Note 1.2 x 10^4 means 1.2 times ten to the power of 4 (etc)
1. (a) (i) Stress = force / area C1
force = stress x area
= 180 x 10 ^ 6 x 1.5 x 10 ^ –4
= 27000 (N) A1
(ii) Y M = stress / strain C1
= 180 x 10^6 / 1.2 x 10^–3 or using the gradient C1
= 1.5 x 1011 N m–2 A1
(b) brittle
elastic/ graph shown up to elastic limit
obeys Hooke’s law / force α extension / stress α strain
no plastic region B3
MAX 3
[8]
2. (a) One reading from the graph e.g. 1.0 N causes 7 mm C1
Hence 5.0 (N) causes 35 +/- 0.5 (mm) A1
(allow one mark for 35 +/- 1 (mm)
(b) (i) Force on each spring is 2.5 (N) C1
extension = 17.5 (mm) allow 18 (mm) or reading from graph A1
[allow ecf from (a)]
(ii) strain energy = area under graph / ½ F x e C1
= 2 x 0.5 x 2.5 x 17.5 x 10 ^–3
= 0.044 (J) A1
[allow ecf from (b)(i)]
(c) E = stress / strain C1
Stress = force / area and strain = extension / length C1
extension = (F x L) / (A x E)
= (5 x 0.4) / (2 x10^–7 x 2 x 10^11)
= 5.(0) ^ 10–5 (m) A1
(d) strain energy is larger in the spring B1
extension is (very much larger) (for the same force) for the spring B1
[11]
3. (a) (i) F = kx / k is the gradient of the graph C1
k = 2.0 / 250 x 10^–3 = 8.0 A1
Correct unit for value given in (a)(i)
i.e. 0.008 or 8 x 10^–3 requires N mm–1.
Allow N m–1 / kg s–2 if no working in (a)(i).
Do not allow unit mark if incorrect physics in part (a)(i) B1
(ii) W = ½ (F x extension) / area under the graph C1
= ½ x 2.0 x 0.250
= 0.25 (J) A1
(b) (i) F = 8 x 0.15 = 1.2 (N) A1
(ii) Hooke’s law continues to be obeyed / graph continues as a straight
line / k is constant / elastic limit has not been reached B1
(c) (i) 1. correct time marked on the graph with a V (t = 0.75 s or 1.75 s) B1
2. tangent in the correct place for downward velocity or implied
by values B1
value between 0.95 to 1.1(m s–1) A1
(ii) 1. X marked in a correct place (maximum or minimum on graph) M1
2. relates the extension / compression to F = kx to explain why the
force is a maximum or maximum extension gives max force or
maximum extension gives max acceleration A1
[12]
4. cast iron: brittle
brittle explained as having no plastic region
elastic
elastic explained as returning to original length when
the load is removed / linear graph / Hooke’s law obeyed
or equivalent words MAX 3
copper: ductile
ductile explained as can be formed into a wire
initially elastic
plastic where it stretches more and more with little
increase in stress
plastic explained as does not return to its original length
when the load is removed
reference to necking at the end MAX 3
polythene: easy to deform / deformed with a small force
plastic
ductile
polymeric MAX 2
MAX 8
QWC: spelling, punctuation and grammar B1
organisation and logic B1
[10]
5. (a) The extension of a spring is directly proportional to the applied force M1
as long as the elastic limit is not exceeded) A1
(b) (i) Correct pair of values read from the graph
force constant = 12/0.080 C1
force constant = 150 (N m–1) A1
(ii) extension, x = × 80 (= 133.33) (mm) C1
(E = ½ Fx)
energy = ½ × 2/ × 133.33 × 10–3
energy = 1.33 (J) A1
(iii) The spring has not exceeded its elastic limit B1
(iv) (elastic potential energy = kinetic energy)
M1
m and k are constant, therefore x prop v. M1
[9]
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