JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech I Year ENGINEERING MECHANICS Previous Question Paper (January - 2021 - R18)
Answer any five questions. All questions carry equal marks.
Main
Prove Varignon’s principle of moments.
Answer
Varignon's principle of moments states that the algebraic sum of the moments of a system of coplanar forces about a given point in their plane is equal to the moment of their resultant force about the same point.
Consider two forces F1 and F2 acting at a point A in a plane. Let their resultant be R acting at the same point A. Let O be any point in the plane at a perpendicular distance d from the line of action of the resultant R. Let d1 and d2 be the perpendicular distances from O to the lines of action of F1 and F2 respectively.
The moment of the resultant about O is M = R × d. By the law of parallelogram of forces, the components of R along the x and y axes are Rx = F1x + F2x and Ry = F1y + F2y. The moment of a force about the origin (0,0) is given by the cross product of the position vector r and the force vector F, which is r × F = xFy - yFx.
Summing the moments of the individual forces about the origin:
Rearranging the terms:
Since F1y + F2y = Ry and F1x + F2x = Rx, this becomes:
Thus, the sum of the moments of the individual forces is equal to the moment of the resultant force.
Differentiate between:
- Concurrent and non-concurrent forces
- Coplanar and non-coplanar forces
- Moment of force and couple.
Answer
Differences between force systems and moments:
- Concurrent and non-concurrent forces: Concurrent forces are forces whose lines of action all intersect at a single common point. Non-concurrent forces are forces whose lines of action do not meet at a single point.
- Coplanar and non-coplanar forces: Coplanar forces are forces that lie in the same two-dimensional plane. Non-coplanar (or spatial) forces are forces that act in three-dimensional space and do not lie in a single plane.
- Moment of force and couple: A moment of force is the measure of the tendency of a single force to rotate a body about a specific point or axis. A couple consists of two parallel forces that are equal in magnitude, opposite in direction, and separated by a perpendicular distance; it produces pure rotation without translation, and its moment is independent of the point about which it is calculated.
Three cylinders weighing 100 N each and of 80 mm diameter are placed in a channel of 180 mm width as shown below figure 1. Determine the reactions exerted by a) the cylinder A on B at the point of contact and b) the cylinder B on the base and on the wall.
Answer
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The efficiency of a screw jack will be maximum for raising a load W, if α = -450 - φ/2. Derive an expression for the above condition and prove that the maximum efficiency is given by:
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Define the terms moment of inertia and radius of gyration.
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Prove that the moment of area of any plane figure about a line passing through its centroid is zero.
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Derive an equation for mass moment of inertia of circular plate of radius ‘R’ and thickness ‘t’ about its diameter.
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A car accelerates uniformly from a speed of 30 Km/Hr to a speed of 75 Km/Hr in 5 secs. Determine the acceleration of the car and the distance traveled by the car during 5 secs.
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State the law of conservation of momentum.
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Two blocks of weight 150 N and 50 N are connected by a string and passing over a frictionless pulley as shown in figure 2. Predict the acceleration of blocks A and B and the tension in the string.
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Two weights 800 N and 200 N are connected by a thread and they move along a rough horizontal plane under the action of a force of 400N applied to the 800 N weight as shown in figure 3. The coefficient of friction between the sliding surface of the weights and the plane is 0.3. Using Alembert’s principle, determine the acceleration of the weight and tension in the Thread.
Answer
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