Engineering Mechanics (KME-402) - AKTU Question Paper 2022-23

State and prove the following theorems of moment of inertia: (i) Perpendicular axis theorem. (ii) Parallel axis theorem

A gun of mass 3 × 104 kg m/s as shown in below figure recoil; (ii) if the recoil is overcome by an average force of 60 kN, how far will the gun travel and how long will it take

Define pure torsion? List the assumptions made in t orsion theory. Derive the torsion equation. where, T = Maximum twisted torque. R = Radius of shaft. Ip = Polar moment of inertia.
= Shear stress. C = Modulus of rigidity.  = The angle of twist (radians), and  = Length of shaft

A string ABCDE whose extremity A is fixed has weights W at B and C, and passes round a smooth peg at D carr ying a weight of 800 N at the free end E as shown in below figure. If in a state of equili and AB and CD makes angle of 150 calculations for: (i) The tensions in portions AB, BC, CD and DE of the string. (ii) The values of weights W

Two block A and B weighting 50 N and 80 N in below figure. The coefficient of friction betwee n ground and block B is 0.1 and that between block B and block A is 0.28. State whe ther B is stationary with respect to ground and A moves or B is stationary wi th respe determine the minimum value of weight W in the pan so that motion starts. State and prove the following theorems of moment of inertia: Perpendicular axis theorem. Parallel axis theorem. A gun of mass 3 × 104 kg fires projectile of mass 456 kg with a velocity of 305 as shown in below figure . Determine (i) with what initial velocity will the gun if the recoil is overcome by an average force of 60 kN, how far will the gun travel and how long will it take. Define pure torsion? List the assumptions made in t orsion theory. Derive the twisted torque. R = Radius of shaft. = Polar moment of inertia. = Shear stress. C = Modulus of rigidity. = The angle of twist (radians), and

Draw the bending moment and shear force diagram for o verhanging figure below

Analyze the forces in each member of truss shown in figure below. All the members are of 3 m length

Find the moment of inertia about the centroid horizontal axis of the a rea shown shaded in the below figure. The section consists of triangle ABC, semi BC as diameter, and a circular hole of diameter 4 cm with its center on BC

Determine the centroid of the wire part of the following: Draw the bending moment and shear force diagram for overhanging beam shown in the Analyze the forces in each member of truss shown in figure below. All the members are of part of the following: inertia about the centroid horizontal axis of the a rea shown shaded in the below figure. The section consists of triangle ABC, semi BC as diameter, and a circular hole of diameter 4 cm with its center on BC. Determine the centroid of the wire shown in below figure . beam shown in the Analyze the forces in each member of truss shown in figure below. All the members are of inertia about the centroid horizontal axis of the a rea shown shaded in the below figure. The section consists of triangle ABC, semi -circle on BC as diameter, and a circular hole of diameter 4 cm with its center on BC

At a certain instant a body of mass 10 kg falling f reely under the force of gravity, was found to be falling at the rate of 20 m/s. what force will stop the body in i) 2 seconds and ii) 2 meters

Blocks A and B weighing 10 N and 4 N respectively a re connected by a weightless rope passing over a frictionless pulley and are pla ced on smooth inclined planes making 60° and 45° with the horizontal as shown in The tension in the string and from rest

Define pure bending? List the assumptions made in b ending theory. Derive the bending equation. where, M = Moment of resistance. I = Moment of inertia of the section about neutral axis. E = Young’s modulus of elasticity. R = Radius of curvature of neutral axis, and = Bending stress

Illustrate the stress and the relation for strain energy. part of the following: At a certain instant a body of mass 10 kg falling f reely under the force of gravity, was found to be falling at the rate of 20 m/s. what force will stop the body in 2 seconds and Blocks A and B weighing 10 N and 4 N respectively a re connected by a weightless rope passing over a frictionless pulley and are pla ced on smooth inclined planes making 60° and 45° with the horizontal as shown in figure below . Determine: The tension in the string and (ii) Velocity of the system 3 seconds after starting part of the following: Define pure bending? List the assumptions made in b ending theory. Derive the M = Moment of resistance. I = Moment of inertia of the section about neutral axis. E = Young’s modulus of elasticity. R = Radius of curvature of neutral axis, and = Bending stress. Illustrate the stress and strain diagram for ductile and brittle material. Al so derive the relation for strain energy. At a certain instant a body of mass 10 kg falling f reely under the force of gravity, was found to be falling at the rate of 20 m/s. what force will stop the body in Blocks A and B weighing 10 N and 4 N respectively a re connected by a weightless rope passing over a frictionless pulley and are pla ced on smooth inclined planes . Determine: (i) Velocity of the system 3 seconds after starting Define pure bending? List the assumptions made in b ending theory. Derive the strain diagram for ductile and brittle material. Al so derive