JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year ENGINEERING MECHANICS Previous Question Paper (August/September - 2022 - R18)
Answer any five questions
All questions carry equal marks
Main
Explain various types of coplanar and non-coplanar system of forces with neat sketches.
Answer
A system of forces is classified based on whether the lines of action of the forces lie in the same plane or different planes, and whether they intersect at a common point.
Coplanar Force Systems: All force vectors lie within a single plane.
- Coplanar Concurrent: All forces meet at a single point (e.g., forces acting on a particle).
- Coplanar Non-concurrent: Forces lie in the same plane but do not intersect at a single point.
- Coplanar Parallel: All forces are parallel to each other and lie in the same plane; they may be like (same direction) or unlike (opposite direction).
Non-coplanar Force Systems: Force vectors act in three-dimensional space.
- Non-coplanar Concurrent: All forces meet at a common point but act in different planes.
- Non-coplanar Non-concurrent: Forces act in different planes and do not intersect at a common point.
- Non-coplanar Parallel: All forces are parallel to each other but act in different planes.
Determine the magnitude and direction for the system of coplanar non-concurrent forces acting on a beam as shown in the figure 1.
Answer
To find the resultant of a coplanar non-concurrent force system acting on a beam, follow these steps:
- Resolve all forces into their horizontal (ΣFx) and vertical (ΣFy) components using the given angles.
- Calculate the algebraic sum of all horizontal components: ΣFx = F1cosθ1 + F2cosθ2 + ...
- Calculate the algebraic sum of all vertical components: ΣFy = F1sinθ1 + F2sinθ2 + ...
- Determine the magnitude of the resultant force R using the formula: R = √(ΣFx² + ΣFy²)
- Determine the direction (angle θ) of the resultant with respect to the horizontal axis: θ = tan⁻¹(|ΣFy / ΣFx|)
- Calculate the resultant moment (ΣMO) about a chosen point O on the beam to find the line of action of the resultant, using the principle that the moment of the resultant equals the sum of the moments of individual forces.
A 250 kN cylinder is supported by a frame ABC which is hinged to the wall at A as shown in the figure 2. Determine the reactions at the points A, B, C and D. Neglect the weight of the frame.
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Find the centroid of the Z-section shown in figure 3. The thickness at all sections is 20 mm.
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The three blocks with weights as shown in figure 4 are placed on a 20° inclined plane so that they are in contact with each other and at rest. Determine which, if any, of the blocks will move and the friction force acting under each. Assume that under blocks 'A' and 'C', the coefficients of friction are μs=0.50 and μk=0.40 while under B they are μs=0.30 and μk=0.20.
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State and prove the perpendicular axis theorem for area moment of inertia.
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Explain why moment of inertia is always positive while product of inertia can be positive or negative.
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A homogeneous block with a mass density of 7850 kg/m3 with the dimensions as shown in figure 5 has a hole of 30 mm diameter drilled at its centre. Determine its mass moment of inertia about the vertical axis.
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A car covers 100 m in 10 seconds, while accelerating uniformly at a rate of 1 m/s2. Determine (i) initial and final velocities of the car, (ii) distance travelled before coming to this point assuming it started from rest, and (iii) its velocity after the next 10 seconds.
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A balloon is ascending from the ground at a constant acceleration of 0.5 m/s2. After 30 seconds from the start, a ball is released from the balloon. Determine the velocity with which it will strike the ground and the time taken to reach the ground.
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State the work-energy principle.
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In figure 6, a force of 30 N is applied on the lower block of 5 kg mass, over which another block of 3 kg mass rests. Determine the acceleration of the blocks and the tension in the string assuming it to be inextensible. The coefficient of kinetic friction for all contact surfaces is 0.15.
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