VELAMMAL COLLEGE OF ENGINEERING AND TECHNOLOGY MADURAI DEPARTMRNT OF MECHANICAL ENGINEERING. Subject Code. Mechanics

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1 VELAMMAL COLLEGE OF ENGINEERING AND TECHNOLOGY MADURAI DEPARTMRNT OF MECHANICAL ENGINEERING Year / Sem / Branch I Year / II Sem / CSE Subject Code GE 204 Subject Name Engineering Mechanics Faculty In charge Mr. G. Manikandan Assignment Topics: Moment of force, Application of varignon s theorem, Couple, Equivalent force couple system. Answer all the questions: 1) State the varignon s theorem of moments. 2) Define the moment of the force about a point. 3) What is meant by couple? 4) What is meant by force couple system? 5) The forces acting on the angle section are shown in the fig. Determine the moment produced by them about the point O. 6) The moment produced by the force F acting on the bracket as shown in the fig at O is 14N-m (anticlockwise). Determine the value of force F. 7) A system of four forces A, B, C, D of magnitudes 10 KN, 15 KN, 18KN and 12 KN acting on a body are shown in rectangular co-ordinates as shown in figure. Find the moment about origin.

2 8) Calculate the resultant moment about the corner B as shown in fig. 9) Four forces of magnitude and direction acting on a square ABCD of side 2m are as shown in figure. Calculate the magnitude and direction and also locate its point of application with respect to the sides AB and AD. 10) Determine the magnitude and line of action of resultant forces as shown in figure. 11) Determine the magnitude and line of action of resultant forces as shown in figure

3 12) Replace the given system of forces acting in the lever as shown in fig by an equivalent force couple system at O. 13) Resolve the force system shown in figure acting on the frame by an equivalent force couple system at A. Also replace the system by an equivalent resultant force and indicate the point of application of this force in the horizontal member BC. 14) A beam AB as shown in fig has a equivalent force couple system at A as 15KN force acting vertically downward and a clockwise couple of moment of 60 KN-m. Determine the values of force F, angle Ө and the point of application of the force F from A.

4 15) A 4.8m beam is subjected to the forces as shown in fig. Reduce the given system of forces to (a) a single force (b) an equivalent force couple system at A (c) force couple system at B. 16) The three forces and a couple of magnitude M =18 Nm are applied to an angled bracket as shown in fig. (a) Find the resultant of this system of forces. (b) Locate the points where the line of action of the resultant intersects line AB and the line BC. 17) A 300 x 150 mm plane is subjected to four forces as shown in figure. Find the resultant of two forces and the two points at which the line of action of action of the resultant of resultant intersects the edge of the plate. 18) A 3000N vertical force is applied to the end of the lever which is attached to the shaft at O as shown in fig. Determine i) The moment of 3000N force about O. ii) The magnitude of horizontal force applied at A, which creates the same moment about O. iii) The smallest force applied at A, which create the same moment about O. iv) How far from the shaft a 750N vertical force must act to create the same moment about O.

5 19) Replace the couple and force as shown in fig by an equivalent single force applied to the lever. Determine the distanced from the shaft to the point of application of this equivalent force. 20) Four coplanar non-concurrent forces act on a square of side 2m as shown in fig. Locate the resultant force. 21) A rectangle as shown in fig has AB = 200mm and BC = 150mm. Calculate the magnitude, direction and position of the resultant force. 22) A system of parallel forces are acting on the rigid bar as shown in fig. Reduce the system to i) a single force ii) a single force and couple at A. iii) a single force and couple at B.

6 23) A rigid bar is subjected to a system of parallel forces as shown in fig. Reduce the system of forces to a i) a single force and couple at A. ii) a single force and couple at B. 24) Reduce the system of forces as shown in fig. into a force couple system at A. 25) Reduce the system of forces in belts as shown in fig. into a force couple system at O. 26) Replace the force at A by an equivalent force and couple moment at point P as shown in fig.

7 27) Three forces and a couple M acting on an angled bracket as shown in fig. Find the moment of the couple if the line of the resultant force is to pass through i) Point A ii) Point C. ANSWERS: 5) Mo = 390 Nm (Anticlockwise) 6) F = 198 N. 7) M A = 0; M B =9.24 knm(anticlockwise); M C = kn-m (anticlockwise); M D = knm (clockwise) 8) M B = 99.1 KNm 9) R = N α =32 at a distance of 2.598m from A along B and at a distance of 1.625m from A along D 10) R = 20.97N α =47.06 at a distance of 2.094m from A perpendicular to line of the resultant force 11) R = -6KN, at a distance of 3.25m from A. 12) Equivalent Force at O = 600N. Equivalent Couple at O = 90Nm. 13) Equivalent force at A = N Equivalent couple at A = Nm Point of application is 1.80 m from B in BC. 14) F =10KN =36.87 Point of application from A =5.0m 15) i) R = -600N at distance of 3.13m from A ii) R = -600N at A, Couple 1878 Nm Clockwise iii) R = -600N at B, Couple 1002 Nm Anticlockwise 16) R=149.32N α =22.95 Location = mm from A, from B in the downward direction 17) R=223.6N α =26.56 Location 35mm from A, 335 mm from F.

8 18) i) 900 Nm ii)f =1734.1N iii)f =1500N iv) X =1.2m 19) 17.5 cm 20) R =13.79 KN α =39 in first quadrant at 0.8mm on side DC from D. 21) R =10.2 KN α =11.31 at 40mm from A on AD 22) i) Single force :-60N location :0.75m ii) Single force: -60N Couple at A: 45 Nm Clockwise iii) Single force: -60N Couple at A: 165 Nm Anticlockwise 23) i) 15N force and 25 Nm Clockwise Couple. ii) 15N force and 12.5 Nm Anticlockwise Couple 24) 62.47N force at 6.91 and 72.4 Nm Clockwise Couple. 25) 84.9 N force at and 8 Nm Clockwise Couple. 26) 375N force and 737 Nm Anticlockwise Couple. 27) i) 29.7 Nm anticlockwise. ii) Nm anticlockwise. Faculty In-charge HOD / MECH

MOMENT OF A FORCE ABOUT A POINT

MOMENT OF A FORCE ABOUT A POINT The tendency of a body to rotate about an axis passing through a specific point O when acted upon by a force (sometimes called a torque). 1 APPLICATIONS A torque or moment