GPE AND KE PG. 144 & 145, SYLLABUS 4.11 &
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1 GPE AND KE PG. 144 & 145, SYLLABUS 4.11 & 4.12
2 STARTER: MULTIPLE-CHOICE QUIZ
3 TODAY S LEARNING OBJECTIVES ARE TO Calculate (a) (b) The kinetic energy of objects Changes in gravitational potential energy of objects Starter: (1 minute) How do you increase: a) The kinetic energy of an object b) The gravitational potential energy of an object End
4 800kg car travelling at 6 m/s An 80kg man at the top of a 60m ladder A 0.1kg bullet travelling at 675 m/s A 3000 kg helicopter hovering at 20 m 0.7kg ball travelling at 60 m/s A 20 kg child on top a 300m building What factors does the GPE depend on? What factors does the KE depend on? Which has the most KE? Which has the most GPE?
5 KEY WORDS Kinetic Energy 운동에너지 Mass 큰덩어리 Speed 속도 Energy 중력위치에너지 Gravity 중력 Height 높이
6 A LONG WAY DOWN How would you describe a bungee jumper? As someone who is: l brave l unwise l energetic l full of gravitational potential energy (GPE). GPE is the amount of energy an object has because of its position above the ground, i.e. its height.
7 WHAT IS GRAVITATIONAL POTENTIAL ENERGY? The gravitational potential energy (GPE) of an object on Earth depends on its mass and its height above the Earth s surface. l When a bungee jumper starts to fall he starts to lose GPE. l As the elastic cord pulls the bungee jumper back up, he gains GPE.
8 HOW IS GPE CALCULATED? The GPE of an object can be calculated using this equation: GPE = mass gravitational field strength height GPE = m x g x h l Mass is measured in kilograms (kg). l Gravitational field strength is measured in newtons per kilogram (N/ kg), usually taken as 10 N/kg on Earth. l Height is measured in metres (m). l GPE is measured in joules (j).
9 CALCULATING GPE QUESTION 1 An osprey with a mass of 2 kg flies at a height of 200 m above the ground. How much gravitational potential energy does the osprey have? GPE = mass gravitational field strength height = = 4,000 J
10 CALCULATING GPE QUESTION 2 An apple with a mass of 200 g falls 3 m from its branch to the ground. How much GPE will the apple have lost when it reaches the ground? GPE lost = mass gravitational field strength = change in height = 6 J
11 QUESTION 3 Calculate the gravitational potential energy gained by a student of mass 70kg climbing a flight of stairs of height 4m. GPE = m x g x h = 70kg x 10N/kg x 4m GPE = J
12 WHAT IS KINETIC ENERGY? The word kinetic comes from the Greek word kinesis, meaning motion. Kinetic energy is the energy an object has because it is moving. All moving things have kinetic energy, but the amount of energy they have is not just dependent on how fast they are moving. What other factors affect the kinetic energy of a moving object?
13 HOW IS KINETIC ENERGY CALCULATED? The kinetic energy (KE) of an object can be calculated using this equation: KE = ½ mass velocity 2 = ½mv 2 l Mass is measured in kilograms (kg). l Velocity is measured in metres per second (m/s). l KE is measured in joules (j).
14 CALCULATING KINETIC ENERGY QUESTION A car with a mass of 1,500 kg travels at a velocity of 20 m/s. What is the kinetic energy of the car? kinetic energy = ½ mass velocity 2 = ½ 1, = 300,000 J = 300 kj
15 REARRANGING THE KE EQUATION Sometimes it is necessary to rearrange the kinetic energy equation in order to calculate the mass or the velocity of a moving object. KE = ½mv 2 What are the rearranged versions of this equation for calculating mass and velocity? m = 2KE v 2 v = 2KE m
16 CALCULATING VELOCITY QUESTION A lorry has a mass of 20,000 kg. If its kinetic energy is 2.25 MJ, at what velocity is it travelling? KE = ½ mass velocity 2 velocity = = 2KE 2 = 15 m/s mass 2,250,000 20,000
17 THE KINETIC ENERGY OF CARS
18 DANGEROUS SPEEDING? Use the KE = ½mv 2 equation to fill in the kinetic energy values in the table below for two cars each travelling at two different velocities. 1,000 kg 2,000 kg 20 m/s KE = 200 kj KE = 400 kj 40 m/s KE = 800 kj KE = 1600 kj Which factor mass or velocity has the greatest effect on the kinetic energy of a moving object? Doubling the mass causes the KE to double. Doubling velocity causes the KE to quadruple.
19 QUESTION 4 Calculate the mass of a train if its kinetic energy is 2MJ when it is travelling at 4m/s. KE = ½ x m x v 2 2MJ = ½ x mass x (4m/s) J = ½ x mass x = 8 x mass = mass mass = kg
20 QUESTION 6 Calculate the speed of a ball of mass 400g if its kinetic energy is 20J. KE = ½ x m x v 2 20J = ½ x 400g x (speed) 2 20 = ½ x 0.400kg x (speed) 2 20 = x (speed) = (speed) = (speed) 2 speed = 100 speed = 10 m/s
21 800kg car travelling at 6 m/s An 80kg man at the top of a 60m ladder A 0.1kg bullet travelling at 675 m/s A 3000 kg helicopter hovering at 20 m 0.7kg ball travelling at 60 m/s A 20 kg child on top a 300m building What factors does the GPE depend on? What factors does the KE depend on? Which has the most KE? Bullet: 22780J Car: 14400J Ball: 1260J Which has the most GPE? Helicopter: J Child: J Ladder: 4800J
22 TASK: 15 MINUTE WS End
23 ANSWERS KE 1. 50KJ 200KJ J m/s GPE J J 4a) 120m 4b) 15360J
24 Plenary Answers COMPLETE kinetic energy mass speed 8 J 4 kg 2 m/s 27 J 6 kg 3 m/s 1000 J 80 kg 5 m/s 6.4 kj 200 kg 8 m/s 3.2 J 400 g 4 m/s
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