Work done by a force kinetic and potential

Work done by a force, kinetic and potential energy Definition of the Joule

Objectives: • To understand that work done is the same as energy transferred • To know how to calculate the work done by a force • To learn the definition of the ‘Joule’ • To be able to calculate the kinetic energy of an object • To be able to calculate the gravitational potential energy of an object • To be able to carry out calculations involving transfer of KE to GPE and GPE to KE

What is work? What happens when a rocket is launched into space? When the rocket’s engines are fired, chemical energy in the fuel is transferred to kinetic energy in the rocket. When energy is transferred, work is done. 3 of 27 © Boardworks Ltd 2011

Work and energy What is the link between work and energy? work done = energy transferred This means the units for work are the same as the units for energy – joules. For example, if a person does 500 J of work pushing a car, then 500 J of energy is transferred. In the same way, if a person transfers 250 J of energy when they carry a box up some stairs, then 250 J of work is done. 4 of 27 © Boardworks Ltd 2011

To calculate the work done by a force we use the equation: Work done = force X distance moved in the direction of the force What are the units of force, distance and work done? You need to learn this! 5 of 27 © Boardworks Ltd 2011

Definition of the Joule One Joule is the energy transferred to an object when a force of one Newton moves an object a distance of one metre in the direction of the force. It is a derived unit (as is the Newton) and therefore we must be careful to always use SI units in calculations

Calculating work done question 1 A cyclist peddles a bicycle with a force of 1, 000 N and moves it 250 m. How much work has been done by the cyclist? work = force × distance done = 1, 000 × 250 = 250, 000 J = 250 k. J 7 of 27 © Boardworks Ltd 2011

Calculating work done question 2 A car engine moves a car with a force of 10 k. N and does 500 k. J of work. How far has the car travelled? work done = force × distance work done distance = force = 500, 000 10, 000 = 50 m 8 of 27 © Boardworks Ltd 2011

Work and energy: true or false? 9 of 27 © Boardworks Ltd 2011

How is GPE calculated? The GPE of an object can be calculated using this equation: GPE = mass × gravitational field strength × height 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). 10 of 36 © Boardworks Ltd 2011

Mass x gravitational field strength = weight (Newtons)

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 = 2 × 10 × 200 = 4, 000 J 12 of 36 © Boardworks Ltd 2011

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? change GPE = mass × gravitational field strength × in height lost = 0. 2 × 10 × 3 = 6 J 13 of 36 © Boardworks Ltd 2011

What is the useful energy transfer taking place as the apple falls to the floor? 14 of 36 © Boardworks Ltd 2011

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). 15 of 36 © Boardworks Ltd 2011

If our apple lost 6 Joules of gravitational potential energy as it fell, and we ignore air resistance, how much kinetic energy will it have when it reaches the ground? 6 Joules

How fast will the apple be moving?

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, 500 × 202 = 300, 000 J = 300 k. J 18 of 36 © Boardworks Ltd 2011

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 19 of 36 © Boardworks Ltd 2011

KE, mass and velocity calculations 20 of 36 © Boardworks Ltd 2011

Energy transfer of roller coasters 21 of 36 © Boardworks Ltd 2011

Falling objects How can you calculate the energy an object will gain as it falls from a height? Since GPE lost = KE gained, the falling object will gain kinetic energy equal to the gravitational potential energy it had before it started falling. GPE = mass × gravity × height KE = ½mv 2 mgh = ½mv 2 This is only true if air resistance and friction are ignored. 22 of 36 © Boardworks Ltd 2011