Find out the centroid of the shaded area, Mechanical Engineering

Find out the centroid of the shaded :

Find out the centroid of the shaded area shown in Figure

689_Find out the centroid of the shaded.jpeg

Solution

Net area of shaded portion of Figure

= The area of full circle of radius r (A1) -   the area of cut out circle of radius r/2 ( A )

= π r 2 - π r 2 / 4 = 3 π r 2 / 4

 Area A2 is to be considers as negative area.

Let moment of areas around G (the needed C. G.); ∑ Ai xi = 0 since the lever-arm of the Resultant area A regarding G is zero,

A1  x1 + (- A 2 ) x2  =  A × (0) = 0

∴ π r 2  (- x) + ( - π r 2 /4)    × (- (r/2)+  x¯ )} = 0

 (an anticlockwise moment)   (an anticlockwise moment)

∴ -  (3 π r /4 ) x¯ +   π r3/(4 × 2) = 0

∴ x¯ = +  r/6

Positive sign of x show that with respect to the origin O of reference axes x and y, x¯ = OG is along with positive direction of x axis. As the centres O and A of the two area (A1) and (- A2) are taken along x axis; G lies on AO.

Posted Date: 1/29/2013 12:45:06 AM | Location : United States







Related Discussions:- Find out the centroid of the shaded area, Assignment Help, Ask Question on Find out the centroid of the shaded area, Get Answer, Expert's Help, Find out the centroid of the shaded area Discussions

Write discussion on Find out the centroid of the shaded area
Your posts are moderated
Related Questions
Norma l Temperature and Pressure (N.T.P.): The conditions of temperature and pressure at 0°C (273K) and 760 mm of Hg respectively are called normal temperature and pressure (

example on operation sheet?

A 10 kg block slides down a smooth inclined surface as shown in Figure. Show the terminal velocity of the block if the 0.1 mm gap among the block and the surface have SAE30 oil at

Factor of Safety: Factor of safety is number used to determine working stress. It is fixed based on experimental works on material. It accounts all uncertainties like, mate

Fatigue crack propagation: If it is assumed that no plastic deformation occurs around crack tip and law of fatigue crack propagation for place of above Example is da/dN =  10

Q. Explain the working of Die Casting? In the die casting process the, mould used for a casting is permanent called a die casting. it is shown in figure. It is thus quite diffe

Step s for Solving Problem for Finding Maximum Power: 1. Use formula stress (σ) = force (Maximum Tension)/Area Where;  Area = b.t that is, T max = σ.b.t 2. Unit mass (

In the drawing, the weight of the block on the table is 380 N and that of the hanging block is 215 N. Ignore all frictional effects, and assuming the pulley to be massless.

Performance of Heat engine: Performanc e of HP:   It is measured by thermal efficiency that is the degree of useful conversion of heat received into work.

Calculate the shear flow in each wall of the fuselage section below. The flange areas are 1 sq in and the web thicknesses are 0.05 in. The material has modulus E = 10 mpsi and G =