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Physics A2 1*External written examination
*2 hours
*compulsory short answer questions and some extended written answers
*These questions have elements of synoptic assessment drawing together different
strands of the spec.
*24% of A level
4.1 Deformation of Solids
4.1.1 state Hooke’s law and use F = kxto solve simple problems;
4.1.2 demonstrate an understanding of the terms elastic and plastic deformation
and elastic limit;
4.1.3 distinguish between limit of proportionality and elastic limit;
4.1.4 define stress, strain and the Young modulus;
4.1.5 perform and describe an experiment to determine the Young modulus;
4.1.6 use the equation for strain energy, E = 12 F x = 12 kx2 ;
4.1.7 demonstrate an understanding of the importance of the stress, strain and
Young modulus of a material when making design and economic decisions
about materials use;
Hooke’s Law
Hooke’s Law for any elastic material states:
Physics A2 1 1
, 💡 “Up to a maximum load, known as the limit of proportionality, the extension
of an elastic material is proportional to the applied load”
Hooke’s Law may be written as the equation F = kxWhere F is the applied load in
N, k is the Hooke’s Law constant or spring constant in Nm⁻¹, and x is the extension
of the specimen under test, in m.
The graph below illustrates how the load and extension are related for a typical
metal wire.
From (0,0) up to the Limit of Proportionality the line is straight. This is the region
where the wire obeys Hooke’s Law.
Beyond the Limit of Proportionality the line curves: there is no longer direct
proportion between load and extension. Between this point and the Elastic Limit, the
wire is undergoing elastic deformation.
A point is then reached which is the Elastic Limit, The point where any further load
will cause the wire to be permanently stretched.
Beyond the elastic limit the wire will reach its ‘yield point’, past which the molecular
structure is being permanently changed as crystal planes slide across each other.
💡 “A wire stretched beyond its Elastic Limit is said to be ‘Plastic’, and is
undergoing Plastic Deformation.
The Elastic Limit is;
💡 “The maximum load a specimen can experience and still return to its
original length when the deforming force is removed.”
The wire may stretch enormously before it finally breaks.
Physics A2 1 2
, Stress, Strain and Young Modulus
STRESS
💡 Stress, or σ, is defined as: “The applied force per unit area of cross
section”
F
The equation for stress is σ = A
where σ is the stress, in Nm⁻² or Pa, F is the
applied force, in N, and A is the cross sectional area, in m².
STRAIN
💡 Strain, or ε, is defined as: “The ratio of the change in length of a specimen
to its original length”
ΔL
The equation for strain is ε = L
where ε is strain, which as no units, ΔL is the
change of length in m, and L is the original length is m.
YOUNG MODULUS
Generally the application of a tensile stress to a material produces a corresponding
strain. Provided the stress is not too large, the strain is directly proportional to the
stress.
💡 Young Modulus is defined as: “The ratio of stress to strain within the Limit
of Proportionality.”
The equation for Young Modulus is E = σε where E is Young Modulus, in Nm⁻² or
Pa, σ is stress, in Nm⁻² or Pa and ε is strain, with no units.
PRACTICAL MEASUREMENT OF YOUNG MODULUS OF A METAL
Physics A2 1 3
, In this experiment, we use two wires, a reference wire and the test wire, suspended
from a common support in the ceiling. Both wires should be made of the same
material, have the same cross section area and be approximately the same length.
This ensures that errors arising from thermal expansion as a result of temperature
changes in the wires are minimised. The wires should be as long as possible to
obtain the greatest possible extension of the test wire. A Vernier gauge is necessary
to measure the small extension with respect to the reference wire.
Initially the length of the test wire should be measured in mm, and recorded as L.
This is the distance from point of suspension to the vernier scale.
Using a micrometer screw gauge, the diameter of the test wire, d is found from 6
different points along the wire which are then averaged. The removes the possibility
of erroneous results. The cross sectional area of the wire can then be calculated.
Load the reference wire with 5N of mass to keep it taught. The test wire can then be
loaded in steps of 10N from 10N to about 100N, and for each step extension of test
wire and force are recorded, and stress and strain for each calculated.
The table below shows typical results:
From this information, a graph of stress (y) against strain (x) can be plotted, where
the straight line gradient is equal to the Young Modulus of the wire. If you continued
to measure stress and strain for increasing loads, we would eventually plot a graph
like the one below.
Physics A2 1 4
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