JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech I ENGINEERING MECHANICS Previous Question Paper (June - 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
State and explain the triangle law of forces and polygon law of forces.
Answer
Triangle Law of Forces: If two forces acting at a point are represented in magnitude and direction by the two sides of a triangle taken in order, their resultant is represented in magnitude and direction by the third side of the triangle taken in the opposite order.
Polygon Law of Forces: This is an extension of the triangle law. If a number of forces acting at a point are represented in magnitude and direction by the sides of a polygon taken in order, their resultant is represented in magnitude and direction by the closing side of the polygon taken in the opposite order.
Three forces acting on a rigid body, are represented in magnitude, direction and line of action by the three sides of a triangle taken in order. Prove that the forces are equivalent to a couple whose moment is equal to twice the area of the triangle.
Answer
Let the three forces P, Q, and R act along the sides AB, BC, and CA of a triangle ABC, taken in order. Let the magnitudes of these forces be proportional to the lengths of the sides, such that P/AB = Q/BC = R/CA = k, where k is a constant.
To find the resultant, we can replace each force with an equivalent system. Consider the moment of these forces about any point O in the plane of the triangle. The sum of the moments of the forces about O is:
where h1, h2, and h3 are the perpendicular distances from O to the sides AB, BC, and CA respectively. Since the forces are proportional to the sides, we can write P = k(AB), Q = k(BC), and R = k(CA).
Substituting these into the moment equation:
The expression (AB × h1 + BC × h2 + CA × h3) represents twice the area of the triangle ABC (2 × Area). Thus, the sum of the moments is M = k(2 × Area). Since the resultant of the three forces forming a closed triangle is zero (the forces are in equilibrium if they act at a point), but here they act along the sides of a triangle, they form a couple. The moment of this couple is constant regardless of the point about which the moment is taken, and it is equal to twice the area of the triangle multiplied by the constant of proportionality k.
How will you distinguish between static friction and dynamic friction?
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Determine the centroid of the area remaining after a circle of diameter r is removed from a circle of diameter D.
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State and explain the theorem of parallel axis for the moment of inertia of a plane lamina.
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Calculate the moment of inertia about horizontal and vertical gravity axis of the section of the given figure.
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Determine the moment of inertia of a circle about its diametral axis from the first principles.
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Describe the method of finding out the moment of inertia of a composite section.
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Derive the differential equation of curvilinear motion.
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What is the work done by the weight of a body if it is moved horizontally?
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State the principle of conservation of energy? What is the fundamental interpretation of kinetic energy.
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A car is travelling east at a constant speed 7 m/s, at the same time another car starts from rest towards north with a constant acceleration of 2 m/s2. Determine the position, velocity and acceleration of second car relative to the first car after 5 seconds.
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State and explain D’Alembert’s principle and its application in plane motion.
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The speed of the flywheel increases from 300 to 600 rev/min in 10 seconds. If the diameter of the wheel is 2m, Determine the angular acceleration and number of revolutions made during this period of 10 seconds. Find the normal and tangential acceleration at the rim of the wheel at the end of 10 seconds.
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Explain the instantaneous centre of rotation of a plane motion.
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State and discuss the principle of work and energy.
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