chapter in the Student Book. Summary of the chapter Higher ... · PDF fileacceleration using ticker tape, video clips, software ... Hooke’s law Non-Hookean behaviour ... Energy conservation

Salters Horners AS/A level Physics 1 Teacher Notes

© University of York, developed by University of York Science Education Group. Page 1 of 5 This sheet may have been altered from the original.

Chapter 1

HFS

HIGHER, FASTER, STRONGER

Overview of chapter Table 1.1 summarises the content and skills covered in this chapter, and Table 1.2 lists the learning outcomes required by the exam specification. The latter are also listed as Achievements in the final section of the chapter in the Student Book.

Table 1.1 Summary of the chapter Higher, Faster, Stronger

Outline and reference to student materials Key points Skills Notes

Section 1.1

Biomechanics

Introductory video and reading

Scope of physics in analysing and improving performance

Section 1.2

Describing motion

Analysing speed record data

Activity 1

Additional Sheet 1

Plotting and extrapolating a graph

Average speed

Application of number

GCSE revision

Discussion of distance and direction

Activity 2

Additional Sheet 2

Idea of vectors

GCSE revision

Calculations with velocity and acceleration

Additional

Sheet 3

Activity 3

Equations for uniformly accelerated motion

Free fall


GCSE revision

Section 1.3

Motion graphs

Finding instantaneous velocity and acceleration using ticker tape, video clips, software ...

Activity 4 Analysis using small time intervals

Practical work

Use of ICT


... and graphs Additional

Sheet 4

Activity 5

Additional Sheet 5

Gradients of displacement–time and velocity–time graphs


Optional extension: differentiation

Analysing graphical records of motion to find overall change of displacement and change of velocity

Activity 6

Additional Sheets 6 and 7

Area under velocity–time and acceleration–time graphs

Equations for uniformly accelerated motion

Use of ICT


Optional extension: integration

Timing free fall to determine g

Activity 7 Free fall Practical skills Application of number

CORE PRACTICAL

Section 1.4

Force and acceleration

Calculations with force, mass and acceleration

Use of force sensor and graphing software

Additional Sheet 8

Additional Sheet 4

Force, mass and acceleration

Newton I and II

Weight and gravitational field

Use of ICT


GCSE revision

Drawing and labelling diagrams to show pairs of forces

Activity 8

Activity 9

Newton III

Equilibrium


Section 1.5 Momentum

Analysing collisions using momentum

Relating momentum conservation to Newton II and III

Activity 10 Momentum

Conservation of linear momentum

Practical work


Section 1.6

Summing up Part 1

Use of key terms from Part 1

Activity 11 Study skills

Communication

SAMPLE MATERIA

L



Chapter 1

HFS


Section 2.1

Hanging on

Measuring and calculating forces in equilibrium

Activity 12

Activity 13

Activity 14

Activity 15

Additional Sheet 9

Activity 16

Activity 17

Vectors and scalars

Equilibrium of forces

Free-body diagrams

Combining vectors in 2D by calculation and by drawing

Resolving vectors into components

Practical work

Application of number Study skill

Section 2.2

On the ropes

Obtaining and analysing force-extension measurements

Activity 18 Stiffness

Hooke’s law

Non-Hookean behaviour

Practical work


GCSE revision

Section 2.3 Balancing

Applying principle of moments to extended objects in equilibrium

Activity 19

Activity 20

Principle of moments

Centre of gravity


Practical work

Section 2.4

Summing up

Part 2



Communication

Section 3.1

Energy return shoes

Discussions of ‘scientific’ advertising and of ‘energy vocabulary’

Additional Sheet 10

Activity 22

Activity 23

Energy transfer and conservation

Kinetic and potential energy

Communication GCSE revision

Calculating ‘energy return’ when jumping ...

Activity 24 Work done by force

Efficiency Gravitational potential energy

Practical work


GCSE revision

... and running Activity 25

Additional Sheet 4

Kinetic energy Application of number

GCSE revision

Section 3.2

Speed skiing

Calculations relating speed to distance moved along slope

Work done when force not along direction of motion


Section 3.3

Pumping iron

Measurement of power in physical activities

Activity 26

Activity 27

Power Practical work

Use of ICT Application of number

GCSE revision

Section 3.4

Summing up

Part 3



Section 4.1

Bungee jumping

Analysis of bungee jump in terms of energy

Activity 29

Energy stored in distorted materials Area under force– displacement graph

Energy conservation

Practical work


Section 4.2

Pole vaulting

Calculations relating to pole vault records

Energy conservation

Material properties


Section 4.3

Summing up Part 4

Use of key ideas from Part 4

Study skills


Section 5.1

Ski jumping

Exploration of factors affecting range of ski jump

Activity 30

Activity 31

Activity 32

Motion of a horizontally launched projectile

Independence of vertical and horizontal motion

Practical work Application of number

Section 5.2

Throwing

Exploration of factors affecting range of shot-put

Activity 33

Range of a projectile launched at an angle


Use of ICT

Optional extension work

SAMPLE MATERIA

L



Chapter 1

HFS


Section 5.3

Summing up Part 5

Use of key ideas from Part 5

Activity 34

Activity 35

Practical work Application of number

Section 6.1

Summing up the chapter

Use of key ideas from the whole chapter

Activity 36

Activity 37

Study skills

Communication Application of number

Section 6.2

Questions on the whole chapter

Questions and calculations

Additional Sheet 11 Application of number

Consolidation and revision

Section 6.3

Achievements

Chapter tests Additional

Sheets 12, 13, 14, 15

Communication


Questions illustrate style of external test

SAMPLE MATERIA

L



Chapter 1

HFS

Table 1.2 Learning outcomes specified for Higher, Faster, Stronger

Statement from Examination Specification Section(s) in this chapter

1 know and understand the distinction between base and derived quantities and their SI units 1.2, 1.4, 1.5, 2.3, 3.1

2 demonstrate their knowledge of practical skills and techniques for both familiar and unfamiliar experiments

1.3, 1.4, 1.5, 2.1, 2.2, 2.3

3 be able to estimate values for physical quantities and use their estimate to solve problems 1.4, 3.1, 3.3, 4.3

5 be able to communicate information and ideas in appropriate ways using appropriate terminology 3.1, 3.3, 3.4, 5.3

9 be able to use the equations for uniformly accelerated motion in one dimension:

s = 2

tvu )(

v = u + at

s = ut + 21 at2

v2 = u2 + 2as

1.2, 1.3

10 be able to draw and interpret displacement/time, velocity/time and acceleration/time graphs 1.3

11 know the physical quantities derived from the slopes and areas of displacement/time, velocity/time and acceleration/time graphs, including cases of non-uniform acceleration, and understand how to use the quantities

1.3

12 understand scalar and vector quantities, and know examples of each type of quantity and recognise vector notation

1.2, 2.1

13 be able to resolve a vector into two components at right angles to each other by drawing and by calculation

2.1

14 be able to find the resultant of two coplanar vectors at any angle to each other by drawing, and at right angles to each other by calculation

2.1

15 understand how to make use of the independence of vertical and horizontal motion of a projectile moving freely under gravity

5.1, 5.2

16 be able to draw and interpret free-body force diagrams to represent forces on a particle or on an extended but rigid body

2.1, 2.3

17 be able to use the equation ∑F = ma, and understand how to use this equation in situations where m is constant (Newton’s second law of motion), including Newton’s first law of motion where a = 0, objects at rest or travelling at constant velocity

Use of the term terminal velocity is expected

1.4, 2.1

18 be able to use the equations for gravitational field strength g = F/m and weight W = mg 1.4

19 CORE PRACTICAL 1: Determine the acceleration of a freely falling object 1.3

20 know and understand Newton’s third law of motion and know the properties of pairs of forces in an interaction between two bodies

1.4

21 understand that momentum is defined as p = mv 1.5

22 know the principle of conservation of linear momentum, understand how to relate this to Newton’s laws of motion and understand how to apply this to problems in one dimension

1.5

23 be able to use the equation for the moment of a force, moment of force = Fx where x is the perpendicular distance between the line of action of the force and the axis of rotation

2.3

24 use the concept of centre of gravity of an extended body and apply the principle of moments to an extended body in equilibrium

2.3

25 be able to use the equation for work ∆W = F∆s including calculations when the force is not along the line of motion

3.1, 3.2

26 be able to use the equation Ek = 21 mv2 for the kinetic energy of a body 3.1

27 be able to use the equation ∆Egrav = mg∆h for the difference in gravitational potential energy near the Earth’s surface

3.1, 4.1, 4.2

28 know, and understand how to apply, the principle of conservation of energy including use of work done, gravitational potential energy and kinetic energy

3.1, 4.1, 4.2

29 be able to use the equations relating power, time and energy transferred or work done

P = E/t and P = W/t

3.3

30 be able to use the equation

efficiency = input] power) (orenergy [total

output] power) (orenergy [useful

3.2

SAMPLE MATERIA

L



Chapter 1

HFS

This chapter uses the context of sport to cover some work on motion, forces and energy. Much of this work involves revision and extension of material from GCSE.

The chapter is designed to be taught before Good Enough to Eat (which introduces some basic ideas about solid materials) and Spare Part Surgery (which develops some more advanced ideas about solid materials). However, Good Enough to Eat could be taught in parallel with Parts 3 to 5 of this chapter.

There is quite a bit of GCSE revision as well as some new material. If you are confident that your students already have a firm grasp of GCSE material, it would be wise only to spend a short time on the revision activities or to omit them entirely. However, going over familiar ground can be valuable, particularly in activities that help develop students’ skills in using ICT and in working with others. There are many good ICT resources available to enhance this chapter; our recommendations are listed in the Technician Notes along with details of suppliers.

Part 1 of the chapter shows how graphs and equations are used in the science of biomechanics to describe and analyse uniform and non-uniform motion, for example of a sprinter. Conservation of linear momentum is introduced. In Part 2, the equilibrium of forces in rock climbing and gymnastics and the elastic behaviour of climbing ropes are used to introduce vector diagrams and calculations, the principle of moments, and force–extension graphs. Part 3 introduces ideas of work and of kinetic and potential energy in order to look into some of an advertiser’s claims for training shoes, applies the same ideas to speed skiing, and then extends them to include power in order to analyse weight training and other physical activities.

In Part 4, energy and elastic behaviour are brought together in a study of bungee jumping and pole vaulting. Part 5 looks at ski jumping and shot-putting, revisiting ideas about motion and vectors from Parts 1 and 2 in order to analyse the motion of projectiles.

Part 6 looks back over the whole chapter and helps students to draw together the physics. A recurring theme in the chapter is that of using graphs to display data and to deduce further information from gradients and areas.

As each part of this chapter builds on work from earlier parts, and ideas are continually being revisited, revised and extended, it would be best if the whole chapter could be taught by one teacher. However, if necessary, Part 2 could be taught in parallel with Part 1 and, once Parts 1 and 2 are finished, Part 5 could be taught separately from Parts 3 and 4.

SAMPLE MATERIA

L



Chapter 1

HFS

1 RUNNING

1.1 Biomechanics The Institute of Physics 2012 schools lecture ‘Physics and the Games: a winning formula’ provides a good introduction to this chapter. Delivered by a team of sports engineers, the lecture illustrates how Newtonian physics underlies the world of sport and how engineering and technology are used in sports.

The IOP’s 2004 schools lecture ‘Sport vs Physics’, delivered by a sports scientist, covers some of the same ground and is also excellent.

Rather than showing a whole lecture all at once, short sections could be used throughout the teaching of this chapter.

Videos of both lectures are available as downloads: go to www.pearsonhotlinks.co.uk, search for this title and click on this activity.

1.2 Describing motion

ACTIVITY 1 RECORD TIMES

No sheet

This short introductory activity can be used to check that students know how to plot graphs and to introduce (or review) the conventions for writing units and labelling axes; that is, units such as m s–1 are expressed in index notation, and axes and tables are labelled with ‘quantity/unit’.

Speed

Additional Sheet 1

Students should be familiar with average speed from GCSE work, but the delta notation may need some discussion. Questions on Additional Sheet 1 can be used to revise the key ideas, and to check whether students are happy with rearranging equations and dealing with units. The worked answers show how to include units at every step. This would also be a good opportunity to discuss precision and significant figures.

In the right direction

Additional Sheet 2

ACTIVITY 2 VECTORS AND SCALARS

No sheet

As an alternative to the activity described in the Student Book, you could provide students with cards, each with the name of a physical quantity (e.g. force, temperature). If each student has one card, the ‘vectors’ and ‘scalars’ could be asked to sort themselves into two groups at opposite ends of the room.

For some students, this activity will be a revision of GCSE work. Even so, students often find it difficult to appreciate that work (motion by a force) and kinetic energy are scalars, because they are associated with motion that is often in a straight line. Making a link with the ‘amount of fuel’ needed to do work or increase kinetic energy might help here.

In Part 1 of this chapter, we deal only with one-dimensional motion. The examples on Additional Sheet 2 show how positive and negative signs are used to denote directions of displacements and velocities.

SAMPLE MATERIA

L



Chapter 1

HFS

Acceleration

Additional Sheet 3

Again, we hope that the calculations on acceleration in Questions 1 to 4 will be GCSE revision for most students, and that they will already be familiar with gravitational acceleration and free fall. If they are not, or in any case could do with a reminder, we suggest issuing Additional Sheet 3 (which provides two worked examples) and doing some or all of the following demonstrations.

ACTIVITY 3 FREE FALL

Demonstration

No sheet

Galileo’s experiment

Show, and discuss, the dropping of two unequal masses (e.g. two pebbles). ‘Common sense’ says the heavier one falls faster. Galileo’s counter-argument went as something like this. ‘Imagine two identical stones of equal mass. When released from a height, they will fall side by side. If they are now glued together they will still fall side by side, but now their combined mass is twice their individual mass.’

Guinea and feather

Demonstrate the importance of air resistance using the classic ‘guinea and feather’ in an evacuated tube.

Hammer and feather on the Moon

Show a video clip of Neil Armstrong dropping a hammer and feather on the moon. Go to www.pearsonhotlinks.co.uk, search for this title and click on this activity.

SAFETY

Beware of implosion. Use a safety screen and ensure eye protection is worn.

1.3 Motion graphs The use of graphs to describe and analyse motion is an important element of this chapter. You might like to start with the following demonstration.

Using a motion sensor

A ‘motion sensor’ (strictly, a position sensor) for use with a computer allows students to generate and discuss position–time graphs. Students can explore the shapes of graphs they produce when moving towards or away from the sensor. Ask them to move so as to generate graphs with particular shapes (harder than it sounds!). Points to bring out include: steepness of graph is related to speed of motion; flat graph corresponds to remaining at rest.

The Student Book discusses graphs of uniform motion. It is worth spending time making sure students know what they are doing in Questions 5 to 8 before moving on to analysis of non-uniform motion.

ACTIVITY 4 NON-UNIFORM MOTION

Activity Sheet 4

The purpose of this activity is to illustrate how measurements of position at successive small time intervals can be used to deduce velocity during non-uniform motion, and how changes in velocity can in turn be used to calculate acceleration. Students could be asked to plot displacement–time, velocity–time and acceleration–time graphs from their results. You could discuss the advantages and disadvantages of using shorter or longer time intervals. Shorter time intervals reveal changes in the velocity and acceleration, but require more arithmetic. You might like to raise the issue of making the time intervals so short that the measurements are dominated by uncertainties.

Beware of prolonging this activity to the point of tedium. Students will probably appreciate quite early on that the calculations are repetitive and could be automated.

SAMPLE MATERIA

L



Chapter 1

HFS

ACTIVITY 5 PRODUCING GRAPHS OF MOTION

Activity Sheet 5

Additional Sheet 4

The aim of this activity is to reinforce ideas about motion, and to give students experience in using the Tracker motion analysis software. Additional Sheet 4 gives some guidance. Make sure that they have enough time to ‘play’ with the software and become confident in using it, and that each student produces graphs of displacement, velocity and acceleration.

Going the distance

Additional Sheets 6 and 7

Students often take a while to get used to the idea of the area under a graph. Two points, in particular, are worth emphasising. First, the ‘area’ under a graph is found using the numbers on the axes; it is not the actual area occupied on the paper. Second, the area must extend down to zero on the y-axis; if the graph is plotted with the y-axis starting above zero, then part of the area will be chopped off. (Areas under graphs will be used again later in this chapter.)

ACTIVITY 6 TANGENTS AND GRADIENTS

Additional Sheet 5

For many students, this might be the first time they have encountered the idea of a tangent to a graph, and the idea of a gradient. Make sure that they appreciate that drawing a tangent and finding its gradient is equivalent to calculating x/t (or v/t) using a very small time interval.

For extra practice, students could use graphs of their own measurements from Activity 5. If they join the plotted points with a smooth curve, they should then find that the gradient of a tangent on their displacement graph gives a velocity close to the one they calculated for that time interval. They could do likewise with graphs generated by Tracker.

Additional Sheet 5 shows how differential calculus can be used to derive analytical expressions for velocity and time in some instances. It is intended for those students who are studying maths alongside physics and who might appreciate seeing this application of calculus.

Uniform acceleration

When the acceleration is uniform, the area under the velocity–time graph leads to the useful equation s = ut + 2

1 at2. Additional Sheet 6 sets out this derivation in slightly more detail than in the Student Book, for benefit of students who might appreciate a reminder about areas of triangles. The questions on this topic use s = ut + 2

1 at2 in some calculations relating to free fall and to the following demonstrations.

SAMPLE MATERIA

L



Chapter 1

HFS

ACTIVITY 7 FINDING g BY TIMING FREE FALL

Demonstrations followed by CORE PRACTICAL.

Activity Sheet 7

Testing free fall by ear

Tie metal washers to a length of thin string so that the distances of each washer from the end are in the proportions 1 : 4: 9 : 16 : 25 and so on (see Figure 1.1). Anchor one end to the floor at the foot of a stairwell and hold the string vertically from the top of the stairs. When the string is let go, each washer in turn hits the floor after the same time interval, giving rise to a regular series of ‘clinks’.

Figure 1.1 Apparatus for testing free fall by ear

Reaction time

Students could test their answers to Question 3 on Additional Sheet 6. You could also demonstrate the pub trick of dropping a £5 note between someone’s finger and thumb: if they grasp the note as it falls, without moving their hand down to keep up with it, they get to keep it. The time for a note to fall through its length (about 0.12 m) is about 0.15 s – human reaction time is typically at least 0.2 s.

Non-uniform acceleration

Additional Sheet 7 shows how integral calculus can be used to derive analytical expressions for displacement and velocity in some instances. Like Additional Sheet 4, it is intended for those students who are studying maths alongside physics and might appreciate seeing a physical application of calculus.

Measuring g

This activity has been designated as a CORE PRACTICAL.

Students use an electronic timer (or stopwatch) to determine g.

If they have not used light gates before, this is a good introduction; it is quite difficult to get an accurate answer. Students could experiment with different-length cards and different distances between light gates.

The electronic timing method gives a good example of manipulating data to obtain a straight-line graph, the gradient of which can be used to find a constant. This could be a good place to introduce error bars and the idea of finding the uncertainty in g from the maximum and minimum gradients of the line.

SAFETY

Make sure no-one can enter the stairwell as the washers are dropped by placing a student at each access point. Ensure eye protection is worn. SAMPLE M

ATERIAL

Salters Horners AS/A level Physics 1 Additional Sheet 2


Chapter 1

HFS

IN THE RIGHT DIRECTION

In Part 1 of this chapter we are concerned only with motion in one dimension (back and forth along a straight line), and we use positive and negative signs to denote the direction of a vector as the following examples show.

Displacements A swimmer swims two lengths of a 25 m pool (‘there and back’). What distance does he travel, and what is his overall displacement?

distance = 25 m + 25 m = 50 m

When dealing with displacement, we must choose one direction to be positive and the other negative. The choice is arbitrary. Suppose we choose ‘outwards’ to be positive and ‘back’ to be negative.

displacement when swimming first length = +25 m

displacement when swimming second length = –25 m

and so

total displacement = 25 m – 25 m = 0 m

(he is back where he started).

MATHS REFERENCE

Index notation and powers of ten

See Maths note 1.1

Index notation and units

See Maths note 2.2

Velocities The car in Figure 2.1 is travelling west at 12 m s–1. Later, it is travelling east at 12 m s–1. What are (a) its change in speed and (b) its change in velocity?

Figure 2.1 A car travels west and then east

(a) There is no change in speed.

(b) The car would have to slow to a stop and then move off in the opposite direction at 12 m s–1. If we choose east to be positive, then west is negative.

initial velocity = –12 m s–1

final velocity = +12 m s–1

change in velocity = final velocity – initial velocity

= +12 m s–1 – (– 12 m s–1) = +24 m s–1 (Equation 2 in Student Book)

SAMPLE MATERIA

L

SAMPLE MATERIA

L

To be safe

ty rev

iewed

Salters Horners AS/A level Physics 1 Activity Sheet 7


Chapter 1

HFS

FINDING g BY TIMING FREE FALL

ACTIVITY

Carry out some explorations of freely falling objects that show how the time of fall is related to the distance fallen. Use your results to find the acceleration due to gravity.

PRACTICAL SKILLS REFERENCE

Scientific questions and information research

See Practical Skills note 1.1

Planning and experimental design

See Practical Skills notes 2.1 and 2.2

Carrying out practical work


Analysis and interpretation of data


Conclusion and evaluation


Scientific questions and information research Many falling objects can be considered to be in ‘free fall’ (Figure A7.1). Their motion can be analysed to find a value for g, the acceleration due to gravity.

Figure A7.1 Free fall

Your task:

make some measurements on a free-falling object and use those measurements to work out a value for g.

As you prepare to carry out the laboratory work, here are some things to think about and research:

(i) What is free fall and how is it defined?

Under what conditions can a body be considered to be in free fall? (Hint: consider the force(s) involved.)

What is the accepted value of g close to the Earth’s surface? What are its SI units?

(ii) Methods of determining g.

A basic method is described below. You might be able to use a similar method, depending on the apparatus that is available for you to use.

Aim to research at least one alternative approach and give a brief outline of it, together with any advantages and disadvantages.

(iii) Relevant equations.

If you are able to measure u, v and t directly, then you can use

g = t

uv

Explain why this equation is really v = u + at (Equation 3b from the Student Book).

If you cannot measure speed directly with your method, consider which equation of uniformly accelerated motion is best to use. (It needs to include acceleration (a = g), but it cannot have a second unknown (v) in the same equation.)

SAMPLE MATERIA

L

To be safe

ty rev

iewed



Chapter 1

HFS

Planning and experimental design

SAFETY

In this experiment, there are unlikely to be major safety issues. However, you should still think carefully about the design of the apparatus and how everyone can be safe in its vicinity. Think also about possible damage to apparatus. List any safety issues in this experiment and note how you will deal with each one. Table A7.1 shows one way to record this.

Safety issue How it will be minimised

Table A7.1 Table for recording safety issues

Consider how you might modify your experimental design to address safety issues. Discuss your findings with the teacher prior to starting the experiment.

Apparatus and methodology

This is a basic method using an electronic timer.

Time the fall of a steel object from rest through a known distance using apparatus set up as in Figure A7.2.

Figure A7.2 Electronic timing apparatus for Activity 7

The timing mechanism may consist of an electromagnet and trapdoor connected to a scaler timer. Starting the timer releases the ball from the electromagnet, and as the ball goes through the trapdoor on the floor it stops the timer.

Alternatively, the ball may be held against two contacts connected to the scaler timer. Releasing it starts the clock, and the clock stops when the sound of the ball hitting the floor is picked up by a small microphone on the floor.

If you do not have access to an electronic timer and will instead be using a stopwatch, consider how to alter the method to reduce the impact of human reaction time on your measured times and so improve the overall result.

What should you use for your falling object? All objects fall at the same rate in free fall, so in principle the nature of an object (size, shape, and so on) is irrelevant. Explain why, in practice, a steel ball is a good choice for this particular method.

Variables

Decide what you are going to measure: this will depend on the method you use.

You may decide to make and record some other measurements.

How will you measure the distances through which your object falls? Use an appropriate measurement device and explain how you will use it.

Should you aim to drop your object through a long distance or a short one? How might this choice affect your results?

Decide how many different heights would be appropriate to try, and also how many repeats would be appropriate for each height.

SAMPLE MATERIA

L

To be safe

ty rev

iewed



Chapter 1

HFS

Carrying out practical work

Carry out the experiment following your own plan and any instructions that you have been given, and with appropriate safety precautions.

If unexpected issues arise, deal with them sensibly, taking advice where needed and make a note of them to include in your final report.

Record all measurements – including repeated ones – as soon as they are taken, in tables with appropriate significant figures and units. Make a blank table for recording your measurements and include columns for quantities that you will calculate. Table A7.2 gives some headings, but you will need to add one more.

Trial number Distance fallen s/m Time taken t/s Mean time/s

Table A7.2 Partial results table for determining g


MATHS AND PRACTICAL SKILLS REFERENCE

Linear relationships

See Maths note 5.2

Gradient of a linear graph

See Maths note 5.3


See Practical skills notes 4.1 and 4.2


See Practical skills notes 5.1 and 5.2

This method gives a good example of manipulating data to obtain a straight-line graph, the gradient of which can be used to find a constant.

The motion is described by

s = ut + 21 at2 (Equation 6a in Student Book)

where s is the distance fallen by the ball and t is the time taken.

The initial velocity u = 0 and here the acceleration is g, so:

s = 21 gt2

You could measure t for just one distance and use the equation above to find g, but you will get a better value if you take several measurements with different distances and use a graph to find an average value for g.

What shape of graph do you get if you plot s against t?

Can you find g from the graph?

A straight-line graph would be much more useful.

y = mx + c

is the equation of a straight line. If c = 0, then

y = mx

Therefore, if s is plotted on the y-axis against t2 on the x-axis the graph will be a straight line through the origin. The gradient of the line will be 2

1 g.

If using ICT for tables and graphs, use settings that give correct numbers of significant figures, sensible scales and labelling, graph grid lines and sharply marked data points.

Draw a line of best fit. Think about whether or not it should pass through the origin (remember our equation has been simplified to one of the form y = mx).

Calculate the gradient. (Use a large right-angled triangle to do this. Why should you do this?)

SAMPLE MATERIA

L

To be safe

ty rev

iewed



Chapter 1

HFS


The conclusion of an experimental investigation such as this should be a clear statement of the result, an analysis of the strengths and weaknesses of the experiment, and detailed suggestions for one or two improvements.

The scatter of the points about the best straight line on a graph relates to uncertainty in the data. The maximum and minimum gradients of lines on your straight-line graph provide an estimate of the uncertainty in g, so you can state your result as follows:

Acceleration due to gravity = best experimental value uncertainty

Comment on how close your experimental result is to the accepted value for g. Calculate the percentage difference between your experimentally determined value of g and the accepted value quoted on exam data sheets of 9.81 m s–2. Consider whether your experiment might be expected to produce a result that is higher or lower than the accepted value.

Comment on how your apparatus and method might be improved. Consider whether the uncertainty in measuring height is more significant than the uncertainty in measuring time.



Chapter 1

HFS

CHAPTER TEST 1: MOMENTUM AND FORCES 30 marks total

Answer ALL the questions. Write your answers in the spaces provided.

The marks for individual questions and the parts of questions are shown in round brackets, for example (2).

There are 9 questions in this test.

You will be assessed on your ability to organise and present information, ideas, descriptions and arguments clearly and logically, including your use of grammar, punctuation and spelling.

1 Which of the following is not a vector? (1)

A velocity

B distance

C acceleration

D force.

2 Which statement about momentum is incorrect? (1)

A Momentum is a vector quantity.

B Momentum is conserved in collisions.

C Momentum has the SI unit kg m s–2.

D A resultant force is needed to change the momentum of an object.

3 Which of these statements about Newton’s third law are true? (1)

(1) The two forces are equal in size.

(2) The two forces are opposite in direction.

(3) Two different objects are involved.

A (1) only

B (1) and (2) only

C (1) and (3) only

D all of them.

SAMPLE MATERIA

L



Chapter 1

HFS

MARK SCHEME FOR CHAPTER TEST 1

Deduct a maximum of 2 marks on the paper for a numerical answer given without its unit or with an inappropriate number of significant figures.

1 B (1)

2 C (1)

3 D (1)

4 B (1)

5 (a) Centre of mass is at 50 cm mark – shown by X on diagram. (1)

(b) The ruler is uniform, so there is equal weight on either side of the pivot point, meaning that anticlockwise moment equals clockwise moment. (1)

(c) Weight of ruler = 0.100 kg × 9.81 N kg–1 = 0.981 N. (1)

Anticlockwise moment of ruler’s weight about pivot = 0.981 N × 0.20 m

= 0.1962 N m. (1)

To give an equal clockwise moment, force F = 0.1962 N m/0.30 m

= 0.654 N. (1)

(Total for Question 5 = 5 marks)

6 (a) B and C (1)

(b) Appropriate line drawn as gradient on graph

= 20 m s–1. (2)

(c) Appropriate area marked on graph

= 625 m. (2)


7 Award 1 mark for each of the following points up to a maximum of 4 if all three laws are discussed. Maximum 3 marks if not all laws are discussed.

(i) Newton I: Skater initially at rest because no resultant force acts on him. (1)

Weight and normal contact force have equal size and opposite direction. (1)

(ii) Newton III: Skater exerts force on wall, wall exerts equal and opposite force on skater. (1)

Newton II: While in contact with wall, skater experiences a resultant force, (1)

which accelerates him away from the wall. (1)

(iii) Newton I (and/or II): Skater has constant (horizontal) velocity because no resultant (horizontal) force is acting (friction with ice must be negligible). (1)


8 (a) Zero (1)

(b) Zero (1)

(c) The momentum of the larger fragment (m1v1) is equal in size (but opposite in direction) to the momentum (m2v2) of the smaller fragment:

234 u × v1 = 4 u × v2 (1)

The speeds are therefore in inverse ratio to their masses:

v2/v1 = m1/m2 = 234/4 = 58.5. (1)


SAMPLE MATERIA

L

Salters Horners AS/A level Physics 1 Technician Notes


Chapter 1

HFS

HIGHER, FASTER, STRONGER

Additional Sheets

Additional Sheet 1 Speed Section 1.2

Additional Sheet 2 In the right direction Section 1.3

Additional Sheet 3 Acceleration Section 1.2

Additional Sheet 4 Tracker Activities 5, 8 and 26

Additional Sheet 5 Velocity and acceleration by differentiation Section 1.3

Additional Sheet 6 Area under a graph Section 1.3

Additional Sheet 7 Displacement and velocity by integration Section 1.3

Additional Sheet 8 Force and acceleration Section 1.4

Additional Sheet 9 Components and resolution of vectors Section 2.1

Additional Sheet 10 Energy Section 3.1

Additional Sheet 11 Answers to questions on the whole chapter Section 6.2

Additional Sheet 12 Chapter test 1: Momentum and forces Section 6.3

Additional Sheet 13 Mark scheme for chapter test 1 Section 6.3

Additional Sheet 14 Chapter test 2: Energy and projectiles Section 6.3

Additional Sheet 15 Mark scheme for chapter test 2 Section 6.3

Software and videos Tracker

Tracker is a free video analysis and modelling tool built on the Open Source Physics (OSP) Java framework. It is designed to be used in physics education.

Tracker is recommended for Activities 5, 8 and 25, and for activities in later chapters (notably Transport on Track in the second year of the course). It can be downloaded from www.pearsonhotlinks.co.uk, search for this title and click on this activity.

The software requires Java 1.6 or higher and also supports QuickTime 7 (Windows/Mac).

The Tracker website provides instructions for use and tutorials. Sample videos can also be downloaded from the Tracker site.

Multimedia Motion

This software was recommended in earlier versions of SHAP. It is no longer available. You may have copies in your school/college, though it might not work on operating systems more advanced than Windows 98. It is appropriate for Activities 5, 8, 23 and 26.

ScienceScope

Data-logging equipment and software, available from:

ScienceScope Abingdon House 146 London Road West Bath BA1 7DD Phone: 01225 850020 Website: www.sciencescope.co.uk

SAMPLE MATERIA

L



Chapter 1

HFS

Activities

Activity 1 Record times

This is a paper-based activity. No laboratory apparatus is needed.

No sheet

Activity 2 Vectors and scalars


No sheet

Activity 3 Free fall

Demonstration

No sheet

Apparatus

SAFETY

Beware of implosion. Use a safety screen and issue eye protection.

Galileo’s experiment

two or more pebbles of unequal size

Guinea and feather

vacuum pump

1p coin

circle of paper, same size as coin

safety screen

eye protection

Classic demonstration, consisting of a plastic tube, at least 5 cm bore and approximately 1 m long, rubber bungs fitted to both ends. One bung has a hole bored to fit a short glass tube, which is connected to a vacuum pump with pressure tubing. A Hoffman clip on the tubing allows the sealed evacuated tube to be disconnected from the pump.

Hammer and feather on the Moon: see the NASA website (go to www.pearsonhotlinks.co.uk, search for this title and click on this activity).

Multimedia Motion CD-ROM (see above)

IBM-compatible computer running Microsoft Windows (see above)

Activity 4 Non-uniform motion

Probably a class practical (using ticker timers) or a whole-class, student-assisted demonstration (using video).

Activity Sheet 4

Apparatus

Either:

ticker timer

power supply

leads

ticker tape

SAMPLE MATERIA

L



Chapter 1

HFS

or:

metre rule (plus chalk or masking tape for marking 1 m intervals on a wall or fence)

camcorder and computer software, or video camera and recorder with good stop-frame facility and video monitor

acetate sheets

marker pens (preferably water-soluble)

Activity 5 Producing graphs of motion Activity Sheet 5

Additional Sheet 4

Apparatus

Using Tracker

Tracker software (see notes above)

Using a motion sensor

motion sensor

PC

connection lead

power supply

see notes on Data Harvest or ScienceScope above

Activity 6 Tangents and gradients


No sheet

Activity 7 Finding g by timing free fall

SAFETY

Make sure nobody is in the stairwell while this demonstration is taking place by placing a student at each access point. Issue eye protection.

Demonstration and core practical

Activity Sheet 7

Apparatus

Testing free fall by ear

thin string, longer than the top-to-ground-floor height of your nearest convenient stairwell

metal washers (at least 5)

Tie the washers to the string so that their distances from the end are in the proportions 1 : 4 : 9 : 16 : 25 and so on (see Figure 1.2).

Figure 1.2 Apparatus for testing free fall by ear

SAMPLE MATERIA

L



Chapter 1

HFS

Reaction time

metre rule

thin card (to cut into strips and stick onto rule)

scissors

Measuring g

This has been designated a core practical.

steel ball 1–1.5 cm diameter

scaler timer

Either:

electromagnet and trapdoor system

or:

small microphone and two leads or stiff wires taped to a ruler so that they just project over the end and can rest on the ball as in Figure 1.3

Figure 1.3 Apparatus for measuring g by timing

Activity 8 Inverse dynamics

Activity Sheet 8

Additional Sheet 4

Apparatus

Tracker software (see notes above)

Activity 9 Measuring forces directly

Probably a whole-class, student-assisted demonstration.

Activity Sheet 9

Apparatus

computer

Data Harvest or ScienceScope force sensor and graphing software (see above)

SAMPLE MATERIA

L

Documents

chapter in the Student Book. Summary of the chapter Higher ... · PDF fileacceleration using ticker tape, video clips, software ... Hooke’s law Non-Hookean behaviour ... Energy conservation