2. Explain what is meant by the "instantaneous or virtual centre of a link," and show that 3. 66 KD being the connecting rod of an engine in any position, K the crank pin and T the point where the line of the rod cuts a line drawn through the centre of the crank shaft at right angles to the line of stroke. For any train of spur-wheels, whatever wheels it may actually consist of, there may always be supposed substituted, for kinematic or mechanical purposes, one pair of wheels of known radii and centres, these wheels corresponding to the centrodes of the first and last wheels of the train." Explain and discuss this statement, illustrating your remarks by neat sketches. 4. Make diagram sketches of the accompanying mechanisms, find all the virtual centres, and briefly discuss the characteristics of each mechanism. 5. Explain clearly the following terms-Centrode, pair of elements, inversion of a kinematic chain, epicyclic gearing, reverted wheel train, cam, eccentric. APPLIED MECHANICS II. 1. Explain the following terms-Bending Moment, Moment of Resistance, Modulus of a Section, Moment of Inertia, Coefficient of Elasticity, Coefficient of Rigidity, Elastic Limit, Yield Point, Vibrating, Primitive, and Statical Strength, Working Stress, Factor of Safety. 2. Prepare a tabulated statement, giving the following particulars (a) Tensile strength of cast-iron, wrought-iron, structural steel, iron-bark and Oregon pine timber. (b) Shearing strength of rivet steel, Oregon pine and ironbark timber. (c) Compressive strength of cast-iron, iron-bark and Oregon pine timber, concrete and sandstone. (d) Modulus of rupture of cast-iron, structural steel, ironbark and Oregon pine timber. (e) The limit of elasticity, yield point, general, local and total extension of structural steel. 3. Investigate the equations and sketch the diagrams showing the distribution of bending moments and shearing stresses in the following cases:— (a) A beam 20 feet span, loaded with a uniformly distri- (c) A beam 20 feet long supported at one end, and at a point 4. Prove that the intensities of shearing stress on two planes at right angles to each other are equal. Investigate the intensity of shearing stress in a beam of rectangular section, and prove the equation— 5. Show how to design a plate web girder of 30 feet span to carry a live load of one ton per foot run, and a dead load of one quarter of a ton per foot run. Illustrate your remarks by sketches, showing cross section of girder, sizes of plates and angles, also the diameter and pitch of the rivets. 6. Write an Essay on the method of determining the saf working stresses on steel structures; or, Write an Essay on the design of timber viaducts. DESCRIPTIVE GEOMETRY. No written description is required, but the various projections should be appropriately lettered.) 1. (Plane Geometry) (a) Given a straight line AB and two points P and Q outside it, find a point C in AB such that CP, CQ make equal angles with AB. (b) Draw a circle to pass through a given point A to touch two given lines CD, CE between which A lies. (e) Show how to construct (i.) an ellipse, (ii.) a parabola, assuming any data you desire. (d) Draw the hypocycloid when the director or fixed circle is 3 inches in diameter and the generator or rolling circle is 4 inches in diameter. 2. (a) Given the plans and elevations of two lines AB and AC, find the corresponding projections of the line AD which bisects the angle BAC. (b) Given the traces of two intersecting planes, find the angle between them. 3. Assume a series of 5-foot contours to represent the surface of a hill whose summit is, say, 50 feet above the surrounding level plain, and obtain the plan and true shape of the section of the hill made by (a) any vertical plane passing through the summit, and (b) a plane inclined at 60° to the horizontal and also passing through the summit. 4. Draw the plan of a pyramid with a square base, lying on one of its sides, and obtain an elevation on each of three vertical planes which are mutually inclined at angles of 60°. 5. A prism (with hexagonal base) stands on the horizontal plane with its axis vertical. Determine the shadow cast by parallel rays, so arranged that the shadow is projected partly on the vertical and partly on the horizontal plane. 6. Draw diagrammatically the elevation of a bicycle showing the outlines (only) of the two wheels and the frame, and obtain its perspective projection when the frame of the bicycle (standing vertically) is inclined to the picture or perspective plane. Assume the necessary data. (Students are advised to draw this perspective projection to a reasonably large scale.) CHEMISTRY, PHYSICS, MATHEMATICS AND PHYSIOGRAPHY. The same papers as those set in the First Year of Science. SECOND YEAR EXAMINATION. APPLIED MECHANICS I. 1. Describe carefully Carnot's Cycle, using steam as the working substance, and contrast it with the so-called Clausius Cycle. In the Carnot Cycle given that the upper and lower limits of pressure are 90 and 20 pounds per square inch respectively, find in foot pounds the amount of work done per pound of steam used. 2. (a) Steam enters at a pressure of 180 lb. per square inch (absolute); is cut-off at one-third stroke, and expands according to the law "p. v. constant." Find the average pressure (absolute) during the forward stroke, neglecting clearance. If the back pressure is 17 lb. (absolute) per square inch, and the area of the piston is 112 square inches and the stroke 24 inches, what is the indicated horse-power for that side of the piston when the engine makes 100 revolutions per minute? (b) Find an expression for the work done during the adiabatic expansion of a gas. 3. Describe an apparatus for drawing an oval valve diagram for a simple slide valve. How would you construct such a diagram for any particular engine? Show clearly the relationship between the oval diagram and the indicator card. 4. "When steam expands adiabatically it becomes wetter unless it is very wet to commence with." Explain what is meant by this statement, and discuss it with the aid of an entropy-temperature diagram. If steam at a pressure of 80 lb. per square inch and quality 90 per cent. expands adiabatically till its pressure is 40 lb. per square inch, what will its quality be? 5. Make neat sketches of any form of boiler with which you are acquainted, showing clearly the various details. 6. An experimental plant consisting of a compound engine and boiler is fitted with a surface condenser, and a complete test of the performance of the plant is required. Make a list of the apparatus and instruments required, indicating their position and general arrangement by means of a diagrammatic plan of the plant. Draw up tabular forms showing the quantities to be observed by each assistant, and also those quantities to be deduced from the observations. (NOTE.—Nothing in the nature of an essay on engine testing is required, but a precise statement of the kind indicated in the question.) APPLIED MECHANICS II. Students in Mechanical and Electrical Engineering are required to take Sections A and B; Students in Civil or Mining Engineering are required to take Sections A and C. A. 1. (a) A cable 700 feet long (and weighing 15 lb. per foot) hangs vertically down a shaft having a metal ball (weight 250 lb.) attached to its lower end. If 450 feet of the cable are wound in in 4 minutes (thus leaving 250 feet still hanging in the shaft) at what rate in HorsePower is the work done? (b) A train weighing 100 tons is driven up an incline of of inertia. |