Presentation on theme: "2.1d Mechanics Work, energy and power"— Presentation transcript:
12.1d Mechanics Work, energy and power Breithaupt pages 148 to 159
2AQA AS Specification Lessons Topics 1 & 2 Work, energy and power W = Fs cos θP = ΔW / ΔtP = Fv3 & 4Conservation of energyPrinciple of conservation of energy, applied to examples involving gravitational potential energy, kinetic energy and work done against resistive forces.ΔEp = mgΔhEk = ½ mv2
3Work (W) Work is done when a force moves its point of application. work = force x distance moved in the direction of the forceW = F sunit: joule (J)work is a scalar quantity
4If the direction of the force and the distance moved are not in the same direction: θobjectW = F s cos θThe point of application of force, F moves distance s cos θ when the object moves through the distance s.
5Question 1Calculate the work done when a force of kN moves through a distance of 30 cmwork = force x distance= 5 kN x 30 cm= 5000 N x 0.30 mwork = 1500 J
6Question 2Calculate the work done by a child of weight 300N who climbs up a set of stairs consisting of 12 steps each of height 20cm.work = force x distancethe child must exert an upward force equal to its weightthe distance moved upwards equals (12 x 20cm) = 2.4mwork = 300 N x 2.4 mwork = 720 J
7Question 3 W = F s cos θ = 800 N x 50 m x cos 30° = 40 000 x cos 30° Calculate the work done by the wind on the yacht in the situation shown below:W = F s cos θ= 800 N x 50 m x cos 30°= x cos 30°= xwork = Jwind force = 800 Ndistance moved by yacht = 50 m30°
8Complete: Answers 400 N 300 m 60° 0 J * 400 N 5 km 0° 2 MJ 200 μN ForceDistanceAngle between F and sWork400 N5 km0°2 MJ200 μN300 m60 mJ50 N6 m60°150 J3 m90°0 J400 N300 m60°0 J ** Note: No work is done when the force and distance are perpendicular to each other.
9Force-distance graphs The area under the curve is equal to the work done.area = work= ½ F sFsforcedistancearea = work doneFsforcedistancearea = workfound by counting squares on the graph
10QuestionCalculate the work done by the brakes of a car if the force exerted by the brakes varies over the car’s braking distance of 100 m as shown in the graph below.Work = area under graph= area A + area B= (½ x 1k x 50)+ (1k x 100)= (25k) + (100k)work = 125 kJ2force / kNdistance / m1area Aarea B
11work done = energy change Energy (E)Energy is needed to move objects, to change their shape or to warm them up.Work is a measurement of the energy required to do a particular task.work done = energy changeunit: joule (J)
12Conservation of Energy The principle of the conservation of energy states that energy cannot be created or destroyed.Energy can change from one form to another.All forms of energy are scalar quantities
13Some examples of forms of energy Kinetic energy (KE)Energy due to a body’s motion.Potential energy (PE)Energy due to a body’s positionThermal energyEnergy due to a body’s temperature.Chemical energyEnergy associated with chemical reactions.Nuclear energyEnergy associated with nuclear reactions.Electrical energyEnergy associated with electric charges.Elastic energyEnergy stored in an object when it is stretched or compressed.All of the above forms of energy (and others) can ultimately be considered to be variations of kinetic or potential energy.
14kinetic energy = ½ x mass x (speed)2 Kinetic Energy (EK)Kinetic energy is the energy an object has because of its motion and mass.kinetic energy = ½ x mass x (speed)2EK = ½ m v2Note: v = speed NOT velocity.The direction of motion has not relevance to kinetic energy.
15Question 1Calculate the kinetic energy of a car of mass 800 kg moving at 6 ms-1EK = ½ m v2= ½ x 800kg x (6ms-1)2= ½ x 800 x 36= 400 x 36kinetic energy = J
16Question 2Calculate the speed of a car of mass 1200kg if its kinetic energy is JEK = ½ m v215 000J = ½ x 1200kg x v2= x v2÷ 600 = v225 = v2v = 25speed = 5.0 ms-1
17Question 3Calculate the braking distance a car of mass 900 kg travelling at an initial speed of 20 ms-1 if its brakes exert a constant force of 3 kN.k.e. of car = ½ m v2= ½ x 900kg x (20ms-1)2= ½ x 900 x 400= 450 x 400k.e. = JThe work done by the brakes will be equal to this kinetic energy.W = F sJ = 3 kN x s= 3000 x ss = / 3000braking distance = 60 m
18Complete: Answers 3.2 J 1.5 x 1011 J 8 kg 400 g 4.0 ms-1 3.2 J 3000 kg MassSpeedKinetic energy400 g4.0 ms-13.2 J3000 kg10 kms-160 mJ8 kg300 cms-136 J50 mg12 ms-13.6 mJ3.2 J1.5 x 1011 J8 kg12 ms-1
19Gravitational Potential Energy (gpe) Gravitational potential energy is the energy an object has because of its position in a gravitational field.change in g.p.e.= mass x gravitational field strength x change in heightΔEP = m g Δh
20QuestionCalculate the change in g.p.e. when a mass of 200 g is lifted upwards by 30 cm.(g = 9.8 Nkg-1)ΔEP = m g Δh= 200 g x 9.8 Nkg-1 x 30 cm= kg x 9.8 Nkg-1 x 0.30 mchange in g.p.e. = 0.59 J
21Complete: Answers 3 kg 1.6 Nkg-1 4000 m 144 J mass g Δh ΔEP 3 kg 400 cm120 J200 g1.6 Nkg-130 m9.6 J7 kg4000 m280 kJ2000 g24 Nkg-13000 mm144 J3 kg1.6 Nkg-14000 m144 J
22Falling objectsIf there is no significant air resistance then the initial gravitational energy of an object is transferred into kinetic energy.ΔEK = ΔEP½ m v2 = m g Δhmgpe = mgΔhke = 0Δhgpe = ke½ Δhv1gpe = ½ mgΔhke = ½ mv12gpe = 0v2ke = ½ mv22ke = mgΔh
23QuestionA child of mass 40 kg climbs up a wall of height 2.0 m and then steps off. Assuming no significant air resistance calculate the maximum:(a) gpe of the child(b) speed of the childg = 9.8 Nkg-1(a) max gpe occurs when the child is on the wallgpe = mgΔh= 40 x 9.8 x 2.0max gpe = 784 J(b) max speed occurs when the child reaches the ground½ m v2 = m g Δh½ m v2 = 784 Jv2 = (2 x 784) / 40v2 = 39.2v = 39.2max speed = 6.3 ms-1
24Power (P) Power is the rate of transfer of energy. power = energy transfertimeP = ΔEΔtunit: watt (W)power is a scalar quantity
25Power is also the rate of doing work. power = work donetimeP = ΔWΔt
26Question 1Calculate the power of an electric motor that lifts a mass of 50 kg upwards by 3.0 m in 20 seconds.g = 9.8 Nkg-1ΔEP = m g Δh= 50 kg x 9.8 Nkg-1 x 3 m= 1470 JP = ΔE / Δt= 1470 J / 20 spower = 74 W
27Question 2Calculate the power of a car engine that exerts a force of 40 kN over a distance of 20 m for 10 seconds.W = F s= 40 kN x 20 m= x 20 m= JP = ΔW / Δt= J / 10 spower = W
28Complete: Answers 600 J 5 W 440 J 20 s 28 800 J 28 800 J 2.5 mJ 50 W energy transferwork donetimepower600 J2 mins5 W440 J20 s22 WJ2 hours4 W2.5 mJ50 μs50 W600 J5 W440 J20 sJJ2.5 mJ50 W
29Power and velocity power = work done / time but: work = force x displacementtherefore: power = force x displacementtimebut: displacement / time = velocitytherefore:power = force x velocityP = F v
30QuestionCalculate the power of a car that maintains a constant speed of 30 ms-1 against air resistance forces of 20 kNAs the car is travelling at a constant speed the car’s engine must be exerting a force equal to the opposing air resistance forces.P = F v= 2 kN x 30 ms-1= N x 30 ms-1power = 60 kW
31Internet LinksReaction time stopping a car - also plots velocity/time graph - NTNUCar Accident & Reaction Time - NTNUWork (GCSE) - Powerpoint presentation by KTKinetic Energy (GCSE) - Powerpoint presentation by KTGravitational Potential Energy (GCSE) - Powerpoint presentation by KTEnergy 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 - FunderstandingEnergy conservation with falling particles - NTNUBall rolling up a slope- NTNU
32Core Notes from Breithaupt pages 148 to 159 What is the principle of conservation of energy?Define work and give its unit. Explain how work is calculated when force and distance are not in the same direction.With the aid of a diagram explain how work can be found from a graph.Explain what is meant by, and give equations for (a) kinetic energy & (b) gravitational potential energy.In terms of energy explain what happens as a body falls under gravity.In terms of energy and work define power.Show that the power of an engine is given by: P = Fv.
33Notes from Breithaupt pages 148 to 150 Work and energy What is the principle of conservation of energy?Define work and give its unit. Explain how work is calculated when force and distance are not in the same direction.With the aid of a diagram explain how work can be found from a graph.Try the summary questions on page 150
34Notes from Breithaupt pages 151 & 152 Kinetic and potential energy Explain what is meant by, and give equations for (a) kinetic energy & (b) gravitational potential energy.In terms of energy explain what happens as a body falls under gravity.Repeat the worked example on page 152 this time where the track drops vertically 70 m and the train has a mass of 3000 kg.Try the summary questions on page 152
35Notes from Breithaupt pages 153 & 154 Power In terms of energy and work define power.Show that the power of an engine is given by: P = Fv.Repeat the worked example on page 154 this time where the engine exerts a force of 50 kN with a constant velocity of 100 ms-1.Try the summary questions on page 154
36Notes from Breithaupt pages 155 & 156 Energy and efficiency Try the summary questions on page 156
37Notes from Breithaupt pages 157 to 159 Renewable energy Try the summary questions on page 159