Exam-style Questions: Stress and Strain
A strain of 1x10-3 for a 1m long wire means an extension of 0.001m.
From the graph, the energy stored per unit volume is
That would be the energy stored if the volume of wire in the test was 1m3. But it�s not. The volume of the wire is in fact:
So the energy in the sample is:
A stress-strain graph is plotted for a sample of wire with cross sectional area of 2.0 x 10-6m2.
How much energy is stored in a 1m length of the wire when the strain is 1.0 x 10-3?
- 1.0 x 105J
- 0.2 x 105J
b) i) Distinguish between elastic and plastic behavior when materials are stretched.
ii) Define elastic limit
c) i) State the SI unit of the Young's modulus.
ii) Describe, with the aid of a diagram, an experiment to determine the Young's modulus of steel in the form of a wire. Explain how to use your readings to obtain the Young's modulus. (You will be awarded marks for the quality of written communication in this part of the question.)
Answer outline and marking scheme for question: 1
a) i) stress = force / (cross sectional) area
ii) strain = extension / (original) length
b) i) elastic returns to its original length /shape when the force/load is removed
plastic does not regain its original length/size when the load is removed
(allow 1/2 if removal of load is not specified but remainder is clear)
ii) force/stress/strain/extension beyond which the material does not return to its original length (when the load is removed)
(point beyond.... scores one only)
c) i) unit: Pa / N m-2
ii) Any seven from:
- Appropriate arrangement drawn
- Measure length
- Apply force and measure the extension
- Take a series of readings
- Measure the diameter
- Graph of stress against strain OR force-extension graph
- Gradient for E OR E= stress/strain OR Gradient = EA/L
- Point of detail e.g. second wire, micrometer used for diameter, Vernier for extension, very long wire
(Marks available: 14)
A wire of a length 1m and diameter of 0.4mm is hung from a ceiling. Find the extension caused in the wire, by attaching a weight of 100N, if the material of the wire has the Young's modulus (E) of 200x1011Nm-2.
(Marks available: 2)
Answer outline and marking scheme for question: 2
i.e. stress/E = strain
Stress = force area =100/cross sectional area =100/(p/4)(8x10-4)2 Pa = 1.99x108 Pa
Strain = 1.99x108/200x1011 = 0.995 x 10-3 m = 0.995mm
A kitchen freezer of total mass 300 kg (including contents) rests ona vinyl plastic floor covering.
a) Calculate the weight of the freezer and its contents.
g = 9.8 N kg-1
weight = ....................... N
b) The feet of the freezer have a total cross-sectional area of 8.0 x 10-4 m2.
The vinyl plastic floor covering has a compressive yield stress of 3.5 MPa.
Show that the feet of the freezer can cause permanent damage to the vinyl plastic floor covering.
(Marks available: 3)
Answer outline and marking scheme for question: 3
a) W = mg = 300 x 9.8 = 2490 N e
b) stress / pressure = W / A = 2490 / 8.0 x 10-4 (1 Mark) m ;
= 3.7 x 106 Pa (> yield stress) (1 Mark) e ; if ecf from a) gives lower than 3.5 MPa explicit comparison needed
(Marks available: 3)