#### Transcript Work & Power

EDEXCEL IGCSE / CERTIFICATE IN PHYSICS 4-3 Work and Power Edexcel IGCSE Physics pages 142 to 149 June 17th 2012 All content applies for Triple & Double Science Edexcel Specification Section 4: Energy resources and energy transfer c) Work and power know and use the relationship between work, force and distance moved in the direction of the force: work done = force × distance moved W = F × d understand that work done is equal to energy transferred know and use the relationship: gravitational potential energy = mass × g × height GPE = m × g × h know and use the relationship: kinetic energy = ½ × mass × speed2 KE = ½ × m × v2 understand how conservation of energy produces a link between gravitational potential energy, kinetic energy and work describe power as the rate of transfer of energy or the rate of doing work use the relationship between power, work done (energy transferred) and time taken: power = work done / time taken P = W / t Work and energy When a force causes a body to move through a distance, energy is transferred and work is done. work done = energy transferred. Both work and energy are measured in joules (J). Work and friction Work done against frictional forces is mainly transformed into heat. Rubbing hands together causes them to become warm. Brakes pads become hot if they are applied for too long. In this case some of the car’s energy may also be transferred to sound in the form of a ‘squeal’ The work equation work done = force applied × distance moved in the direction of the force W=Fxd work, W is measured in joules (J) force, F is measured in newtons (N) distance, d is measured in metres (m) also: force = work done ÷ distance moved and: distance = work done ÷ force W F d Question 1 Calculate the work done when a force of 5N moves through a distance of 3m. W=Fxd = 5N x 3m work = 15 J Question 2 Calculate the work done when a force of 6N moves through a distance of 40cm. W=Fxd = 6 N x 40 cm = 6 N x 0.40 m work = 2.4 J Question 3 Calculate the value of the force required to do 600J of work over a distance of 50m. W=Fxd becomes: F=W÷d = 600 J ÷ 50 m force = 12 N Question 4 Calculate the distance moved by a force of 8N when it does 72J of work. W=Fxd becomes: d=W÷F = 72 J ÷ 8 N distance moved = 9 m Question 5 Calculate the work done by a child of weight 300N who climbs up a set of stairs consisting of 12 steps each of height 20cm. W=Fxd The child must exert an upward force equal to its own weight. Therefore: force = 300N This force is exerted upwards and so the distance must also be measured upwards. = (12 x 20cm) = 2.4m therefore: work = 300 N x 2.4 m work = 720 J Question 6 Calculate the work done by a person of mass 80kg who climbs up a set of stairs consisting of 25 steps each of height 10cm. W=Fxd the person must exert an upward force equal their weight the person’s weight = (80kg x 10N/kg) = 800N the distance moved upwards equals (10 x 25cm) = 2.5m work = 800 N x 2.5 m work = 2000 J Complete Answers work force distance 150 J 50 N 3m 800 J 40 N 20 m 500 J 250 N 2m 80 kJ 4000 N 2m 2 MJ 3.03 400 N 5 km Choose appropriate words to fill in the gaps below: force Work is done when a _______ moves through a distance. energy transferred is also equal to the work The amount of _______ heat done. When a car brakes energy is transformed to ______. equal to the force _________ multiplied by the distance Work done is ______ moved in the __________ of the force. The work done is direction measured in ______ joules if the force is measured in newtons and distance in metres. the _________ WORD SELECTION: energy direction force equal multiplied distance heat joules Gravitational potential energy Gravitational potential energy (GPE) is the energy stored in an object when work is done in moving the object upwards. GPE = mass x g x height GPE = m x g x h GPE is measured in joules (J) mass, m is measured in kilograms (kg) gravitational field strength, g is measured in newtons per kilogram (N/kg) height, h is measured in metres (m) Question 1 Calculate GPE gained when a weightlifter lifts a mass of 120kg up by 2.5m. (g = 10N/kg) GPE = m x g x h = 120kg x 10N/kg x 2.5m GPE = 3000 J Question 2 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 = 2 800 J Kinetic energy Kinetic energy is the energy possessed by a body because of its speed and mass. kinetic energy = ½ x mass x (speed)2 KE = ½ x m x v2 kinetic energy, KE is measured in joules (J) mass, m is measured in kilograms (kg) speed, v is measured in metres per second (m/s) Question 1 Calculate the kinetic energy of a car of mass 1000kg moving at 5 m/s. KE = ½ x m = ½ x 1000kg = ½ x 1000 x = 500 x 25 kinetic energy x v2 x (5m/s)2 25 = 12 500 J Question 2 Calculate the kinetic energy of a child of mass 60kg moving at 3 m/s. KE = ½ x m x v2 = ½ x 60kg x (3m/s)2 = ½ x 60 x 9 = 30 x 9 kinetic energy = 270 J Question 3 Calculate the kinetic energy of a apple of mass 200g moving at 12m/s. KE = ½ x m x v2 = ½ x 200g x (12m/s)2 = ½ x 0.200kg x 144 = 0.100 x 144 kinetic energy = 14.4 J 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 v2 2MJ = ½ x mass x (4m/s)2 2 000 000J = ½ x mass x 16 2 000 000 = 8 x mass 2 000 000 ÷ 8 = mass mass = 250 000 kg Question 5 Calculate the speed of a car of mass 1200kg if its kinetic energy is 15 000J. KE = ½ x m x v2 15 000J = ½ x 1200kg x (speed)2 15 000 = 600 x (speed)2 15 000 ÷ 600 = (speed)2 25 = (speed)2 speed = 25 speed = 5 m/s Question 6 Calculate the speed of a ball of mass 400g if its kinetic energy is 20J. KE = ½ x m x v2 20J = ½ x 400g x (speed)2 20 = ½ x 0.400kg x (speed)2 20 = 0.200 x (speed)2 20 ÷ 0.200 = (speed)2 100 = (speed)2 speed = 100 speed = 10 m/s Complete Answers kinetic energy mass speed 8J 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 3.03g 400 4 m/s Falling objects If there is no significant air resistance then conservation of energy results in gravitational potential energy being converted into kinetic energy as an object falls. gain in KE = loss of GPE m gpe = mgh ke = 0 h v1 gpe = ke gpe = ½ mgh ke = ½ mv12 v2 gpe = 0 ke = ½ mv22 ke = mgh ½h Graphs of GPE and KE TOTAL ENERGY = GPE + KE GPE Energy KE 0 object dropped 0 Time object reaches lowest point Question A child of mass 40kg climbs a wall of height 3m and then steps off. Calculate the speed at which the child reaches the bottom of the wall. Child’s initial gravitational potential energy: GPE = m x g x h = 40kg x 10N/kg x 3m GPE = 1 200 J If air resistance is insignificant then all of this GPE is converted into kinetic energy KE = ½ x m x v2 1200 J = ½ x 40kg x (speed)2 1 200 = 20 x (speed)2 1 200 ÷ 20 = (speed)2 60 = (speed)2 speed = 60 speed = 7.75 m/s Choose appropriate words to fill in the gaps below: potential energy is the energy stored when an Gravitational ________ upwards This energy is released when the object is lifted ________. falls back to its initial position. object _____ Kinetic energy is the energy possessed by an object due to its speed and mass. If the mass of an object is ________ doubled its _______ kinetic energy doubles. If the speed is doubled the kinetic four energy will increase by ______ times. raised When a __________ object is released gravitational potential kinetic energy is converted into _________ energy. WORD SELECTION: falls speed four kinetic potential upwards doubled raised Power (P) Power is a measurement of how quickly work is done. power = work done time taken P= W t power, P is measured in watts (W) work done, W is measured in joules (J) time, t is measured in seconds (s) One watt is the same as one joule per second. Power is also equal to how quickly energy is transformed from one form to another. power = energy change time P=E t Question 1 Calculate the power of a motor that exerts a force of 40N over a distance of 2m for 10seconds. W=Fs = 40 N x 2 m work done = 80 J P=W/t = 80J / 10 s power = 8.0 W Question 2 Calculate the power of an electric motor that lifts a mass of 50 kg upwards by 3.0 m in 20 seconds. gain in GPE = m g h = 50 kg x 10 N/kg x 3 m = 1500 J g = 10 N/kg P=E/t = 1500 J / 20 s power = 75 W Answers Complete: energy transfer 600 J work done time power 600 JJ 600 120 s 55 W 440 J 440 JJ 440 20 ss 22 W 28 800 28 800JJ 28 800 800 JJ 28 2 hours 4W 2.5 mJJ 2500 2.5 kJ 50 s 50 W W 50 Measuring a person’s power 1. Measure the weight, W of person using weighing scales. s total stairs height, h stairs of n steps person of weight, W =nxs 2. Measure the time taken for the person to run up a flight of stairs of height, h 3. Work done = weight x height =Wxh =Wxnxs 4. Power of the person = work done / time taken = (W x n x s) / t Example calculation Weight of person, W = 800N Time taken, t = 3.0 seconds s total stairs height, h stairs of n steps person of weight, W =nxs Stairs: number of steps, n = 12 height of step = 0.20m total stair height, h = 12 x 0.20m = 2.4m Work done = weight x height = 800N x 2.4m = 1920J Power = 1920J / 3.0s = 640W Choose appropriate words to fill in the gaps below: quickly Power is a measure of how ___________ a device does work. Power is equal to work done in _________divided by the joules time taken. power The _________ of a device is also equal to the rate at which a device transforms ___________ from one form to another. energy watts Power is measured in _________, symbol W. thousand A one kilowatt motor will perform one ____________ joules second of work every __________. WORD SELECTION: second quickly watts power joules thousand energy Work and Power Notes questions from pages 142 to 149 1. 2. 3. 4. 5. 6. 7. 8. Give the equation for work done, state the units used and give an example calculation. Give the equation for kinetic energy, state the units used and give an example calculation. Give the equation for gravitational potential energy, state the units used and give an example calculation. Explain how gravitational potential and kinetic energy vary as an object falls. You should copy all the diagrams on page 146 as part of your answer. Give the equation for power, state the units used and give an example calculation. Explain how the power of a person can be measured using a flight of stairs. Answer the questions on page 149. Verify that you can do all of the items listed in the end of chapter checklist on page 149. Online Simulations Work (GCSE) - Powerpoint presentation by KT Kinetic Energy (GCSE) - Powerpoint presentation by KT Gravitational Potential Energy (GCSE) - Powerpoint presentation by KT Bouncing ball with different surfaces showing KE & PE - Freezeway.com Energy Skate Park - Colorado - Learn about conservation of energy with a skater dude! Build tracks, ramps and jumps for the skater and view the kinetic energy, potential energy and friction as he moves. You can also take the skater to different planets or even space! Rollercoaster Demo - Funderstanding Energy conservation with falling particles - NTNU Ball rolling up a slope - NTNU Pulley System - Fendt Bicycle gear distance multiplier demonstration - Freezeway.com BBC AQA GCSE Bitesize Revision: Work, force and distance Potential and kinetic energy Kinetic energy equation