CSVTU Exam Papers – BE I Year – Engineering Mechanics– April-May-2010
BE (1st year)
1. (a) State Lami’s theorem ?
(b) A boat B, as shown in Fig. 1, is in the middle of a canal 100 m wide^ and is pulled through two ropes BA (150 m long) and BC (1,00 m long) by two men on the banks. The pull in BC = P = 150 N. Find the pull Q in BA so that the boat moves parallel to the banks. Find the resultant pull on the boat.
(c) Two identical rollers each of weight Q = 100 N are supported by an inclined plane and a vertical wall as shown in Fig. 2. Assuming smooth surfaces, find the reactions at A, B, & C.
(d) A loading car, as shown in Fig. 3, is at rest on a track formi an arjgle of 25° with the vertical. The gross weight of the cj & its load is 2^500 N .and it is applied at a point 75 cm from the track, cable attached 60 cm from the trai Determine the tension in the cable & reaction at each pair wheels. Neglect frictions.
Q.2 (a) Define point of contraflexure.
(b) Draw the shear force and bending moment diagrE for the beam as shown in Fig. 4.
(c) A truss is loaded as shown in Fig. “5. The span of truss is m . Find out the forces in all the members of “the truss.
(d) A truss is loaded and supported as shown in Fig. 6. Determine the axial forces in the members CE, CG & FG.
Q.3.(a) Define limiting friction.
(b) What is the value of P in the system shown in Fig. 7 to cause the motion to impend ? Assume the pulley is smooth’& coefficient of friction between the other contact surfaces is 0.20.
(c) A ladder of length 4 – m weighing 200 N is placed against a vertical wall as shown in Fig, 8. The coefficient of friction between the wall & the ladder is 0.2 & that between the floor & the ladder is 0.3. The ladder in addition to its own weight has to support a man weighing 600 N at a distance, of 3 m from A. Calculate the minimum horizontal force to be applied at A to prevents slipping .
(d) A belt 100 mm x 10 mm thick is transmittin power at 1200 m/min. The net driving tension is 1.8 times the tension on the slack side. If the safe stress on the belt section is 1.8 N/mm2 calculate the power that can be transmitted at this speed. Assume mass density of the leather as 1 t/m3. Also calculate the absolute maximum power that can be transmitted by this belt & the speed at which this can be transmitted.
Q.4.(a) State product of inertia.
(b) P rove that the moment of inertia of the area of a rectangle as shown in Fig. 9 about its diagonal is given by,
I=a3b3 /6(a2 + b2)
(c) Determine the mass moment of inertia of a unit length L about its centroidal axis normal to rod.
(d) For a z—section as shown in Fig. 10, the moment of inertia with respect to the x and y axes are given to be lx = 154 axes of cm4 and ly = 2668 cm4 Determine the principal axes of section about 0 and the values of the principal inertia.
Q.5.(a) Explain D’Alembert’s principle.
(b) Two weights 800 N and 200 N are connected bl and they move along a rough horizontal plane action ®f a ‘force of 400 – N appljed to the 800 N shown in Fig. 11. The coefficient of friction be sliding surface of the weights & the plane is D’Alembert’s principle determine the acceleration tension in thread.
(c) Determine the constant force P that will give the system bodies shown in>Fig. 12 a velocity of 3 m/s after moving 4m from rest. Coefficient of friction between the-blocks & the plane is 0.3. Pulleys are smooth.
(d) A glass marbel, whose weight is 0.2 N1 falls from a height c 10 m and rebounds to a height of 8 metres. Find the impuls and the average force between the marble and the floor, the time during which they are in contact is 1/10 of a second.