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Chapter 9 – Computing the next move (18 lessons including test) Lesson 9.1 What’s the next move? Content Sports physics, air traffic control, predicting collisions Activities Homework Activity 30S ‘Will the aircraft collide?’ Activity 40S ‘Perspectives on relative velocity’ Activity 25P ‘Remote measurements on distance’ Activity 10S ‘Reconstructing a flight’ Exam questions on relative velocity Activity 50E ‘Tracking aircraft paths by drawing’ Qs 10S ‘Calculated steps’ Qs p193 UP Jan. 07 Q10 Review addition of vector components to give resultant vectors. Calculate relative velocity of two objects by vector subtraction. Use vector subtraction procedure to calculate if two aircraft are on a collision course. Explain principles and practice of radar tracking of moving aircraft. Calculate position and bearing of an aircraft from successive radar pulse measurements. Lesson 1: Begin with a recap of addition of velocity and displacement vectors to give resultant velocity and resultant displacement, as discussed earlier in Chapter 8. Introduce how humans track moving objects when trying to catch a ball (p190), leading into a discussion of how radar is used to track aircraft and avoid collisions. Discuss how to determine whether two aircraft are on a collision course using the procedure outlined on p192. Illustrate this by demonstrating Activity 30S and/or Activity 40S with the default conditions. ‘Try these’ p193 question 7 is an excellent example of how to compute bearing and position from radar measurements. See also Understanding Processes Jan. 07 Q10. 9.2 Speeding up, slowing down UP Jan. 07 Q10 Acceleration, predicting more complex motions, moving along parabolas 25/06/2017 10:17 AM Explore the relationship between acceleration, velocity and displacement using software modelling activities. A. M. James, Matthew Arnold School, Oxford 1 Lesson Content Describe the chain of velocity vectors and displacements for a body undergoing uniform acceleration, with constant time interval between measurements. Explain the above in terms of addition of constant velocity increment in each successive time interval. Know that acceleration is determined by measuring the gradient of a velocity time graph. Lesson 2: Using sequences from Multimedia Motion CD ROM and/or air track, show how the displacement in each successive time interval increases during accelerated motion: no need for analysis at this stage. Now demonstrate, or have students do, Activity 70S, varying the acceleration, and noting the effect on the individual displacement vectors. Discuss what is meant by uniform acceleration, relating to the examples just viewed, and go through the computation rules for uniform acceleration, as per p195. Now have students explore this further using Activity 60S. Activities Homework Sequences from Multimedia Motion CD ROM Activity 60S ‘Introducing acceleration’ Activity 70S ‘Calculating a flight’ Explore the relationship between acceleration, velocity and displacement using software modelling activities. Know that the velocity-time graph for a body undergoing uniform acceleration is a straight line. Know that acceleration is determined by measuring the gradient of a velocity time graph. Know that distance gone equals area under a velocitytime graph. Calculate average speeds from velocity-time graphs using either measurement of distance gone or determination of midpoint of v-t graph. Lesson 3: Use Activity 80S to explore the relationship between displacement, velocity and acceleration graphically for a body undergoing uniform acceleration. Students should vary the acceleration and see the effect it has on the graphs. Consider also how to determine the distance gone (and hence 25/06/2017 10:17 AM A. M. James, Matthew Arnold School, Oxford Activity 80S ‘Constant acceleration with graphs’ Activity 100S ‘Acceleration from graphs’ Qs 10M ‘Displacementtime graph’ Qs 40M ‘Accelerationtime graphs’ 2 Lesson Content average speed) by measuring the area under the v-t graph, and also how the midpoint of the v-t graph gives the average speed. As extension work, Activity 100S gives students the opportunity to analyse the velocity-time graph for a complex motion, to determine the accelerations at various times. Activities Homework Qs 30S ‘Coping with graphs’ Qs 50S ‘Calculating accelerated steps’ UP G492 Specimen Q3, Q5; June 08 Q3; Jan. 08 Q1 Qs 60S ‘Uniform acceleration’ Qs 70S ‘Braking distance and the Highway Code’ Qs 100E ‘Slowing down a bicycle’ Qs p209 Multimedia Motion CD ROM clips Activity 140E ‘Rolling a marble on a parabola’ Activity 130D ‘A thrown tennis ball Qs p203 Qs 110S archery’ Appreciate how to derive the kinematic equations v =u + at, s = ½ (u+v)t, s = ut + ½ at2, v2 = u2 + as. Use the kinematic equations v =u + at, s = ut + ½ at2, v2 = u2 + as to solve motion problems. Recall and use the kinematic equation, s = ½ (u+v)t to solve motion problems. Lesson 4: Go through the derivation of the kinematic equations, as per p197-198. Make sure that sample calculations are included: see ‘Try these’ p203 and the problem sets listed. The equation s = ut + ½ at2 also follows from graphical considerations of the area under a v-t graph. Three of the equations are provided on the formula sheet, the fourth, s = ½ (u+v)t, is not. This last equation is simply displacement = average velocity x time, and also follows from graphical considerations. It may be useful to use the ‘suvat’ procedure as a way of identifying which equation should be used. Know that an objected projected in a gravitational field follows a parabolic path. Analyse parabolic motion in terms of independent horizontal and vertical velocity components. Solve numerical problems involving parabolic motion using kinematic motion equations. Record (x,y,t) data for a projectile motion. Lesson 5: This section could be introduced by showing the “monkey and hunter” game and related animations from the Albemarle teacher resources at 25/06/2017 10:17 AM A. M. James, Matthew Arnold School, Oxford ‘Accurate 3 Lesson Content http://waowen.screaming.net/revision/force&motion/mandh.htm http://physics.k12albemarle.org/teacher . You could also demonstrate this experiment. Stress the independence of horizontal and vertical motions, and the exact correspondence of the vertical component of motion of a horizontally-projected object with that of one dropped vertically. Use Activity 150S (4th model) and/or Albemarle resources to show how an object projected horizontally in a gravitational field follows a parabolic path. Discuss how to analyse the motion in this case using p206, stressing the independence of horizontal and vertical motions, and the fact that they are only linked by time. Relate observations to theory. Now using either Multimedia Motion, Activity 140E (or selfrecorded version) or Activity 130D demonstrate that a projectile fired at an angle follows a parabolic path. Students can now either try analysing a projectile sequence from Multimedia Motion or self-recorded clip to produce (x,y) data for the projectile as a function of time. Explore parabolic motion of projectiles using software modelling activities. Explain parabolic trajectory in terms of addition of changing vertical velocity vector to successive calculated velocities. Analyse (x,y,t) data from parabolic projectile motion to determine initial velocity magnitude and direction. Lesson 6: Students use Activity 150S (models 1-3) to show how the parabolic motion of an object projected at an angle to the horizontal arises from addition of downwards-increasing velocity increment to each successive calculated velocity. Go through how to analyse the (x,y,t) data from previous lesson to obtain initial vertical and horizontal velocity (range = vhoriz x t, vvert from solution of v2 = u2 + 2as) and therefore the initial velocity magnitude and direction. Note that there is a sheet called ‘Projectiles help sheet’ which may be useful here, although it and the accompanying diagram sheet approach 25/06/2017 10:17 AM A. M. James, Matthew Arnold School, Oxford Activities follows a parabolic path’ ‘Monkey and hunter’ experiment (see also Activity 170D) Albemarle resources from http://physics.k12albemarle.org/teacher Homework Activity 150S ‘Modelling parabolic motion’ Activity 174E/File 120L ‘Finding the range of projectiles’ Multimedia Motion CD ROM Qs p203 Qs 80S ‘Throwing a ball’ 4 Lesson Content projectile motion from the perspective of horizontal and vertical velocity components added to give a resultant, rather than the changing vertical velocity component being added to the overall velocity vector to give the resultant. It is also worthwhile at least demonstrating the software part of Activity 174E to show how the parabola is affected by changes to the initial velocity. Activities Homework UP Jan. 08 Q9; Jan. 07 Q6 Qs 60S ‘Uniform acceleration’ Qs 70S ‘Braking distance and the Highway Code’ Qs 100E ‘Slowing down a bicycle’ Worksheet ‘The bouncing ball’ Exam questions on projectile motion Qs 80S ‘Throwing a ball’ Qs 110S ‘Accurate archery’ Qs 90S ‘A slide’ Qs 100D ‘Uncertainties in measuring g’ Qs 110D ‘Variation in braking distance with road conditions’ Qs 120D ‘Variation in braking distance between cars’ Qs p203 Develop problem solving skills using the kinematic equations of motion, including projectiles. Lesson 7: Practise problem solving. Qs 100D, 110D, 120D are good for experimental uncertainties and ‘plot and look’. 9.3 Forces change Projectile motion, achieving prediction in more complex situations 25/06/2017 10:17 AM A. M. James, Matthew Arnold School, Oxford 5 Lesson velocities Content Activities Homework Explore the relationship between force, mass and acceleration experimentally. Lesson 8: Recap GCSE work on Newton’s second law, showing how F = ma is derived from FΔt = Δmv. Use a frictioncompensated ramp, a dynamics trolley, pulley, cord, set of masses and light gates. Sample results are provided on worksheet trolley light gates data. Another version using a single light gate and a single card with a notch is described in Activity 200E. As a simpler alternative, use a dynamics trolley with ticker timer on slopes of varying angles, and plot the acceleration obtained from the ticker tape graph against sine of the slope angle to get g (see also lesson 10). Recall and use the equation F = ma (Newton 2) in solving problems. Know that F in the equation above is the resultant force. Calculate the resultant force on a body from a knowledge of the magnitudes and directions of all the forces acting upon it. Lesson 9: Explore F = ma using Activity 220S. Emphasise that the force in this equation is a resultant force, using Qs 120M140M to give students practice in determining resultant forces (could be homework). Discuss how resultant forces can change velocity of an object in a variety of ways, as per p207. Ramp, trolley, pulley, cord, set of 50 g and 100 g masses, light gates Activity 200E ‘Acceleration and resultant force using a light gate’ Activity 220S ‘Force, mass and acceleration’ Qs 120M ‘Adding forces graphically’ Qs 130M ‘A loading problem’ Qs 140M ‘Landing an aircraft’ Qs 150S ‘Lifting a car’ Qs 160S ‘Newton’s second law’ UP G492 Specimen Q6; June 08 Q6; Jan. 07 Q8; June 08 Q10; Jan. 08 Q4 25/06/2017 10:17 AM Determine experimentally the acceleration due to gravity. Know that the weight of a body is obtained by multiplying its mass by the gravitational field strength (W = mg). A. M. James, Matthew Arnold School, Oxford 6 Lesson Content Use W = mg and F = ma to explain why bodies of different mass fall at the same rate. Lesson 10: Determine the acceleration due to gravity (using Activity 120E, 130E or the ‘Measuring g’ timer kit). Discuss the relationship between mass and weight, as per p206-207, and therefore explain in terms of F = ma why objects of different mass fall at the same rate. You could do a ‘Measuring g’ circus, with different groups trying different methods as listed in Activity 130E. Activities Homework Activity 120E ‘Measuring the acceleration of free fall’ Activity 130E ‘Measuring g in lots of different ways’ ‘Measuring g’ electronic timer experiment Data from the ‘Measuring g’ experiment can be used in the data analysis coursework activity. Reading 10T ‘The mysteries of mass’ Qs 180M ‘F=ma: some tricky problems!’ Explore air resistance experimentally and using software modelling activities. Lesson 11: Optional, so omit if behind schedule. Explore motion in resistive media by doing Activity 260E, and then modelling with Activity 270S. In Activity 270S, it is helpful to adapt the model so that k is a variable. Set k to 1.0. Explore air resistance experimentally and using software modelling activities. Know that the air resistance force is made up of two components, depending on velocity and velocity2. Explain why an object reaches a terminal velocity when falling through air, in terms of resultant forces and F = ma. Lesson 12: Explore the effects of air resistance on the motion of a body using Activity 280S, and, as extension work, Activity 290S. Strictly speaking, this lesson is optional, but it is a very good way of showing the connection between resultant force, acceleration and velocity. 9.4 Transport engineering Activity 260E ‘Falling cupcakes’ Activity 270S ‘Balancing forces on cupcakes’ Activity 280S ‘Modelling resistance’ Activity 290S ‘Throwing in air’ air Qs 190D ‘Cycling through air’ Qs p208 UP June 07 Q10 Transport using flows of energy for a purpose, controlling energy flows to optimize transport properties. Investigate energy transfer in balls bouncing from surfaces Appreciate how to derive the expressions kinetic energy = ½ mv2 and gravitational potential energy = 25/06/2017 10:17 AM A. M. James, Matthew Arnold School, Oxford 7 Lesson Content mgh from work = force x displacement. Recall and use the expressions KE = ½ mv2 and ΔGPE = mgh in solving problems involving energy exchanges. Know that when energy exchange takes place, some of the energy is dissipated as heat. Lesson 13-14: A good place to start is with the experiments on rebounding balls, showing students how to calculate the energy transferred as heat and sound by a consideration of PE before and after a bounce. Derive the expression KE = ½ mv2 energy from a consideration of W = Fs. Alternatively, you could use v2 = u2 + 2as as a starting point. Now show how W = Fs gives rise to ΔGPE = mgh for an object raised in a uniform gravitational field. Show how GPE is changed into KE when an object falls under gravity (no resistive forces). The consistency with the kinematic equations of motion can also be shown. Explore experimentally the relationship between braking force and braking distance, and between speed and braking distance. Explain the relationships in terms of KE of vehicle = braking force x braking distance. Lesson 15: Students investigate the relationship between braking distance and force using Activity 340E. This can be extended to investigating the effect of speed on braking distance. Discuss findings in terms of the relationship KE of vehicle = braking force x braking distance. Explain why vehicles have a maximum speed in terms of balanced driving and resistive forces, and in terms of energy flows. Appreciate how to derive the relationship power = force x velocity. Use the equation power = force x velocity to solve problems involving motion and energy exchanges, 25/06/2017 10:17 AM A. M. James, Matthew Arnold School, Oxford Activities Homework Activity 320E ‘Good on the rebound’ Activity 330E ‘Poor on the rebound’ Qs 200E ‘A bouncing ball’ Qs 210E ‘Landing heavily’ Qs 220S ‘A skateboarder’ Qs 260S ‘Rolling up and down slopes’ UP Jan. 07 Q2; G492 Specimen Q8 Activity 340E ‘Stripping away kinetic energy’ Activity 375E ‘Modelling braking distance’ 8 Lesson Content including, for the more able, motion up a slope. Lesson 16-17: Begin by posing the question as to why every vehicle must have a maximum speed, leading to the conclusion that resistive forces increase with speed, and no further acceleration is possible when the resistive forces balance the driving force provided by the engine. Now get students to explain why streamlining increases the maximum speed, in terms of resistive forces (lesson 13 may help). Now reintroduce the arguments in terms of energy instead of force, and have students do Activity 360S. Go through the treatment on p214, to explain maximum speed in terms of engine power = resistive forces x velocity. Finish with a consideration of energy flows in motion uphill, by considering ‘Try these’ question 7 on p215 and/or some of the examples in the problem sets listed on the right. Do Chapter 9 test. 25/06/2017 10:17 AM A. M. James, Matthew Arnold School, Oxford Activities Homework Activity 360S ‘Energy flows and motion’ Qs 230S ‘Power and cars’ Qs 240W ‘Along the flat and up the hill’ Qs 280S ‘Working out with a cycle’ Qs 270D ‘Retarding a cyclist’ Qs p215 UP June 07 Q6 Qs p217 9