GE 131 - ENGINEERING MECHANICS
PART – A (10 X 2 = 20 Marks)
1. Determine the resultant of the three forces F1 = 2.0i + 3.3j – 2.6k; F2 = - i + 5.2j – 2.9k; and F3 = 8.3i – 6.6j + 5.8k, which are concurrent at the point (2, 2, -5.). The forces are in newtons and the distances are in metres.
2. A force F = (6N)i – (3Nj – (4N)k is acting at a point P whose position vector from the origin 'O' of the coordinate axes is (8 mm)i + (6 mm)j – (4 mm)k. Find the moment of the force about the origin.
3. State Varignon's theorem.
4. State the theorems of Pappus and Guldinus to find out the surface area and the volume of a body.
5. State the Coulomb's laws of dry friction.
6. A belt embraces an angle of 200? over the surface of a pulley of 500 mm diameter. If the tight side tension of the belt is 2.5 kN. Find out the slack side tension of the belt. The coefficient of friction between the belt and the pulley can be taken as 0.3.
7. The motion of a particle in defined by the relation x = t3 – 15 t2 – 20, where 'x' is expressed in metres and 't' in seconds. Determine the acceleration of the particle at t = 3 seconds.
8. A mass of 50 kg. has an initial velocity of 15 m/s. horizontally on a smooth surface. Determine the value of horizontal force that will bring the mass to rest in 4 seconds.
9. Define the term 'coefficient of restitution' of two bodies under impact.
10. State the principle of conservation of linear momentum of a particle.
PART – B (5 x 16 = 80 Marks)
11. A force F acts at the origin of a coordinate system in a direction defined by the angles ?x = 69.3? and ?z = 57.9?. If the component of the force F along y direction is = -174N, determine.
(i) the angle ?y (4 Marks) (ii) the magnitude of the force F (4 Marks) (iii) the components of the force F along x and z directions. (4 Marks) (iv) the component of the force F on a line through the origin (4 Marks) . and the point (1,1,1).
12. (a) A load P of 3500 N is acting on the boom, which is held by a cable BC as shown in Fig.12(a). The weight of the boom can be neglected.
(i) Draw the free body diagram of the boom. (4 Marks) (ii) Find out the tension in cable BC. (8 Marks) (iii) Determine the reaction at A. (4 Marks)
(OR)
(b) Three forces +20N, -10N and +30N are acting perpendicular to x z plane as shown in Fig. Q.12(b). The lines of action of all the forces are parallel to y-axis. The coordinates of the point of action of these forces along x and z directions are respectively (2,3), (4,2) and (7,4), all the distances being referred in metres. Find out.
(i) The magnitude of the resultant force. (4 Marks) (ii) The location of the resultant. (12 Marks)
13.(a) (i) Determine the coordinates of the centroid of the shaded area shown in Fig. Q.13 (a) if the area removed is semicircular. (4 Marks) (ii) Find the moment of inertia of the shaded area about the centroidal axes, the axes being parallel to x and y-axes. (6 Marks) (iii) Find the product of inertia of the shaded area about the centroidal axes. . (6 Marks)
(OR)
(b) Find the mass moment of inertia of the rectangular block shown in Fig. Q.13(b), about the x and y axes. A cuboid of 20 mm x 20 mm x 20 mm has been removed from the rectangular block as shown in the figure. The mass density of the material of the block is 7850 kg/m3.
14.(a) Two masses m1 and m2 are tied together by a rope parallel to the inclined plane surface, as shown in Fig. Q.14(a). Their masses are 22.5 kg. and 14 kg. respectively. The coefficient of friction between m1 and the plane is 0.25, while that of mass m2 and the plane is 0.5. Determine.
(i) the value of the inclination of the plane surface, ?, for which the masses will just start sliding. (6 Marks) (ii) the tension in the rope. (6 Marks) (iii) what will be the friction forces at the mass surfaces. (4 Marks)
(OR)
(b) The driver of an automobile decreases the speed at a constant rate from 72 to 48 km./hour over a distance of 230 m. along a curve of 460 m. radius. Determine the magnitude of the total acceleration of the automobile, after the automobile, after the automobile has traveled 150 m. along the curve.
15.(a) Two steel blocks, shown in Fig. Q. 15(a), slide without friction on a horizontal surface. The velocities of the blocks immediately before impact are as shown. If the coefficient of restitution between the blocks is 0.75, determine (i) the velocities of the blocks after impact and (12 Marks) (ii) the energy loss during impact. (4 Marks)
(OR)
(b) A plate shown in Fig.Q.15 (b) moves in the xy plane as below.
x component velocity of point A = 450 mm/s. x component velocity of point B = -150 mm/s. y component velocity of point C = -900 mm/s. Determine : (i) the angular velocity of the plate and (8 Marks) . (ii) the velocity of the point B. (8 Marks)
