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Ouestion 5
A. Describe THREE (3) applications where tensile strength is primarily factor in material selection. What material would you select for what application and state why?
B. Copper has the atomic radius of Oa 128 nm, an FCC crystal structure and an atomic weight of 63.5 g/mol. Calculate the following:
i. Cell edge length ii. Vc - Unit cell volume iii. Vs — Sphere volume iv. Density,
v. APF - Atomic Pack Factor via Write the Avagador's Number
c. Briefly explain what the factors that caused imperfection in solids are.
A. Make a sketch of the unit cell in a point model form of the following and writer the occupancy numbers and the Coordination numbers:
i. BCC — Body Centred Cubic ii. FCC - Face Centred Cubic iii. HCP - Hexagonal Close Pack
1) Find the spectral components of a periodic train of a square pulse with an even symmetry by applying Fourier series analysis. Consider the period of 1 s for the repetition of the square pulse.
(3) Why do you observe ripples in the synthesis of the periodic train of square pulse?
(4) Why are the ripple absent in the synthesis of the periodic train of triangle pulse?
(5) How the number of ripples is related to the number of harmonics in the
synthesis of the periodic train of square pulse?
(6) What is the effect of varying the number of samples and the frequency as in the steps (7) and (8), respectively?
How does the sine and cosine functions affects the symmetry (either
even or odd) of the synthesised periodic signals?
A steel ball with a mass of 0.5 kg and a radius of 10 mm is dropped from a height of 3 m and strikes a homogeneous sheet with a thickness of 1200 mm which is located on a rigid bed. Calculate the maximum penetration, maximum contact force and maximum contact radius in the following three cases. (Assume a modulus of elasticity of 200 GPa, a yield stress of 250 MPa, and a Poisson's ratio of 0.3 if required.)
A) Rigid ball and Linear Elastic plate
B) Rigid ball and rigid-Perfectly Plastic plate
C) Rigid ball and Linear Elastic-Perfectly Plastic
find that at what distance body A will attain a velocity of 3 m/s when starts from rest. Assume coefficient of friction as 0.2 for block and surface and pulleys are frictionless and weightless
A metal cube(faces 20 mm+-0.1mm) fully sinks into a glass full of water. The diameter of the glass is 60 mm+-0,2 mm.Calculate the water rise level and its cumulative error.
A metal cube(faces 20 mm+-0.1mm) fully sinks into a glass full of water. The diameter of the glass is 60 mm+-0,2 mm.Calculate the water rise level and its cumulative error.
solution of differential Equation
12. (2y² + 3xy-2y+6x)dx + x(x+2y-1)dy=0
13.ydx + (3x xy + 2)dy = 0
14. (x³ + xy² + y)dx + (y² + x²y + x)dy = 0
15. (x² + y²)dx-xydy = 0
16.eyy' = x cos x
17. y'=x-2y cot 2x
solution of the Differential equation
7. (1+y² + xy²)dx + (x²y + y + 2xy)dy =0
8. 2ydx + x(x² Iny-1)dy = 0
9. y(2x+y²)dx + x(y²-x)dy = 0
10.(3x²-2y2)y' = 2xy; x = 1, y = 1
11.(2x-3y)dx + (2y-3x)dy; x = 1, y = 1
