from the original. 5