Mechanics Study Material with Solved Assignments and Essays - Desklib

Ali Talal Mohammed
Contents
TASK 1..........................................................................................................................................................3
Strain, Stress and Young’s modulus of elasticity......................................................................................3
Strain measurement............................................................................................................................3
TASK 2..........................................................................................................................................................4
Elongation, stress and strain....................................................................................................................4
TASK 3..........................................................................................................................................................5
Parallel axis theorem and its application.................................................................................................5
TASK 4..........................................................................................................................................................6
Torsion.....................................................................................................................................................6
Assmptions of torsion..........................................................................................................................6
TASK 5..........................................................................................................................................................7
a) Moment of inertia...........................................................................................................................7
b) Angular velocity and linear velocity.................................................................................................7
c) Time.................................................................................................................................................7
d) Time.................................................................................................................................................7
e) Speed and velocity...........................................................................................................................8
TASK 1..........................................................................................................................................................2
Strain, Stress and Young’s modulus of elasticity......................................................................................2
Strain measurement............................................................................................................................2
TASK 2..........................................................................................................................................................3
Elongation, stress and strain....................................................................................................................3
TASK 3..........................................................................................................................................................4
Parallel axis theorem and its application.................................................................................................4
TASK 4..........................................................................................................................................................5
Torsion.....................................................................................................................................................5
Assmptions of torsion..........................................................................................................................5
TASK 5..........................................................................................................................................................6
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Ali Talal Mohammed
a) Moment of inertia...........................................................................................................................6
b) Angular velocity and linear velocity.................................................................................................6
c) Time.................................................................................................................................................6
d) Time.................................................................................................................................................6
e) Speed and velocity...........................................................................................................................7
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Ali Talal Mohammed
TASK 1
Strain, Stress and Young’s modulus of elasticity
a) Strain and how to measure it experimentally.
Strain is the relative change in shape or rise of an object as a result of external force.
Strain= ∆ l
l0
,
Where l0 is the initial length, ∆ l=l−l0 is the change in the length after application of the force.
Strain measurement
We use the strain gauge. This gauge has a metallic foil which is electrically resistant to changes.
This is measured using Wheatstone bridge and is related to strain by gauge factor as shown below
Gf =
∆ R
Rg
ε
Where ε is the strain, Gf is the gauge factor, ∆ R is the change in resistance caused by strain and Rgis
the resistance of undeformed gauge.
Stress= F
A
Where F is the force applied, A is the cross-sectional area.
The Young’s modulus of elasticity E is given by:
E= Stress
Strain = l0 F
A ∆ l
The larger the E, the stronger the material.
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