# CIE AS & A Level Physics : 6.1 Stress and strain – Exam style question – Paper 2

### Question

(a) A uniform metal bar, initially unstretched, has sides of length w, x and y, as shown in Fig. 3.1. The bar is now stretched by a tensile force F applied to the shaded ends. The changes in
the lengths x and y are negligible. The bar now has sides of length x, y and z, as shown in
Fig. 3.2. Determine expressions, in terms of some or all of F, w, x, y and z, for:
(i) the stress σ applied to the bar by the tensile force
σ = ………………………………………………… 
(ii) the strain ε in the bar due to the tensile force
ε = ………………………………………………… 
(iii) the Young modulus E of the metal from which the bar is made.
E = ………………………………………………… 

(b)  A copper wire is stretched by a tensile force that gradually increases from 0 to 280N. The
variation with extension of the tensile force is shown in Fig. 3.3. (i) State the maximum extension of the wire for which it obeys Hooke’s law.
extension = ………………………………………….. mm 
(ii) Use Fig. 3.3 to determine the strain energy in the wire when the tensile force is 120N.
strain energy = ……………………………………………… J 
(iii) Explain why the work done in stretching the wire to an extension of 12mm is not equal to
the energy recovered when the tensile force is removed.                                                    
[Total: 10]

(a) (i) σ = F / xy
(a) (ii) ε = (z –w) / w
(a) (iii) E =σ / ε
= Fw / xy(z–w)
(b) (i) extension = 2.2 mm (allow 2.0 –2.4 mm)
(b) (ii) strain energy = area under graph/line or ½Fx or ½kx2
= ½ × 120 × 1.4 × 10–3 or ½ × 8.6 × 104 × (1.4 × 10–3)
= 0.084 J
(b) (iii) (some of the) deformation of the wire is plastic/permanent/not elastic
or
wire goes past the elastic limit/enters plastic region
energy (that cannot be recovered) is dissipated as thermal energy/becomes internal energy

### Question

A spring is extended by a force. The variation with extension x of the force F is shown in Fig. 3.1 (a) State the name of the law that relates the force and extension of the spring shown in Fig. 3.1.     
(b) Determine:
(i) the spring constant, in Nm−1, of the spring
spring constant = ……………………………………….. Nm−1 
(ii) the strain energy (elastic potential energy) in the spring when the extension is 4.0cm.
strain energy = ……………………………………………… J 

(c) One end of the spring is attached to a fixed point. A cylinder that is submerged in a liquid is
now suspended from the other end of the spring, as shown in Fig. 3.2. The cylinder has length 5.8cm, cross-sectional area 1.2 × 10−3m2 and weight 6.20N. The
cylinder is in equilibrium when the extension of the spring is 4.0cm.
(i) Show that the upthrust acting on the cylinder is 0.60N.                                                            
(ii) Calculate the difference in pressure between the bottom face and the top face of the
cylinder.
difference in pressure = ……………………………………………. Pa 

(iii) Calculate the density of the liquid.
density = ………………………………………. kgm−3 
(d) The liquid in (c) is replaced by another liquid of greater density.
State the effect, if any, of this change on:
(i) the upthrust acting on the cylinder                                                                                               
(ii) the extension of the spring.                                                                                                           
[Total: 12]

Ans

(a) Hooke’s (law)

(b) (i) k = F / x or k = gradient
e.g. k = 7.0 / 5.0 × 10–2
= 140 N m–1

(b) (ii) E = ½ F x or E = ½ k x2 or E = area under graph
= ½ × 5.6 × 4.0 × 10–2 or ½ × 140 × (4.0 × 10–2)2
= 0.11 J

(c) (i) (upthrust =) 6.20 – 5.60 = 0.60 (N)

(c) (ii)Δp =Δ F / A
= 0.60 / 1.2 × 10–3
= 500 Pa

(c) (iii) (Δ)p = ρg(Δ)h
ρ = 500 / (9.81 × 5.8 × 10–2)
= 880 kg m–3

(d) (i) (upthrust) increases

(d) (ii) (extension) decreases

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