2. Describe, with full theoretical detail, the methods which have been generally used for finding the ratio of the specific heats of gases. Give an account of the theoretical

considerations which lead to a relation between "y" and the complexity of the molecule.

3. Describe, with full detail, the energy losses which occur in iron when subject to cyclic magnetisations. Explain the methods adopted to minimise these losses.

4. Find an expression for the mechanical force on each unit of area of a charged conductor, and shew how it leads to a practical method of measuring differences of potential.

5. Describe, with full theoretical and practical detail, any electrical experiment which you have carried out.

DEPARTMENT OF ENGINEERING.

FIRST YEAR EXAMINATION.

APPLIED MECHANICS I.

Not more than TWO questions out of each section (A, B and C) are to be attempted.

A.

1. (a) What do you understand by the terms-limit of elasticity, co-efficient of elasticity, modulus of rupture, factor of safety, "fatigue" of metals?

(b) Draw up a sample test sheet suitable for recording the results of tensile tests of steel. Supply such a set of results as you might expect to obtain from a test of a piece of ordinary mild steel.

2. Make a neat diagrammatic sketch of either of the large testing machines in the laboratory, showing carefully the knifeedges, lever system, hydraulic plunger, &c. The scale of the diagram should be such that it will occupy the whole of one side of a sheet of exercise paper.

3. Describe with the aid of neat sketches an apparatus for automatically drawing stress-strain diagrams. Sketch accurately and supply descriptive notes of the characteristic stress-strain diagram for wrought iron, when tested in tension. How would you determine the total work done in breaking a piece of wrought iron?

B.

4. Draw accurately the diagrams of bending moment and of shearing stress for the following cases

(a) A cantilever carrying a uniformly distributed load over its whole length and a concentrated load at the end.

(b) A beam supported at both ends and carrying 4 concentrated loads spaced at irregular intervals along its length.

(c) A beam uniformly loaded over half its length.

(d) A beam loaded with two overhanging weights as in the case of the spindle of the alternating-stress machine.

5. A beam of iron-bark (section 12" x 12") was tested in the large testing machine, on a span of 15 feet, and broke with a load of 36 tons. What load per foot run could you put on a beam of the same material 20 feet long, 14 inches deep, and 12 inches wide, allowing a factor of safety of 5?

6. Make a neat dimensioned sketch of a roof truss suitable for a span of 45 feet. Estimate the probable loads that the truss will have to carry under the particular conditions you assume.

C.

7. A manufacturer sells a rolled iron girder (section,-12" deep, 6" wide, " thick in both web and flanges) as being capable of carrying a distributed load of 14 tons on a clear span of 12 feet. Estimate the factor of safety

he allows?

4

8. A perfectly flexible rope (whose weight may be neglected) hangs from two points of support A and F, and weights W1 W2 W3 W, are suspended from four intermediate points B, C, D and E. Determine graphically the stress in each section of the rope, and show how to check the results algebraically.

9. Show how to design an ordinary plate web girder with an effective span of 40 feet and a depth of 4 feet, having given the live load 2 tons and the dead load a ton per foot

run.

APPLIED MECHANICS II.

Not more than Two questions out of each section (A, B and C) are to be attempted.

A.

1. (a) The section of a stream is 12 square feet, the average velocity of the water is 2 feet per second; there is an

available fall of 25 feet. A turbine placed at the bottom
of the fall drives a dynamo, which sends electric power to
a motor at a distance. The efficiency of the turbine is 70
per cent.; of the dynamo, 87 per cent.; 10 per cent. of
the energy from the dynamo is wasted in transmission,
and the efficiency of the motor is 72 per cent.; how much
power is given out by the motor?

(b) The tup of a steam hammer, weighing 4 tons, is allowed
to fall 7 feet on to a piece of iron, which it compresses.
The duration of the compression is half a second. What
is the average compressive force during that time?
(c) A chain weighing 10 lbs. per foot is 240 feet long, and
hangs vertically. What work is done in winding up the
chain on to a drum ?

2. Discuss thoroughly the essential characteristics of a machine.

B.

3. "If we are given a pair of centrodes for two bodies, we have all the data necessary for the complete determination of their motions, that is, for finding all the possible relative positions which they can occupy

Explain and discuss this statement fully, and give some practical illustrations of it.

4. What is meant by epicyclic gearing, and by a reverted wheel train? Give several examples of these, and show how to find the relative angular velocities of the last wheel and the revolving arm.

5. Make a diagrammatic sketch of the acccompanying mechanism, and draw a curve showing the varying angular velocity of the slotted link for a complete revolution of the crank, which is rotating uniformly.

C.

6. Sketch and describe the construction and working of the mechanism, including the driving pulleys, by which the table of a machine for planing metals is moved backwards and forwards.

If the travel of the table is 9 feet, and it makes 80 double strokes per hour, cutting both ways, find the resistance to motion if there is 5 horse-power actually expended at the tool.

7. Make a careful sketch of the spindle of a drilling machine similar to that in the workshop, showing clearly the feed mechanism.

8. Describe, and illustrate by neat sketches, the different forms of toothed gearing used for transmitting motion from one shaft to another, when the shafts (a) are parallel, (b) intersect, and (e) are in different planes.

DESCRIPTIVE GEOMETRY AND DRAWING.

Not more than Two questions out of each section (A, B and C) are to be attempted.

A.

1. A circular hoop, 4 inches in diameter, makes one revolution at uniform angular velocity about a vertical diameter while a bead slides uniformly down the half circumference of the hoop from its highest to its lowest point. Draw the plan and elevation of the path of the bead.

2. (a) The diameters of the generator and director circles are 2 inches and 6 inches respectively. Draw the epicycloid. (b) A cyclist rides a bicycle (gear 66) along a level road. The length of the crank is 7 inches. Draw the curve traced out by the axis of the pedal in relation to the road.

3. (a) Construct a regular polygon of n sides upon a given

base.

(b) Determine geometrically the values, √5, 8 and 10, taking a line 1 inch long as a unit.

(e) Given two straight lines which approach each other, given also a fixed point; through the point draw a third straight line which would meet the two given ones in their intersection, that intersection being inaccessible.

B.

4. (a) Represent by its traces a plane inclined at angles of 45° and 60° to the horizontal and vertical planes of projection respectively.

(b) Draw the projections of a line 3 inches long, lying in this plane and inclined to the horizontal plane at an angle of 30°.