ENGINEERING MECHANICS GATE PI PAPER TECHNICAL SECTION PART 2

METHOD OF MOMENTS Moment of a force with respect to a point >Considering wrench subjected to two forces P and Q of equal magnitude. It is evident that force P will be more effective compared to Q, though they are of equal magnitude. The effectiveness of the force as regards it is the tendency to produce rotation of a body about a fixed point is called the moment of the force with respect to that point. Moment Magnitude of the force x Perpendicular distance of the line of action of force. Point O is called moment centre and the perpendicular distance (i.e. OD) is called moment arm >Unit is N.m

Theorem of Varignon: The moment of the resultant of two concurrent forces with respect to a centre in their plane is equal to the algebraic sum of the moments of the components with respect to some centre . Problem 1: A prismatic clear of AB of length I is hinged at A and supported at B. Neglecting friction, determine the reaction Rb produced at B owing to the weight Q of the bar. Taking moment about point A ! Rb * 1 = Q cosa. 2 COSa 2

Problem 2: A bar AB of weight Q and length 2l rests on a very small friction less roller at D and against a smooth vertical wall at A. Find the angle a that the bar must make with the horizontal in equilibrium Resolving vertically, R, cos -Q Now taking moment about A, R, a cos Qlcos a -0 al coS a

Problem 3: If the piston of the engine has a diameter of 101.6 mm and the gas pressure in the cylinder is 0.69 MPa. Calculate the turning moment M exerted on the crankshaft for the particular configuration Area of cylinder A-(0.1016). 8.107 x 10-3,n. 4 Force exerted on connecting rod, Pressure x Area 0.69x106 x 8.107x103 5593.83 N F i178 380 Now asin 27.93 S cosa F S6331.29N cos Now moment entered on crankshaft, S cosa x 0.178 995.7N 1KN

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Indira Roy

B.Tech Industrial Engineering and Management|| Educator || Painting || sports ||

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Niraj Kumar

3 months ago

thanku sir make all chpater of prelims .

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