Solid Material

1.

rubber is commonly described as being more elastic than steel but steel has a greater modulus of elasticity than rubber. on the axes below, sketch two graphs which illustrate the difference in behaviour of rubber and steel when subjected to stress. S tre s s

S tra in(4)

describe with the aid of diagrams the difference in molecular structure of rubber and steel.

.............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. ..............................................................................................................................................(4) (total 8 marks)

2.

rubber is commonly described as being more elastic than steel but steel has a greater modulus of elasticity than rubber. on the axes below, sketch two graphs which illustrate the difference in behaviour of rubber and steel when subjected to stress. G ra p h s to s h o w : S tre s s(i) S te e l s te e p e r (ii) M a x s tr e s s s te e l 2 ru b b e r (1 ) (1 ) (1 )

(iii) M a x s tr a in r u b b e r 2 s te e l (iv ) O n e o f s e v e r a l p o s s ib le s h a p e m a r k s e .g . r u b b e r b e c o m in g s te e p e r a t la r g e s tr a in s

(1 )

S tra in(4 marks)

ealing, hammersmith and west london college

1

describe with the aid of diagrams the difference in molecular structure of rubber and steel.one point from each line below could be on a diagram rubber: steel: long molecules/polymers/equivalent coiled/tangled/amorphous (1) long range order/lattice/equivalent positive ions/polycrystalline (1) (1) (1) (4 marks) [total 8 marks]

3.

draw a labelled diagram of the apparatus you would use to find the young modulus of copper wire.

(2)

state the measurements you would take. .............................................................................................................................................. ..............................................................................................................................................(1)

how would you use your measurements to obtain a value for the young modulus? .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. ..............................................................................................................................................(3)

explain why the copper is used in the form of a long thin wire. .............................................................................................................................................. ..............................................................................................................................................(2)


2

two wires, x and y, are made from the same material. wire x is three times as long as y and has twice the diameter of y. when a load is suspended from x the wire extends by 8 mm. how much will wire y extend with the same load? .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. extension of wire y = .........................................................(3) (total 11 marks)

4.

draw a labelled diagram of the apparatus you would use to find the young modulus of copper wire.diagram to show: (i) (ii) wire fixed at one end, load at other end and length of wire implied as being at least 1 metre (1) device to aid measurement of small extensions (simplest acceptable marker against fixed ruler) (1) (2 marks)

state the measurements you would take.original length of wire extension / new length of wire diameter / radius / cross-sectional area of wire all three (1) (1 mark)

how would you use your measurements to obtain a value for the young modulus?plot stress (defined) v. strain (defined) or or plot load v. extension substitute values in fl/ae e = gradient or or e= gradient lo/a repeat for different loads (1) either gradient of linear region or use e values to check specimen is still elastic. (1) (3 marks) (1)

explain why the copper is used in the form of a long thin wire.so that a reasonable extension is obtained or so it stretches with a small load. (1) (1) (2 marks)ealing, hammersmith and west london college 3

measurements of extension will have smaller percentage uncertainty. (accept: measurements more accurate).

two wires, x and y, are made from the same material. wire x is three times as long as y and has twice the diameter of y. when a load is suspended from x the wire extends by 8 mm. how much will wire y extend with the same load?length correction 1/3 area factor (4 or (1) 4) (1) (3 marks) [total 11 marks]

extension of wire y = 11 mm (1)

5.

the table and graph show the properties of two materials a and b. material a b 0.34 3.2 brittle young modulus/ 1010 pa ultimate tensile stress/108 pa nature

use the graph to complete the table for material a.(3)

4 S tre s s /1 0 8 P a

2

A

0

0

0 .0 5

S tr a in

0 .1

use the table to draw a graph on the grid below showing the behaviour of material b.(2) (total 5 marks)


4

6.

the table and graph show the properties of two materials a and b.Material A B Young modulus/ 1010 Pa 1.0 0.34 Ultimate tensile stress/108 Pa 2.6 3.2 Nature Plastic / ductile brittle

use the graph to complete the table for material a.(3 marks)

use the table to draw a graph on the grid above showing the behaviour of material b.straight line of appropriate gradient uts 3.2; little plasticity (1) (2 marks) (1)

4 S tre s s /1 0 8 P a

B

A 2

0

0

0 .0 5

S tra in

0 .1[total 5 marks]


5

7.

the graph shows the behaviour of a material when subjected to stress. S tre ss /M P a 5

0 0 1 2 3 4

S tra in

give an example of a material which behaves in this way when put under stress. ........................................................................................................................................... add to the graph a second line which shows the behaviour of a brittle material with a young modulus of approximately 10 mpa.(3)

describe with the aid of diagrams the difference in structure between a crystalline solid and a polymeric one.

........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... ...........................................................................................................................................(4) (total 7 marks)

8.

example: rubber or other suitable material 2nd line on graph: straight line, any length aiming for (0.5, 5) (1) (1) 3 (1)


6

description: crystalline diagram ordered arrangement of atoms/ions atoms in random order/ tangled/coiled (2) [no diagrams, maximum 2/4]

polymeric diagram (2) long molecules/chains of 4[total 7 marks]

9.

describe with the help of a diagram the structure of a polycrystalline material.

.................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................(2)

a force-extension graph for a long thin copper wire is drawn below. 20 F o rc e /N 10

0

0

10

20 30 E x te n s io n /m m

show clearly on the graph the region where the copper wire obeys hookes law. what additional information would be needed in order to calculate the young modulus for copper from this graph? .................................................................................................................................... estimate the energy stored in the wire when it has been extended by 20 mm. energy stored = ...(5) (total 7 marks)


7

10.

structure of a polycrystalline material: [diagram essential. it must be compatible with words and must convey the jigsaw idea, i.e. not a bowl of sugar.] diagram and words convey idea of a number of crystals/grains idea of planes of atoms in different directions region on graph where copper wire obeys hookes law: hookes law region up to (9,15) additional information needed: length and cross-sectional area estimate of energy stored in wire: sensible attempt at area up to 20 mm answer in range 250 270 0.26 j 5[7]

2

11.

(a)

define work.

.................................................................................................................................... ....................................................................................................................................(1)

state an appropriate unit for work. .................................................................................................................................... ....................................................................................................................................(1)

express this unit in terms of base units. .................................................................................................................................... ....................................................................................................................................(2)

(b)

state hookes law. .................................................................................................................................... ....................................................................................................................................(2)


8

the graph shows the stress-strain relationship for a copper wire under tension. S tre s s /1 0 8 P a 2

1

0

0

1

2

3

5 4 3 S tr a in /1 0

use the graph to determine: the ultimate tensile stress for copper ......................................................................... the young modulus of copper .................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................(3)

a copper wire of cross-sectional area 1.7 10 m and length 3.0 m is stretched by a force of 250 n will the behaviour of the wire at this point be elastic or plastic? justify your answer. .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................(2)

6

2

show this point on the stress-strain graph above. label it p.(1)

calculate the extension of the wire. .................................................................................................................................... .................................................................................................................................... extension = ....................................................(2)


9

(c)

explain with the aid of a diagram what is meant by an edge dislocation.

.................................................................................................................................... .................................................................................................................................... ....................................................................................................................................(2)

describe how the presence of dislocations can reduce the risk of metals failing by cracking. you may be awarded a mark for the clarity of your answer. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................(3)

(d)

sketch a force-extension graph for natural rubber showing its behaviour for both increasing and decreasing force.

(2)

use your graph to explain why a rubber band which is repeatedly stretched and relaxed becomes noticeably warmer. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................(2)


10

(e)

read the short passage below and answer the questions about it. the outer layer of a human tooth is made of enamel and is the hardest tissue in the body. it is a typical ceramic with a high compressive strength, low tensile strength and a high young modulus. it is brittle and consists of long crystals of calcium phosphate set vertically on the surface of the underlying dentine. dentine is the main structural material of a tooth. it is a composite material consisting of needle shaped crystals in a collagen fibre matrix. dentine has a much lower young modulus than enamel and is tough. false teeth (dentures) are made from pmma (polymethyl methacrylate), an amorphous polymer with a glass transition temperature of 110c. what is meant by the following term used in the passage? composite material .................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................(2)

draw labelled diagrams to show the difference in molecular structure of a crystalline material and an amorphous polymer.

(3)

the graph shows the behaviour of enamel under tension. S tre ss

S tra in

add to the graph:ealing, hammersmith and west london college 11

(i) (ii)

a line labelled e to show the behaviour of enamel under compression, a line labelled d to show the behaviour of dentine under tension.(4) (total 32 marks)

12.

(a)

work = force distance /displacement (1)2 2

1 1 2

unit = nm or joule/j(1) (1) base units = kg m s (1)(1) (b) hookes law: extension proportional to () force/load or f = kx with f, x defined (1) below the elastic limit or below limit of proportionality (1) ultimate tensile stress = 2.3 ( 10 pa) young modulus = stress/strain [no mark] = any pair off linear region between 0.8, 1 and 1.6, 2.1 (1) = 1.3 10 (pa/n m ) [1.2 1.4] (1)11 2 8

2

3

250 N6 2 attempt to calculate 1.7 10 m or p correctly plotted (1)

elastic because

on straight line/equivalent (1)8

2 1

point p on line at stress = 1.5 10 pa [e.c.f their value of stress] (1) extension of wire: determine strain = 1.1 (10 ) [or 1.2] (1) [either by calculation or by reading off graph] extension = 3 strain [e.c.f.]= 3.3 (3.6) 10 m (c) diagram:3 3

2

(1)

1


12

dislocation is an extra/missing half row/plane of atoms/ions nd [or 2 diagram showing dislocation moved] (1) risk of cracking: quality of written communication (1) D is lo c a tio n m o v e s B lu n ts tip o f c r a c k R e d u c e s tre ss F O R c ra c k g ro w s /m o v e s O R m a n y d is lo c a tio n s ta n g le s to p s a t d is lo c a tio n s tr e s s re d u c e d n o m ark n o m ark (1 ) (1 ) (1 )

1 max 3

(d)

graph: axes and shape (1)

x2

arrow heads or labels [if axes inverted, arrows must be reversed] (1) warmer because: area represents energy or work done [may be labelled on graph] (1) [must refer to graph] converted to heat (in rubber band) (1) (e) any two of: composite material is two (or more) materials bonded/joined/ combined (1) [beware statements which describe a molecule or a compound] to make use of (best) properties of both (1) [may be given as two specific properties, e.g. a strong and a tough material] a named composite other than dentine as an example (1) diagrams:

2

max 2

C r y s ta llin e

O R

P o ly c r y s ta llin e

N o.of p a rtic le s

N o. of p a rtic le s

K .E .3d attempt at lattice (2) 2d attempt (1)

K .E .tight fitting jig-saw (1) (1) planes of atoms labelled (1) (1)


13

amorphous polymer

[several strands: if no blobs then must label one strand molecule (1) graph: D t

3

E e d anywhere in third quadrant (1) to greater stress (1) less steep initially [totally straight, accept] (1) large area (1) 4[32]

13.

state hookes law. .............................................................................................................................................. ..............................................................................................................................................(2)

the graph shows the stress-strain relationship for a copper wire under tension. S tre s s /1 0 8 P a 2

1

0

0

1

2

3

5 4 3 S tr a in /1 0


14

use the graph to determine: the ultimate tensile stress for copper ................................................................................... the young modulus of copper .............................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. ..............................................................................................................................................(3)

a copper wire of cross-sectional area 1.7 10 m and length 3.0 m is stretched by a force of 250 n will the behaviour of the wire at this point be elastic or plastic? justify your answer. .............................................................................................................................................. .............................................................................................................................................. ..............................................................................................................................................(2)

6

2

show this point on the stress-strain graph above. label it p.(1)

calculate the extension of the wire. .............................................................................................................................................. .............................................................................................................................................. extension = ....................................................(2) (total 10 marks)

14.

hookes law:extension proportional to () force/load or f = kx with f, x defined (1) below the elastic limit or below limit of proportionality (1) ultimate tensile stress = 2.3 ( 10 pa) young modulus = stress/strain [no mark] = any pair off linear region between 0.8, 1 and 1.6, 2.1 (1) = 1.3 10 (pa/n m ) [1.2 1.4] (1)11 2 8

2

3


15

250 N6 2 attempt to calculate 1.7 10 m or p correctly plotted (1)

elastic because

on straight line/equivalent (1)8

2 1

point p on line at stress = 1.5 10 pa [e.c.f their value of stress] (1) extension of wire: determine strain = 1.1 (10 ) [or 1.2] (1) [either by calculation or by reading off graph] extension = 3 strain [e.c.f.]= 3.3 (3.6) 10 m3 3

2[10]

15.

(a)

what is meant by the strength of a material?

..................................................................................................................................... .....................................................................................................................................(1)

sketch a stress-strain graph for a copper wire up to its breaking point.

(2)

label on your graph (i) the yield point, (ii) a region in which the wires behaviour is elastic, and (iii) a region in which the wires behaviour is plastic.(3)

(b)

a uniform beam of length 4.0 m and weight 160 n is suspended horizontally by two identical vertical wires attached to its ends. a load of 400 n is placed on the beam 1.2 m from one end. the diagram is a free-body force diagram for the beam. P Q

160 N 400 N


16

calculate the tension in each suspended wire. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... tension =..(4)

(c) F /N 350

0

0

5

e /1 0

6

m

the graph shows the extension e produced by a tension f on solid bone. the bone, of circular cross-section, has a diameter of 35 mm and an unstressed length of 390 mm. calculate the young modulus of bone. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... young modulus =..(3)


17

calculate the energy per unit volume required to stretch the bone by 0.0040 mm. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... energy per unit volume =(4)

(d)

the diagram shows the arrangement of the atoms in a crystal in the region of an edge dislocation. E x tra h a lf-p la n e o f a to m s

A

B draw labelled diagrams to show how the dislocation moves when stress is applied as shown by the arrows a, b. you need only draw one plane of atoms. the first diagram is drawn for you.

(4)

explain why the stress required to deform a perfect crystal is greater than that required to deform one containing dislocations. you may be awarded a mark for the clarity of your answer. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................(3)


18

(e)

engineers like stiff, strong, light and creep-resistant materials. plastics are not stiff enough because their working strain is about 1%, whereas that of a typical engineering material is below 0.1%. the combined requirement for stiffness and lightness is equivalent to a high value of the young modulus e divided by the density . the value for plastics is poor, about one fifth that of metals. the development of composites has already been picked out as a strong growing point. for example, the strength and creep-resistance of glass can be coupled with the toughness of a resin to produce a boat hull.[adapted from j ogborn (ed.): materials and structure, nas physics, penguin 1971]

(i)

explain what is meant by creep. .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... ..........................................................................................................................(3)

(ii)

show that the unit of e/ is m2 s2. .......................................................................................................................... .......................................................................................................................... for copper e/ = 1.5 107 m2 s2. calculate the young modulus of a plastic of density 910 kg m3. .......................................................................................................................... .......................................................................................................................... young modulus =.(4)

(iii)

what, in general, is meant by a composite material? .......................................................................................................................... .......................................................................................................................... what type of composite material is described as being used for a boat hull? .......................................................................................................................... ..........................................................................................................................(2) (total 32 marks)


19

16.

(a) ability of a material to withstand a force without breaking, independent of sample dimensions stress-strain graph: axes (stress on ordinate, strain on abscissa) shape 2 labels in correct places (b) attempt to use principle of moments t1 = 200 n [e.g. 1 for a.c.] and t2 = 360 n [e.c.f.]

1

3

(c)

Fl young modulus = Ax 350 N 0.39m = 0.0175 m 5 10 6 m= 1.9 10 n m2 3

Energy Volume= 280 4 10 6 m 0.0175 2 m 2 0.39 m

= 2.98 j m3 4 (d) half plane displaced and labelled 4 in perfect crystal, all bonds under same force/ (1) all must fail at same time (1) with dislocations one bond/line can fail at a time (1) quality of written communication (e) (i) creep: continued/continual (acting over time) strain/extension/deformation when subject to constant/fixed force/stress (ii) n m and kg m (1) use of n as kg m s (1) 1 1.5 10 7 m 2 s 2 for plastic(s) e/ = 5 (1) 6ms = 3 10 e plastic = (3. 106ms) (910 kg m) (1) = 2.7 109n m/pa (1) a material which uses the properties of two (or more) materials fibre (composite) 2[32]

max 2 1

3

max 4

(iii)


20

17.

what is meant by the strength of a material? ............................................................................................................................................... ...............................................................................................................................................(1)

sketch a stress-strain graph for a copper wire up to its breaking point.

(2)

label on your graph (i) the yield point, (ii) a region in which the wires behaviour is elastic, and (iii) a region in which the wires behaviour is plastic.(3) (total 6 marks)

18.

ability of a material to withstand a force without breaking, independent of sample dimensions stress-strain graph: axes (stress on ordinate, strain on abscissa) shape 2 labels in correct places

1

3[6]


21

19. F /N 350

0

0

5

e /1 0

6

m

the graph shows the extension e produced by a tension f on solid bone. the bone, of circular cross-section, has a diameter of 35 mm and an unstressed length of 390 mm. calculate the young modulus of bone. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... young modulus =..(3)

calculate the energy per unit volume required to stretch the bone by 0.0040 mm. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... energy per unit volume =(4) (total 7 marks)


22

20.

Fl young modulus = Ax 350 N 0.39m = 0.0175 m 5 10 6 m= 1.9 10 n m2 3

Energy Volume= 280 4 10 6 m 0.0175 2 m 2 0.39 m

= 2.98 j m3

4[7]

21.

(a)

a bridge is formed from a uniform concrete beam of weight w supported at each end1 4

by a brick pillar. a vehicle of weight p is stationary

way along the bridge.

on the diagram below draw arrows to show the forces acting on the beam. label each force and state the origin of the upward forces.

concrete beam

(3)


23

(b)

some properties of two materials a and b are given below, material a on the graph, material b in the table. S tre s s /1 0 8 N m 52

4 3 2 1 0 0 0 .0 2 0 .0 4 0 .0 6 S tra in 0 .0 8 0 .1 0

material a b

young 10 modulus/10 pa 3.0

ultimate tensile 8 2 stress/10 n m 3.6

nature tough brittle

use the graph to complete the table for material a.(2)

use the table to draw a graph on the grid above showing the behaviour of material b.(3)

show on the graph the region in which material a obeys hookes law.(1)

material a is in the form of a wire of cross-sectional area 8.8 10 m and length 2.5 m. calculate the energy stored in the wire when it experiences a strain of 0.020. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... energy = ............................................(4)

7

2

(c)

describe the difference between a fibre composite and a laminate. .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................(2)


24

explain how the risk of failure by cracking is reduced in either a fibre composite or a laminate. you may be awarded a mark for the clarity of your answer. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................(3)

(d)

perspex is an amorphous polymer. draw a labelled diagram showing the molecular structure of perspex.

(2)

describe the difference in behaviour of a thermoplastic polymer and a thermosetting polymer when heated. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................(2)

is perspex a thermoplastic polymer or a thermosetting polymer? ....................................................................................................................................(1)

(e)

read the short passage below and answer the questions about it. elastic materials under stress store strain energy. in a car with no springs there would be violent interchanges of gravitational potential energy and kinetic energy every time a wheel passed over a bump. the springs of the car enable changes of potential energy to be stored temporarily as strain energy, resulting in a smoother ride. most ski runs are more bumpy than a normal road. the tendons in the legs of a fast moving skier must be able to store and give up again very large amounts of energy. light aircraft which may have to land on rough ground often have their undercarriages sprung by means of rubber cords.[adapted from structures by j e gordon]


25

explain what is meant by the term strain energy. .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................(1)

why is it important that the springs, tendons and rubber cords mentioned in the passage are not stressed beyond their elastic limits? .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................(1)

useful data: energy stored 1 per unit mass/j kg 130 2500 8000

modern spring steel tendon in leg rubber cord

show that a car of mass 1200 kg would need steel springs of total mass approximately equal to 3 kg to store energy when it encounters pot-holes of depth 3 cm. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................(3)

the sum of the mass of leg tendons of a skier might be of the order of 0.4 kg. estimate the size of bump that a skier of mass 75 kg could theoretically negotiate. .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................(2)


26

sketch a hysteresis curve to show the behaviour under stress of a rubber suitable for springing light aircraft undercarriages.

(2) (total 32 marks)

22.

(a)

diagram:

(P ) (R ) ( S ) [ Ig n o re te n s io n a n d c o m p re s s io n IN th e b e a m ]

(R )

P

W

(P )

(S )

[dotted lines indicate acceptable alternative positions] [reaction force cancels mark] p and w correct at , by eye (1) r and s at or close to ends (1) origin of r and s e.g. brick pillar not tension (1) (b) completion of table: material a b young 10 modulus/10 pa 1.2 or 1.25 3.0 2 line drawn on graph: straight and stops suddenly (1) 8 2 at stress 3.6 10 n m ) if not brittle, then peaks at this value) (1) (and strain 0.012) correct gradient for straight region e.g. through 0.01, 3.0. (1) 10 hookes law marked up to stress 2.7 to 2.9 10 pa [must be labelled] ultimate tensile 8 2 stress/10 n m 3.1 or 3.15 (< 3.2) 3.6 nature tough brittle (2)

3

(1)

3 1


27

energy stored: 10 [accept stress in range 2.4 2.5 10 pa] factor (1) extension = 0.020 2.5 m [0.05 m] (1) 8 2 7 2 f = 2.4 (10 ) n m 8.8 (10 ) m (1) 10 [210 n; 220 n if stress = 2.5 10 pa] 10 = 5.25 j [5.5 j if using stress = 2.5 10 pa] [ue]

(1)

4

[for middle 2 marks candidates may use stressstrainvolume, credit 1 8 2 mark for calculating stressstrain 2.4 (10 ) n m 0.020 and 1 mark 7 2 for volume 8.8 (10 ) m 2.5 m] (c) description: idea that fibre composite is strands of something inside another material laminate is layers of different materials (1) reducing risk: prestressed reinforced concrete as example fibre or laminate quality of language (1) crack grows/moves/travels (1) until it reaches the boundary between layers/matrix material (1) crack spreads along boundary/tip blunted/matrix yields (1) (d) diagram: spaghetti-like arrangement [more than 1 strand] (1) individual strand labelled molecule or blob atom (1) (1) 2

max 3

2

A to m M o le c u le /c h a in o f a to m sdifference: thermoplastic softens on heating/can be remoulded/melts (1) [not becomes plastic] thermoset decomposes/burns/does not soften/remains rigid (1) perspex is a thermoplastic (1) (e) strain energy: is the energy stored /used/created/added/needed when a material is under stress/strained/loaded/stretched or in stretched bonds or is work done when stressed (1) why stress should not be beyond elastic limit: must return to original length when unstressed or must give up stored energy when unstressed or must not deform permanently/plastically (1) car calculation: 2 substitution in mgh 1200 kg 10 m s [9.81] 0.03 m = 360 [350] j (1) 3 kg steel store 390 j or 360 j needs 2.8 kg steel (1) [can also be argued in terms of 390 j 3.3 cm] (1) 3

2 1

1

1


28

tendons: will store 0.4 m 2500 n /(1000) j (1) h = 1.3 m [1.4 m ] [e.c.f. their energy (75 10[9.81]) sketch graph:

(1) [u.e.]

2

F /s tr e s s

L oad U n lo a d

x /s tra inaxes and shape + load line (1) arrow heads/labels + unload line [beware inverted axes] (1) 2[32]

23.

(a) calculate the stress in a steel wire of length 2.6 m and cross-sectional area 7 2 1.5 10 m when it is subjected to a tensile force of 8.0 n. ..................................................................................................................................... .....................................................................................................................................(2)

part of a force-extension graph for such a steel wire is shown below. 10 F o rc e /N 8 6 4 2 0 0 0 .2 0 .4 0 .6 0 .8 1 .0 E x te n s io n /m m

use the graph to find the extension of the wire for an applied force of 8.0 n. .................................................................................................................................... show that the corresponding strain in the wire is approximately 3 10 . ..................................................................................................................................... .....................................................................................................................................4


29

hence determine the young modulus for steel. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... young modulus = .....................................................(4)

calculate the work done in stretching the wire by 0.4 mm. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... work done = .....................................................(3)

a second wire is made of the same steel. it has the same cross-sectional area but twice the length. on the same axes draw the force-extension graph for this wire.(2)

(b)

a horizontal concrete beam rests on two pillars, one at each end, forming a bridge. it supports a large load at its centre. draw the concrete beam and show the regions of the beam which are in tension and the regions which are in compression.

(2)

explain why microscopic cracks in the lower surface of the beam are more dangerous than any which form in the upper surface of the beam. you may be awarded a mark for the clarity of your answer. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................(3)


30

(c)

the photograph is of a bubble raft model of an edge dislocation.

what do the bubbles represent? .....................................................................................................................................(1)

indicate on the photograph where the dislocation in the bubble raft occurs.(1)

(d)

the table gives the properties of three different materials. ultimate tensile stress/10 n m a b c 0.7 100 6506 2

young modulus/10 pa 30 2 40

9

use this data to describe each material as either strong or weak and either stiff or flexible. material a is ................................................. and ...................................................... material b is ................................................. and ...................................................... material c is ................................................. and ......................................................(3)

the materials are cfrp (carbon fibre reinforced polymer), nylon and polythene. identify a, b and c. a is ..................................... b is ..................................... c is ..................................(2)

state which of these materials is/are a composite material(s). .....................................................................................................................................(1)


31

(e)

read the short passage below and answer the questions about it. the toughness of a material can be measured by the energy it absorbs during fracture. toughness can change with temperature. materials which are considered to be tough and exhibit ductile failure at room temperature may be brittle at low temperatures. brittle failure can occur without warning. it has been suggested that temperatures in the north atlantic at the time of the sinking of the titanic were such that the steel of the ships hull was brittle. ductile-brittle transition curves for some materials are shown below. different steels have different transition temperatures so provided the correct steel is selected there are no problems in, for example, laying oil pipelines across alaska (where winter temperatures can be as low as 30 c).

E n e rg y a b so rb e d / J

M ild s te e l C opper N y lo n Z in c

100

100 T e m p e r a tu r e / C

0

[adapted from the institute of materials teacher pack by claire davis]

explain the meaning of the terms (i) ductile ............................................................................................................... ........................................................................................................................... (ii) transition temperature ....................................................................................... ...........................................................................................................................(2)

suggest the temperature below which a component made from mild steel risks brittle failure. .....................................................................................................................................(1)

which of the materials on the graph would not be at risk of brittle failure at low temperatures? explain your answer. ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................(2)

add to the graph the transition curve of a steel suitable for making pipelines which would be laid in alaska.(1)ealing, hammersmith and west london college 32

on the axes below sketch a stress-strain graph to breaking point for mild steel above its ductile-brittle transition temperature.

S tre s s

S tr a in(2) (total 32 marks)

24.

topic b solid materials (a) calculation stress = 8.0 n / 1.5 10 = 5.3 10 pa/n m7 2 7

m

2

(1) 2

(1)

graph: extension = 0.67 mm [accept 0.66 to 0.68] 1 3 strain = 0.67 mm/2.6 10 mm [e.c.f extension from above] n [ignore, 10 error] (1) = 2.6 10 [do not penalise presence of unit] substitute in young modulus = stress/strain [e.c.f stress from above. e.c.f. strain, their value or 3 10 ] [= 2 10 pa/n m11 2 4 4

(1)

4

(200 gpa)]

(1)

calculation of work done 2 find area of triangle or use kx (1) n substitute correct pair of values off line [ignore 10 errors] 4.8 n/4.7 n, 0.4 mm or determine k = gradient = 9.6 104

(1) (1)4

j [ 0.2] [accept n m]

3 j gets 2/3] 2

[allow e.c.f. only for grid error 4.4 n 8.8 10 force-extension graph for wire of twice length: add line as steep to graph [by eye] (2) [less steep, but not approx , 1 out of 2]


33

(b)

diagram of concrete beamC T

no mass: ok straight: ok no supports: ok compression labelled inside/just above top surface (1) tension labelled inside/just below bottom surface (1) [words or arrows] look for a region being shown. if only one point top surface and one point lower surface give 1 out of 2] explanation quality of written communication (1) concrete is strong in compression but weak in tension (must compare i.e. both) (1) upper surface cracks tend to close up and/or lower surface cracks tend to widen (1) further detail, e.g. reference to tension/compression, or crack propagating across beam fracture or stress at tips of cracks discussed or there are no dislocations to blunt the cracks (1) (c) bubble raft bubbles represent atoms or ions (1) dislocation identified by diagonal line, circle, dot description of materials material a is weak and stiff (1) material b is strong (ish)and flexible material c is strong and stiff (1)

2

max 3

(1)

(d)

(1) 3

[if none of the pairs are correct, possible 1 mark for one whole column correct, i.e. weak, strong, strong, weak or stiff, flexible, stiff.] identification of materials a is polythene; b is nylon c is cfrp c correct (1) (1) (1) 2 1 other two correct (e) meaning of terms (i) (ii) ductile: can be drawn into a wire/rolled into a sheet/deforms plastically (1) transition temperature: the temperature at which a material changes from brittle ductile behaviour (1) (1) 2 1

cfrp is composite [only]

steel at risk some figure between + 15 c and 20 c


34

not at risk copper because it absorbs more/lots of energy at lower temperature or graph slopes other way or almost constant or it has no transition temperature (1) [do not penalise if zinc also described/chosen] add to graph a curve of similar shape as steel but shifted to the left sketch graph (1) 1 2

S tre ss

S tr a instraight line, then plastic with plastic region at least 2 linear region kink(s) between linear and plastic curve (1) (1) 2[32]

25.

(a) typical stress-strain curves for two metals, a and b, up to their breaking points are shown below. S tre ss /M P a 300 A

200 B 100

0 0 0 .0 5 0 .1 0 0 .1 5 0 .2 0 S tra in 0 .2 5

which metal is stiffer? justify your answer. ..................................................................................................................................... .....................................................................................................................................(1)


35

stating appropriate magnitudes where possible, explain which metal is (i) stronger ............................................................................................................. ........................................................................................................................... ........................................................................................................................... (ii) more ductile ..................................................................................................... ........................................................................................................................... ...........................................................................................................................(2)

the two metals are mild steel and copper. identify a and b. a = ............................................................. b = .........................................................(1)

estimate the work done per unit volume in stretching material a to its breaking point. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... work done per unit volume = ..................................(3)

high carbon steel can be made harder and more brittle if it is quench hardened. state what is involved in this process. ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................(2)

(b)

draw a labelled diagram of the apparatus you could use in a school laboratory to determine the young modulus of copper in the form of a wire.

(3)ealing, hammersmith and west london college 36

suggest an appropriate length for the wire being tested. ..................................................................................................................................... how would you determine the cross-sectional area of the wire? ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................(3)

state the unit of k, the constant of proportionality in hookes law. .....................................................................................................................................(1)

show that for a wire of length l and cross-sectional area a the young modulus e = kl/a. ...................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................(3)

(c)

describe how a pre-stressed reinforced concrete beam is produced. you may be awarded a mark for the clarity of your answer. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................(4)


37

(d)

read the short passage below and answer the questions about it. copper deforms and breaks at stresses much lower than its theoretical strength. most successful attempts to increase the strength of crystalline materials have centred upon stopping the movement of dislocations by introducing defects into the lattice or by creating a tangle of dislocations. weak materials can also be strengthened by including tough filaments such as glass fibres in them. unfortunately, increasing the number of obstacles also interferes with the movement of electrons in the material. a new family of composites has been developed featuring much finer filaments which are much more closely spaced. a tangle of ultrafine niobium filaments (10 nm thick) in copper increases the coppers strength ten-fold. the filaments occupy only 18% of the volume and the high conductivity and ductility of the copper are retained. draw labelled diagrams to show the way in which a dislocation in a lattice moves.

(3)

state two differences between the filaments in the new and traditional composites. 1 .................................................................................................................................. ..................................................................................................................................... 2 .................................................................................................................................. .....................................................................................................................................(2)

calculate the ratio

cross sec tional area of a copper wire of 1mm diameter cross sec tional area of an ultrafine niobium filament..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ratio = ..........................................................(2)


38

state two advantages of using ultrafine niobium filaments to strengthen copper wire. 1 .................................................................................................................................. ..................................................................................................................................... 2 .................................................................................................................................. .....................................................................................................................................(2) (total 32 marks)

26.

(a) (i) (ii)

comparison of two metals a and b (stress-strain curves) 1 stronger: a since uts/it breaks at 300 mpa ( 20) or since b breaks at 190 ( 30) mpa (1) more ductile: b since strain 0.25 or since a strain = 0.15 (1) 2 1

a is stiffer since steeper /bigger gradient/large young modulus (1)

identify a and b a is mild steel; b is copper (1) estimate of work done in stretching a to breaking point attempt at area [nb not just a triangle] (1) 300 10 pa 0.15 [ignore 10 error] (same stress ranges) (1) 4 + 5 10 j m quench hardening heat and cool (1) rapid cool/plunge into water (1) (b) diagram of apparatus to determine young modulus of copper were firmly fixed to ceiling/beam/end of bench (1) load and ruler/scale (1) means of reading small extensions e.g. pointer against scale/vernier (1) length of wire being tested appropriate length 2 m [less if vernier used] (1) cross-sectional area of wire micrometer (1) diameter in several places (1) unit of k in hookes law n m /kg, s1 2 7 3 6 n

(1)

3

2

3

3

(1)

1


39

show that e = f/a e / l (1) = fl/ae (1) but f/e = k/substitute f = ke (1) (c) pre-stressed reinforced concrete beam any four from: quality of written communication (1) steel (1) wires/cables/rods in tension/stretched or heated (1) pour concrete/cement over and leave to set (1) release tension or leave to cool (1) (d) passage: diagrams of lattice E x tr a h a lf r o w o f a to m s max 4 3

2-d attempt at a lattice [solid lines to represent rows/planes acceptable] (1) extra half row of atoms/ions labelled (1) two diagrams or clearly show that only one bond flips (1) differences filaments more closely spaced in new (1) filaments finer/thinner in new (1) calculation of ratio (0.5 10 3 m) 2 9 2 2 ratio = (5 10 m) or just ratio of (diameters) (1)

3

2

[(510 m) is essential component or (10 10 m)] = 10 (1) advantages they do not interfere with the movement of electrons/high conductivity retained/ do not increase resistance (1) ductility is retained/do not increase brittleness (1) 2[32]10

9

2

9

2


40

27.

(a) the diagram shows part of the range of unit prefixes. complete the diagram below by filling in the empty boxes. m illi g ig a

10

6

10

3

10

3

10

9

(4)

(b)

the stress-strain curves for two materials a and b up to their breaking points are shown below. S tre s s A

B

S tr a in state, giving the reason for your choice in each case, which material is (i) tougher ......................................................................................................... ...................................................................................................................... (ii) stiffer ............................................................................................................ ...................................................................................................................... (iii) more ductile .................................................................................................. ......................................................................................................................(3)

add a third line to the graph above showing the behaviour of a material c which has the following properties: c has a smaller young modulus than a or b, is stronger than a or b and is brittle.(3)


41

(c)

on the axes below sketch a force-extension graph for natural rubber, showing its behaviour for both increasing and decreasing force.

F o rc e

E x te n s io nuse your graph to explain what is meant by elastic hysteresis. you may be awarded a mark for the clarity of your answer. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ...............................................................................................................................

(2)

(3)

(d)

the diagram shows an edge dislocation in a crystal lattice.

label the slip plane on the diagram. explain how an edge dislocation makes it easier for layers of atoms to slip over each other. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ...............................................................................................................................(3)


42

how can a metal be work hardened? ............................................................................................................................... ............................................................................................................................... complete the following sentence by circling any word(s) in the square brackets that describe(s) a metal after it has been work hardened. after work hardening a metal is [ stronger, stiffer, more ductile, more brittle ](3)

describe the process of annealing and explain in microscopic terms why it can return a work-hardened metal to its original softer state. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ...............................................................................................................................(3)

(e)

cycle helmets have a polystyrene foam lining. in the event of an accident the foam lining is compressed (crushed) and provides a stopping distance for the cyclists head, reducing deceleration of the brain. the graph shows the relationship between the force transmitted by a typical foam liner and the amount of linear compression of the foam. F o rc e / N 10 000

5000

0 0 5 10 15 20 25 L in e a r c o m p re s s io n / m m


43

use the graph to calculate the energy stored by this foam liner when it is crushed by 18 mm. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ...............................................................................................................................(4)

calculate the deceleration of a head of mass 5.8 kg when acted upon by a force of 10 000 n. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ...............................................................................................................................(2)

helmets are designed to reduce head decelerations to no more than 200g (g = acceleration of free fall). does this helmet fulfil the design requirements at this force? justify your answer. ............................................................................................................................... ...............................................................................................................................(1)

suggest one reason why a cycle helmet should be replaced once it has suffered an impact. ............................................................................................................................... ............................................................................................................................... ...............................................................................................................................(1) (total 32 marks)


44

28.

topic b -solid materials (a) diagram nano and 10 micro 1 kilo 1 6 mega and 10 [note: spellings must be correct, i.e. not nono, micra, kila, killa, megga etc upper or lower case accepted9

1

1

(b) stress-strain curves for two materials (i) (ii) (iii)

n 9 10

k

m ) is max 2/4] 6 10 )

tougher: b because it has larger area/greater energy density stiffer: b because steeper slope/greater young modulus more ductile: b because greater strain in plastic region

1 1 1

line added to graph for material c [mark alongside graph] straight with sudden loop/straight line with sudden stop smallest gradient greatest stress (c) force extension graph [mark alongside graph ] shape correct, both start 2 mm origin and no obvious dips arrows or labels [correct] explanation of elastic hysteresis quality of written communication areas/lines/energy/work different up-down/loading-unloading area of loop represents energy dissipated/heating/internal energy/increase temperature (d) diagram 1 1 1 1 1 1 1 1

T h is re g io n fo r S L IP p la n eexplanation

A n y o n e o f th o se " p la n e s " o r h o riz o n ta l a rro w

plane labelled, horizontal layer with 1 less/1 more atom/in between any reference to (interatomic) bonds only one row of bonds needs to be broken (at a time) (compared with whole plane of atoms at a time) [or could be implied, e.g. carpet ruck analogy]ealing, hammersmith and west london college

1 1 145

work hardening hammering/rolling/plastic deformation/hit repeatedly [not putting under strain, stretching, repeated loading and unloading] completion of sentence by selection of word(s) stronger 1 more brittle 1 [one correct, one incorrect 1/2 ; if > two circled apply -1 per error] process of annealing and explanation in microscopic terms metal is warmed/heated [not melted] and cooled slowly/allowed or left to cool getting rid of (log jammed) dislocations/recrystallises/creates larger crystals or atoms become more ordered/organised (e) use of graph to calculate energy stored by foam liner find area of triangle or 1/2 fx read off value, 9000 n correct value (81) [e.c.f. for value e.g. 8000 n 72 (j) joules [not nm, nmm] deceleration of a head of mass 5.8 kg use f = ma 1 answer 1700 (1724) m s-2 helmet design requirements yes, with figures to justify < 200 9.81 m s or 1700/9.8 [allow, gas 9.8 or 10] [e.c.f.] reason why a cycle helmet should be replaced after impact replaced because foam does not recover after crushing or equivalent, e.g. not elastic e.g. permanently damaged / cracked / fractured [not damaged or scratched only][32]2

1

1 1 1 1 1 1 1

1

1

1

29.

(a) energy density is the energy stored per unit volume. show that the expression energy density = stress strain is homogeneous with respect to units. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................(4)


46

(b)

state hookes law. ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................(2)7 2

a brass wire of length 2.8 m and cross-sectional area 1.5 10 m is stretched by a force of 34 n. the wire extends by 5.3 mm. calculate the young modulus of brass. assume the stretched wire is still within the hookes law region. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................(4)

the wire obeys hookes law for forces up to 46 n. on the axes below draw a force-extension graph for this brass wire in the hookes law region. 50 F o rc e / N 40 30 20 10 0 0 2 4 6 8 E x te n s io n / m m(2)

10

how could the graph be used to find the energy stored in the wire when it is stretched by a force of 24 n? ..................................................................................................................................... .....................................................................................................................................(1)


47

a second wire is made from the same brass and has the same length but a greater crosssectional area. this wire is also stretched by a force of 24 n. does the second wire store more energy, the same energy or less energy than the original wire? justify your answer. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................(3)

(c)

the stress-strain curves for perspex and polythene up to their breaking points are drawn below. S tre s s P e rsp e x P o ly th e n e

S tra in describe the differences in behaviour of perspex and polythene when they are stretched until they break. you may be awarded a mark for the clarity of your answer. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................(5)


48

(d)

draw a labelled diagram showing the molecular structure of an amorphous thermoplastic polymer such as perspex.

(2)

how does the molecular structure of a thermoset such as melamine differ from that of perspex. ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................(1)

(e)

a rod of quench hardened carbon steel can have its surface properties changed by tempering. what must be done to the rod to temper it? .....................................................................................................................................(1)

in what way do the properties of the surface of the rod change during this process? .....................................................................................................................................(1)

the graph below shows how the tensile strength of glass in the form of fibres depends upon the cross-sectional area a of the fibres.

1 .5 T e n s ile s tre n g th / 1 09

Pa 1 .0

0 .5

0 .0

0

5

10

15

20

25

30

1 A

m m

2


49

complete the sentence below by circling the correct term within the brackets. thin glass fibres are { the same strength as, stronger than, weaker than } thick glass fibres.(1)

use the graph to determine the tensile strength of a glass fibre of cross-sectional area 0.125 2 mm . ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................(2)

could a glass fibre of cross-section 0.125 mm (0.125 10 m ) safely support a mass of 20 kg? justify your answer. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................(3) (total 32 marks)

2

6

2

30.

(a)

expression3

energy density = joule/m (1) stress = n/m (1) strain = m/m or no unit stated (1) j = n m / kg m s (1) (b) hookes law tension/force proportional to extension or formula with symbols defined (1) up to a certain limit/limit of proportionality (1) [accept elastic limit] 22 2 2

4


50

calculation of young, modulus of brass

Fl stress = 34 n/1.5 10 m or e= Al used (1)7 2

strain = 5.3 10 m/2.8 m [ie substitution] [ignore 10 ] (1) young modulus = 1.2 10 [no ecf] (1) 2 1 2 pa / n m [not kg m s ] (1) graph [mark alongside] straight line from origin to 46 n (1) going through 34 n, 5.3 mm (1) energy stored by finding area/area shaded/ fx up to 24 n (1) second wire less energy stored (1) less extension (1) smaller area under graph or smaller fx (1) (c) differences in behaviour any five from: (d) quality of written communication perspex brittle polythene large plastic deformation / tough perspex stiffer/polythene smaller young modulus [not just gradient] perspex stronger/polythene smaller breaking stress / uts perspex higher limit of proportionality/obeys hookes law to higher stresses than polythene/similar or inverse (1) (1) (1) (1) (1) max 5 3 1 211 n

3

4

diagram a tangle of squiggles (1) with (long) molecule or atoms identified on a squiggle / polymer chain (1) differences in molecular structure thermoset has strong cross links (1) 1

2


51

(e)

tempering heat and (allow to) cool (1) how properties change make softer / less hard / less brittle (1) completion of sentence stronger (1) 1 use of graph to determine tensile strength 1/a = 8 (mm ) (1) 9 strength = 1.1 10 pa [ue] (1) strength of glass fibre and its safety see or use w = mg (196 200 n) (1) stress = 200/0.125 10 pa [ignore 10 error] [no ue] (1) 1.6 10 compared with value above and yes/no (1) [or reverse argument to 14 kg][32]9 6 n 2

1 1

2

3

31.

(a) show that the energy stored in a stretched wire below the limit of proportionality 2 can be written w = k(x) where k is the hookes law constant. (2)

on the axes below sketch a graph showing how energy stored w varies with extension x of a wire below its elastic limit. W

0

0

x

(2)


52

(b)

the graph shows the stress-strain relationship for copper. S tre s s / 1 0 8 P a 2

1

0

0

1

2

3

5 4 3 S tra in / 1 0

use the graph to determine the young modulus of copper. (4)

a student is measuring the extension of a copper wire for a number of forces. why should a long wire be used in this experiment? (1)

the wire has a radius of 7.1 10 m. calculate the stress produced when the wire is stretched by a force of 280 n. (3)

4

mark this point on the stress-strain graph. label it p.(1)

is the behaviour of the wire at this stress likely to be elastic or plastic? justify your answer. (1)


53

(c)

explain with the aid of a single diagram what is meant by an edge dislocation.

(2)

describe how the presence of dislocations can reduce the risk of metals failing by cracking. you may be awarded a mark for the clarity of your answer. (4)

(d)

describe how high density polythene (hdpe), melamine and perspex behave on heating. hdpe ...........................................................................................

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