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Answer

y= e^(ax+b)

take log both sides

logy = (ax+b) loge = a loge x + b loge

Differentiating w.r.t  x

1/y dy/dx  =  a loge  + 0 ( since differetiation of constant is Zero)

Hence, dy/dx  = a loge . y  = a loge. e^(ax+b)

                          Hence, the result.

 

Answer

Regular Prism :

Prism is a polyhedron with two congruent bases, and having parallelograms as additional faces. A right prism has edges perpendicular to the base. Finally, a regular prism is a right prism with a regular polygon as the base. A hexagonal prism is a prism with a hexagonal base.

           There will be six equilateral triangles in the base of the prism.

           Since, the length of each side of the Prism = 1 m

           Hence, the Area of each triangle =    ½ x base x height

                                                                   =   ½ x 1 m  x 0.865 m

           Total Area of the base = 6 x ½ x 0.865 sq. m.

          Height of Prism = 1 m

           Volume of Prism  =  1 x 6 x ½ x 0.865 cu.m.= 2.595 cu. M.

         

Answer

1.     Slip Systems

In single crystals there are preferred planes where dislocations move (slip planes). There they do not move in any direction, but in preferred crystallographic directions (slip direction). The set of slip planes and directions constitute slip systems.

The slip planes are those of highest packing density. How do we explain this? Since the distance between atoms is shorter than the average, the distance perpendicular to the plane has to be longer than average. Being relatively far apart, the atoms can move more easily with respect to the atoms of the adjacent plane. 

BCC and FCC crystals have more slip systems that is more ways for dislocation to propagate. Thus, those crystals are more ductile than HCP crystals (HCP crystals are more brittle).

2.     Slip in Single Crystals

A tensile stress s will have components in any plane that is not perpendicular to the stress. These components     are resolved shear stresses. Their magnitude depends on orientation :.  

     tR = s cos f cos l

     If the shear stress reaches the critical resolved shear stress tCRSS, slip (plastic deformation) can start. The stress      needed is:

     sy = tCRSS / (cos f cos l)max

     at the angles at which tCRSS is a maximum. The minimum stress needed for yielding is when f = l = 45            degrees: sy = 2tCRSS. Thus, dislocations will occur first at slip planes oriented close to this angle with respect to the      applied stress.

 

Answer

Space-Lattice:- A space lattice is an array of points showing how particles (atoms, ions or molecules) are arranged at different sites in three dimensional spaces.”

Answer

Various types of heat treatment processes are:

(a) Annealing

(b) Normalizing

(c) Hardening

(d) Tempering

Purpose – For annealing are:

(a) To soften the metal. i.e. While working on metals in cold condition, it becomes hard. For further work on the metal without any cracks, it should be soften by annealing process.

(b) To improve machinability.

(c)  To refine grain size, structure and to improve mechanical properties.

(d) To relieve internal stresses which were developed during working over the metal.

(e) To modify physical properties.

(f)  To increase ductility of metal.

(g) To prepare the steel for cold working.

Normalising :

Purpose : To normalise the surface structure for further machining .

 

 

 

Answer

Escape velocity is the speed that an object needs to be traveling to break free of a planet or moon's gravity well and leave it without further propulsion. For example, a spacecraft leaving the surface of Earth needs to be going 7 miles per second, or nearly 25,000 miles per hour to leave without falling back to the surface or falling into orbit.

Answer

Iron-Carbon based alloy containing at least 0.5 percent silicon, 0.6 percent copper, 1.65 percent manganese, and minute quantities of chromium, nickel, molybdenum, and/or tungsten. Steel that does not contain specified or standard amount of one or more alloying elements is termed carbon steel.  

Answer

The Equation for Work Done by Spring force  for displacement  x and spring constatt k is,

 W = - 1/2 K X^2

Answer

W= F S Cos (theta)

The work done will be maximum when the value of theta will be zero.

Answer

The minimum force required to move a body of mass m on a rough horizontal surface having coefficient of friction U

= U.N, where N is the normal force at the contact surface.

= U.mg, where N=mg.