CAIE A-Level Physics 6.1 Stress and Strain

Practise analysing springs and wires using force, extension, stress, strain and Young modulus, including Hooke’s law and experimental evaluation.

Exam points

identify tensile and compressive deformation and use load, extension, compression and limit-of-proportionality language with force–extension evidence
apply Hooke’s law and k = F/x to calculate force, extension, spring constant or equivalent spring behaviour
calculate stress, strain and Young modulus from force, area, extension and original length, interpreting graphs and units
describe and evaluate a Young-modulus experiment using appropriate measurements, apparatus, controls and repeated data

Covered syllabus points

6.1.1—Deformation is caused by tensile or compressive forces (forces and 6.1.2—The terms load, extension, compression and limit of proportionality 6.1.3—Hooke’s law 6.1.4—The formula for the spring constant k = F / x 6.1.5—The terms stress, strain and the Young modulus 6.1.6—The Young modulus of a metal in the form of a wire

[Maximum number: 1]

The diagram shows a beam supported on two pivots.

Figure for Question 6.1 Stress and strain question 1 — CAIE A-Level Physics AS

Which statement describes the state of the top surface X and of the bottom surface Y ?

Both X and Y are in compression.

Both X and Y are in tension.

X is in compression and Y is in tension.

X is in tension and Y is in compression.

[Maximum number: 4]

Fig. 4.1 shows the variation with extension x of the tensile force F for two wires, G and H, made from the same material.

Fig. 4.1

The elastic limit has not been exceeded for G or H.

(a)

For the lines in Fig. 4.1:

[ 1 ]

(i)

state what is represented by the gradient

[ 1 ]

(b)

Wires G and H are joined together end-to-end to form a composite wire of negligible weight. The composite wire hangs vertically from a fixed support.

A block of weight of 2.0 N is attached to the end of the wire, as shown in Fig. 4.2.

Fig. 4.2

[ 3 ]

(i)

Use Fig. 4.1 to determine:
- the extension $x_{\mathrm{G}}$ of wire G

x_{\mathrm{G}}=

mm
- the extension $x_{\mathrm{H}}$ of wire H .

x_{\mathrm{H}}=

[ 1 ]

$x_{\mathrm{G}}=0.39 \mathrm{~mm}$ and $x_{\mathrm{H}}=0.29 \mathrm{~mm}$

A1

(ii)

The original length of wire G is L and the original length of wire H is 1.5 L.

Calculate the ratio

\frac{\text { cross-sectional area of wire } \mathrm{G}}{\text { cross-sectional area of wire } \mathrm{H}}

ratio =

[ 2 ]

E=F L / A x or stress / strain =F L / A x

C1

$A_{\mathrm{G}} / A_{\mathrm{H}}=1 \times\left(0.29 \times 10^{-3}\right) /\left[1.5 \times\left(0.39 \times 10^{-3}\right)\right]$

C1

ratio = 0.50

A1

[Maximum number: 5]

One end of a wire is attached to a fixed point. A force F is applied to the wire to cause extension x. The variation with F of x is shown in Fig. 5.1.

Fig. 5.1

The wire has a cross-sectional area of $4.1 \times 10^{-7} \mathrm{~m}^{2}$ and is made of metal of Young modulus $1.7 \times 10^{11} \mathrm{~Pa}$ . Assume that the cross-sectional area of the wire remains constant as the wire extends.

(a)

State the name of the law that describes the relationship between F and x shown in Fig. 5.1.

[ 1 ]

(b)

The wire has an extension of 0.48 mm .

Determine:

[ 4 ]

(i)

the stress
stress = Pa

[ 2 ]

$\sigma=F / A$

C1

$\begin{aligned} =36 /\left(4.1 \times 10^{-7}\right) =8.8 \times 10^{7} \mathrm{~Pa} \end{aligned}$

A1

(ii)

the strain.

strain =

[ 2 ]

Young modulus $=\sigma / \varepsilon$ or $F / A \varepsilon$

C1

$\begin{aligned} \varepsilon =8.8 \times 10^{7} /\left(1.7 \times 10^{11}\right) =5.2 \times 10^{-4} \end{aligned}$

A1

All question bank results loaded

Covered syllabus points

6.1 Stress and strain question 1

6.1 Stress and strain question 2

Question (a)

Question (i)

Question (b)

Question (i)

Question (ii)

6.1 Stress and strain question 3

Question (a)

Question (b)

Question (i)

Question (ii)