Engineering Mechanics - May 2013
First Year Engineering (Semester 1)
TOTAL MARKS: 80
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks. 1 (a) Find forces P and Q such that resultant of given system is zero.
(4 marks) 1 (b) A cylinder B, WB=1000 N, dia 40 cm, hangs by cable AB=40 cm rests against a smooth wall. Find out reaction at C and TAB.
(4 marks) 1 (c) A block of weight 1000 N is kept on a rough inclined surface. Find out range of P for which the will block will be in equilibrium.
(4 marks) 1 (d) A curvilinear motion of a particle is defined by VX= 25 - 8t m/s and y=48 - 3t2m. At t=0, x=0, Find out position, velocity and acceleration at t=4 sec.(4 marks) 1 (e) State D' Alembert's principle with two examples.(4 marks) 2 (a) Find out resultant of given (lever) forces system w.r.t. "B"
(6 marks) 2 (b) Two identical cylinders dia 100 mm weight 200 N are placed as shown. All contacts are smooth. Find out reaction at A,B and C.
(8 marks) 2 (c) A ball of mass m kg hits an inclined smooth surface with a velocity VA=3 m/s. Find out velocity of rebound.
(6 marks) 3 (a) Find centoid of the shaded area.
(8 marks) 3 (b) Explain conditions for equilibrium for forces in space.(6 marks) 3 (c) Explain work energy principle.(6 marks) 4 (a) Find the support reaction at Hinge A and Roller B.
(8 marks) 4 (b) Explain x-t, v-t and a-t curves in Kinematics. (6 marks) 4 (c) Collar B moves up with velocity VB=2 m/s. Rod AB is pinned at B. Find out angular velocity of AB and velocity of A.
(6 marks) 5 (a) Find out forces in FB and BE using method of section and other members by method of joints.
(8 marks) 5 (b) A stone is thrown vertically upwards and returns to the starting point at the ground in 6 sec. Find out max. height and initial velocity of stone.(6 marks) 5 (c) Explain instantaneous centre of rotation.(6 marks) 6 (a) Force F=(3j - 4j + 12k)N acts at point A(1, -2, 3). Find -
(i) Moment of force about origin
(ii) Moment of forces about point B(2,1,2)m(4 marks) 6 (b) Find out min, value of P to start the motion.
(8 marks) 6 (c) For a particle in rectilinear motion a= -0.05V2 m/s2, at v=20 m/s, x=0. Find x at v=15 m/s and accn at x=50 m.(4 marks) 6 (d) Sphere A is supported by two wires AB, AC. Find out tension in wire AC :-
(i) before AB is cut
(ii) just after AB is cut