Subject Code: R13110/R13 I B. Tech I Semester Regular Examinations Jan./Feb ENGINEERING MECHANICS

Transcription

1 Set No - 1 I B. Tech I Seester Regular Exainations Jan./Feb ENGINEERING MECHANICS (Coon to CE, ME, CSE, PCE, IT, Che E, Aero E, AME, Min E, PE, Metal E) Tie: 3 hours Max. Marks: 70 What is the principle of transissibility? State triaular la of forces. What is the use of this la? Locate the centroid of a seicircle of radius r. Find the ass oent of inertia of a slender rod. State D Alebert principle givi equations. Explain the concept of ork? What are the units of ork? 1.(i) (ii) (iii) (iv) (v) (vi) Question Paper Consists of Part-A and Part-B Anseri the question in Part-A is Copulsory, Three Questions should be ansered fro Part-B ***** PART-A [ ] PART B To sooth circular cylinders, each of eight W= 1000N and radius 15c, are connected at their centres by a stri AB of leth 40c and rest upon a horizontal plane, supporti above the a third cylinder of eight 2000N and radius 15c as shon in fig1. Find the force in stri AB and the pressure produced on the floor at the points of contact D and E. 2.(a) Fig: 1 Page 1 of 3

2 Set No (a) A sall block of unknon eight is placed on an inclined plane hich akes an ale of 300 ith the horizontal plane. The coponent of this eight parallel to the inclined plane is 100N. Find the eight of the block. Find the area oent of inertia about the centroidal axes for a given area shon in the fig 2. State and prove the parallel axis theore. Fig.2 4.(a) 5.(a) [5+11] A toer is 100 in height. A particle is dropped fro the top of the toer and at the sae tie another particle is projected upard fro the foot of the toer. Both the particles eet at height of 40. Find the velocity ith hich the second particle is projected upard. What do you understand by Potential Energy and Kinetic Energy of a body? The four coplanar forces are acti at a point as shon in the fig.3. One of the forces is unknon and its agnide is shon by P. The resultant is havi a agnide of 500N and acti alo x-axis Deterine the unknon force P and its inclination ith x-axis. Fig.3 Page 2 of 3

3 Set No Fig.4 Prove that of oent of inertia of a circular section about an horiz horizontal ontal axis and passi through C.G of the section is given by Π D4/64. State and prove Pappus theores I and II. Distiuish beteen area oent of inertia, polar oent of inertia and ass oent of inertia. 7.(a) 6.(a) A body eighi 196.2N slides up a 600 inclined plane under the action of applied force 400N acti parallel to the inclined plane. The coefficient of friction is equal to 0.2. The body oves fro rest. Deterine (i) Acceleration of the body (ii) Distance travelled by the body in 5 seconds (iii) Work done by the body in 5 seconds. (iv) Moen of the body after 5 seconds. [4+12] Explain and define the ter Free Body diagra. Dra the free body diagra and calculate the tensions in AC and BC shon in fig.4. Page 3 of 3

4 Set No - 2 I B. Tech I Seester Regular Exainations Jan./Feb ENGINEERING MECHANICS (Coon to CE, ME, CSE, PCE, IT, Che E, Aero E, AME, Min E, PE, Metal E) Tie: 3 hours Max. Marks: 70 (v) (vi) (vii) A body eighi 600N is lifted by to ropes passi over a sooth pulley as shon in fig1. Deterine F1 andf2. 2.(a) (iv) (ii) (iii) A force of 200N is acti at a point and akes an ale of 1200 and 600 ith the x and y axes respectively. Find the coponent of the force and express it as vector. Explain and define the ter Free Body Diagra. Define radius of gyration. What is the radius of gyration of a circle of diaeter d about its diaeter? Derive the expression for the product of inertia for a rectale ith B x D about the axes through the edges. State the condition for the dynaic equilibriu of a body under translation. State the ork energy principle for the body rotati about fixed axis. State any to iportant las of friction. [ ] PART-B 1.(i) Question Paper Consists of Part-A and Part-B Anseri the question in Part-A is Copulsory, Three Questions should be ansered fro Part-B ***** PART-A Fig.1 Page 1 of 3

5 Set No (a) [6+10] A stone dropped into a ell is heard to strike the ater after 7secs. Find the depth of the ell, if the velocity of sound is 450/s. The eight of a body on earth is 980N. If the acceleration due to gravity on earth is 9.80 /s2, hat ill be the eight of the body on (i) The oon, here gravitational acceleration is 1.6 /s2 and (ii) The sun, here gravitational acceleration is 270 /s2. State and prove Varignon s theore. A body eighi 20N is projected up a 200 inclined plane ith a velocity of 12/s, coefficient of friction is Find the axiu distance S that the body ill ove up the inclined plane. 5.(a) Fig.2 Copute the ass oent of inertia of a circular plate. 3.(a) A cone of height 20c and radius of base 5c is truncated fro its apex by a height of 5c. Locate the centre of gravity of the truncated cone. [6+10] For the syste shon in the fig 2., deterine the agnide P so that the syste just starts to ove don. Assue that the pulley is sooth and coefficient of friction as 0.26 for horizontal and inclined planes. Page 2 of 3

6 Set No - 2 To spheres, each of eight 1000N and radius 25c rest in a horizontal channel of idth 90c as shon in the fig.3. Find the reactions on the points of contact A, B and C. Locate the centroid of the shaded area as shon in the fig.4 7.(a) Fig.3. Differentiate beteen rectilinear otion and curvilinear otion. 6.(a) Fig.4 Deterine the second oent of an area of a right aled triale ith respect to its base. Page 3 of 3

7 Set No - 3 I B. Tech I Seester Regular Exainations Jan./Feb ENGINEERING MECHANICS (Coon to CE, ME, CSE, PCE, IT, Che E, Aero E, AME, Min E, PE, Metal E) Tie: 3 hours Max. Marks: 70 Question Paper Consists of Part-A and Part-B Anseri the question in Part-A is Copulsory, Three Questions should be ansered fro Part-B ***** PART-A 2. 3.(a) A force vector is represented by a line AB. The coordinates of point A are (2, 4, 3) and of point B is (1,-5, 2) respectively. If the agnide of force is 10N, then deterine the (i) Coponents of the forces alo x, y and z axis (ii) Ales ith the x, y and z axis. (iii) Specify the force vector. [16] A force of P is directed fro a point A (4,1,4) etres toards a point (-3,4,-1) eters. If it causes a oent of Mz = 1900N, deterine the oent of P about x-axes and yaxes. Deterine the ass oent of inertia of a right circular cone shon in the fig.1 belo 1.(i) State the parallelogra la of forces. (ii) What is the principle of transissibility? (iii) What is centroid of a (a) rectale triale ith respect to base (c) triale ith respect to apex. (iv) What is the oent of inertia of triaular laina (b x h) about its horizontal centroidal axis. (v) State the ipulse oen principle. Write its equation. (vi) Derive relation beteen aular velocity and linear velocity. (vii) Differentiate beteen neatics and netics. [ ] PART-B Fig.1 [6+10] Page 1 of 2

8 Set No (a) A toer is 150 height. A particle is dropped fro the top of the toer and at the sae tie another particle is projected upard fro the foot of the toer. Both the particles eet at height of 80. Find the velocity ith hich the second particle is projected upard. Derive ork energy equation. A horizontal bar 10 lo and of negligible eight rests on rough inclined plane as shon in the fig-2. If the ale of friction is 150, ho close to B ay the 200N force be applied before otion ipends? 200 N 100 N 2 6.(a) 7.(a) B Fig-2 A body eighi 40N is projected up a 400 inclined plane ith a velocity of 16/s, coefficient of friction is Find the axiu distance S that the body ill ove up the inclined plane. Define the ters: coplanar parallel forces, like parallel forces and unlike parallel forces. Derive the equations of otion of a body ovi alo a circular path ith unifor aular acceleration [6+10] Deterine the volue generated by rotati the shaded area shon in fig-3 about x-x axis. x A 4.(a) 1 c 1 c 4 c 6 c 6 c Fig-3 Deterine the centroid of the triale (b x h) about the base fro basic principles. [12+4] Page 2 of 2

9 Set No - 4 I B. Tech I Seester Regular Exainations Jan./Feb ENGINEERING MECHANICS (Coon to CE, ME, CSE, PCE, IT, Che E, Aero E, AME, Min E, PE, Metal E) Tie: 3 hours Max. Marks: 70 Question Paper Consists of Part-A and Part-B Anseri the question in Part-A is Copulsory, Three Questions should be ansered fro Part-B ***** PART-A Mention the Coulob s las of friction. What is the converse la of polygon la of forces. State Pappus theores I and II. Differentiate beteen polar oent of inertia and product of inertia. Find the force acti on a body of ass 100 kg and produci an acceleration of 2 /s2 in the direction. (vi) Find the ork done in drai a body eighi 500N through a distance of 5 alo a horizontal surface by force of 300N hose line of action akes an ale of 300 ith the horizontal. [ ] PART-B 2. 1.(i) (ii) (iii) (iv) (v) If the force ultiplier of a force P acti fro A to E is P= 40N/, referri Fig-1. Find out the folloi (i) Coponent of P alo AC (ii) Moent of P about D. E 4 Y 6 D 6 O 8 Z 4 A 3 9 X W B C Fig-1 Page 1 of 3 P [16]

10 Set No (a) Find the centroid of the shaded area shon in fig-2. r.t. x and y axes. y Fig.2 Find the oent of inertia of the area shon in shaded area in fig.3, about edge AB. X 5 c 5c 15c Fig.3 Explain the las of otion for a body in rotational otion. A heel rotati about a fixed axis at 20 rp is uniforly accelerated for 70s duri hich it akes 50 revolutions. Find the aular velocity at the end of this interval and also the tie required for the speed to reach 100rp. A block is lyi over a 100 edge on a horizontal floor and leani against a vertical all and eighi 1500N is to be raised by applyi a horizontal force to the edge. Assui coefficient of friction beteen all the forces in contact to be 0.3, deterine the iniu horizontal force to be applied to raise the block. Derive ork energy equation. Write about the folloi (i) Free body diagra ith exaple (ii) Equations of equilibriu. An autoobile travels 800 in 50s hen it is accelerated at a constant rate of 0.8/s. Deterine the initial and final velocity and also the distance travelled for the first 14s. [6+10] Page 2 of 3 4.(a) 5.(a) 6.(a)

11 Set No (a) Find the oent of inertia of T-section shon in fig: 4.r.t. its centroid x and y axes. 20c 10c 4c Fig: 4 Deterine the centroid of the rectaular section by integration 3c Page 3 of 3