Answer:
Option e)
Explanation:
Dimensional Analysis helps in the analysis of relationship between physical quantities, checking its dimension thus checking the accuracy of a given or to find the dimensions of a quantity or the degree of correctness of an equation.
Dimensional analysis has some of the applications that are listed below:
- To establish a relationship between physical quantities
- To check the accuracy of a given formula
- To derive units of a physical quantity
- To convert system of units in one another.
Explanation:
You can use Hollomon's equation to estimate this.
Y_f is the flow stress.
K is the strenght coefficient or constant.
e is the strain
n is the strain hardening exponent.
You should be able to solve for e given the data in the problem statement.
Answer:
The smallest wire diameter that can be used is 1 cm
Explanation:
First, we find the smallest diameter using the criterion of maximum normal stress:
Max. Stress = 150 x 10^6 Pa = F/A
150 x 10^6 Pa = 12000 N/(πd²/4)
d² = (12000 N)(4)/(150 x 10^6 Pa)(π)
d = √1.0185 x 10^-4 m²
d = 0.010 m = 1 cm
Now, we find the smallest diameter using the criterion of maximum strain:
Max. Strain = Max. Change in Length/Original Length = 0.025 m/50 m
Max. Strain = 5 x 10^-4 mm/mm
Now,
Max. Strain = Stress/E = (F/A)/E = F/AE
using values:
5 x 10^-4 mm/mm = (12000 N)/(200 x 10^9 Pa)(πd²/4)
d =√(12000 N)(4)/(5 x 0^-4)(200 x 10^9 Pa)(π)
d = 0.012 m = 1.2 cm
Now, by comparison in both cases it can be noted that the smallest value of the diameter is <u>1 cm</u>, which is limited by maximum stress.
Answer:
[012] :
Here x component is zero. That is why this is in y- z plane
[721] :
This is in all three plane .It means it is in space.
[110] :
Here z component is zero.
That is why this is in x -y plane
From the cubic unit directions we can easily understand all given directions [012], [721], [110].