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## A Force system consisting of four forces and its resultant are shown in fig.1. Determine magnitude of unknown forces P1 and P2

Equating the forces vertical and horizontal, you can get the answer. P1 = 7.87 kN, P2 = 56.610 kN

Equating the forces vertical and horizontal, you can get the answer. P1 = 7.87 kN, P2 = 56.610 kN

See less## Value of (cosπ/4+isinπ/4) ^4 is………

Method 2: For imaginary number's multiplication we have, (a+ib)(c+id) = (ac - bd)+ i(ad + bc) -------------- Equation 1 In the question, a = c = cos(pi/4) and b = d = sin(pi/4); ac = (cos(pi/4))^2, -------------- Equation 2 bd = (sin(pi/4))^2, -------------- Equation 3 ad = bc = cos(pi/4)sin(pi/4) -Read more

Method 2:

For imaginary number’s multiplication we have,

(a+ib)(c+id) = (ac – bd)+ i(ad + bc) ————– Equation 1

In the question, a = c = cos(pi/4) and b = d = sin(pi/4);

ac = (cos(pi/4))^2, ————– Equation 2

bd = (sin(pi/4))^2, ————– Equation 3

ad = bc = cos(pi/4)sin(pi/4) ————– Equation 4

(cos(pi/4) + sin(pi/4))^4 = [(cos(pi/4) + sin(pi/4))^2]^2

For convenience let (cos(pi/4) + sin(pi/4))^2 = t,

Question now is t^2 = ?

So,

t = (cos(pi/4) + sin(pi/4))^2 = [cos(pi/4) + sin(pi/4)][cos(pi/4) + sin(pi/4)]

Putting Equation 2,3,and 4 in 1, t will become;

t = [cos^2(pi/4) – sin^2(pi/4)] + i[cos(pi/4)sin(pi/4) + cos(pi/4)sin(pi/4)]

= [cos^2(pi/4) – sin^2(pi/4)] + i[2sin(pi/4)cos(pi/4)]

Now, cos^2X – sin^2X = cos2X, 2sinXcosX = sin2X, putting these values above;

t = cos(2pi/4) + i[sin(2pi/4)] = cos(pi/2) + i[sin(pi/2)] = 0 + i = i

Note: cos(pi/2) = 0, sin(pi/2) = 1, i^2 = -1

t = cos(pi/2) + i[sin(pi/2)] = 0 + i = i

Hence, t^2 = (i)^2 = -1

See less## what is annealed state ?

https://learnmechanical.com/heat-treatment/#Heat_Treatment_Process A state where a material gets free from the internal stress developed on the material due to its mechanical working, via the process of annealing.

https://learnmechanical.com/heat-treatment/#Heat_Treatment_Process

A state where a material gets free from the internal stress developed on the material due to its mechanical working, via the process of annealing.

See less## How to calculate Daimand packing efficiency

In Diamond Cubic Packing, we have: 4 atoms at tetrahedral voids with its contribution of 1 atom per unit cell (1 x 4 = 4), 6 atoms at Face center with its contribution as 1/2 per unit cell (1/2 x 6 = 3), 8 atoms at Corners with its contribution as 1/8 per unit cell (1/8 x 8 = 1). So, number of atomsRead more

In Diamond Cubic Packing, we have:

4 atomsattetrahedral voidswith its contribution of 1 atom per unit cell(1 x 4 =

4),6 atomsatFace centerwith its contribution as 1/2 per unit cell(1/2 x 6 =

3),8 atomsatCornerswith its contribution as 1/8 per unit cell (1/8 x 8 =1).So, number of atoms per unit cell (

n)= 4 + 3 + 1 = 8Now,

Atomic Packing Factor (A.P.F) =

{n x (Total volume of atom in a unit cell)}/{Volume of unit cell}= {8 x (4/3) x 3.141 x (R^3)}/

a^3Here,

a(Edge Length) = 8R/(3)^1/2 = 8R/root(3).= ((3)^1/2) x 3.141 / 16 = 0.34

Therefore,

See lessAPF = 0.34

Packing efficiencywill be (0.34 x 100) =34%## What is age hardening? explain process for age hardening a material. what happens if we age the material for a very long time?

Age hardening is a process for strengthening of Non ferrous material. It is heat treatment technique follows 3 step. In 1st step solutionizing is being that means heated the alloy in single phase region. In 2nd step quenching should be done that is very fast colling from single phase region. In 3rdRead more

Age hardening is a process for strengthening of Non ferrous material. It is heat treatment technique follows 3 step.

In 1st step solutionizing is being that means heated the alloy in single phase region.

In 2nd step quenching should be done that is very fast colling from single phase region.

In 3rd step ageing that means we have to put the system for a certain period of time. That leads to formation of fine particles known as gp zone.

If we age more time in that situation size of particle increses which leads to decrease the strength.

See less## What is the reason for under riser crack in nickel base alloy(cw12mw, cw6mc)?

Ananth does this occur before or after you are heat treating?

Ananth does this occur before or after you are heat treating?

See less## the temporary shutdown of blast furnace is called

campaign time

campaign time

See less## Why mild Steel has lower susceptibility to crevice corrosion than Stainless Steel? if Stainless Steel is replaced with mild steel then what will happen?

https://askmemetallurgy.com/question/why-mild-steel-has-lower-susceptibility-to-crevice-corrosion-than-stainless-steel/ Refer to Kathirvelan's answer, it makes sense

Refer to Kathirvelan’s answer, it makes sense

See less## Why aren’t ferritic and austenitic stainless steels heat treatable?

Ferritic and stainless steel are not treatable because of low carbon content.

Ferritic and stainless steel are not treatable because of low carbon content.

See less## At which temperature oxidation corrosion occur?

By oxidation corrosion, I assume you mean dry corrosion. Dry corrosion occurs at a high temperature. The temperature will be different for each metal and alloy. You can gauge the temperature by looking at the Ellingham diagram, which shows where an oxide will be formed.

By oxidation corrosion, I assume you mean dry corrosion. Dry corrosion occurs at a high temperature. The temperature will be different for each metal and alloy. You can gauge the temperature by looking at the Ellingham diagram, which shows where an oxide will be formed.

See less## can corrosion be reduced by applying impressed current to a pipeline in which water is continuously flowing?

Yes, this method is called impressed current cathodic protection. Please check the video for more details.

Yes, this method is called impressed current cathodic protection. Please check the video for more details.

See less## How do sulfide inclusions (such as MnS)in steel affect pitting corrosion? What is the effect of oxide inclusion( such as Al2O3) in steel on corrosion properties, specially on pitting?

Yes, sulfide inclusions do affect pitting corrosion, provided they are on the surface of the sample. The reason is pitting begins from the surface. So, if there is an inclusion present on the surface, it will react with the cathodic species to form H2S and form a pit in its place. Oxides act as siteRead more

Yes, sulfide inclusions do affect pitting corrosion, provided they are on the surface of the sample. The reason is pitting begins from the surface. So, if there is an inclusion present on the surface, it will react with the cathodic species to form H2S and form a pit in its place.

Oxides act as sites of galvanic coupling with the matrix. If the oxide has a more positive potential w.r.t the matrix, it will cause the matrix around it to corrode and pit.

See less