Agricultural Education — Examination Papers, 1880. cxiii 
EXAMINATION IN MECHANICS AND NATURAL 
PHILOSOPHY. 
Maximum Number of Marks, 200. Pass Number, 100. 
Tlmrsday, Maij 13th, from 10 a.m. till 1 p.m. 
1. Where is the centre of gravity of a circuhir plate, of a square 
plate, and of a triangular plate ; each plate being very thin and of 
uniform density ? 
If the square plate is bent along a diagonal so that the two parts 
are at right angles to each other, where is its centre of gravity now 
situated ? 
2. Define the co-efficicut of friction and the angle of friction. 
A body weighing 100 lbs. is placed on a horizontal table ; a thread 
fastened to it passes horizontally over a small pulley at the edge of 
the table ; it is found that the body will just not slide, when a weight 
of 17-5 lbs. is hung to the end of the thread. What is the co-efficieut 
of friction between the body and the tabic ? If the string were cut 
and the table tilted up, find (by construction or calculation) the 
number of degrees in its angle of inclination to the horizon when the 
body is just on the point of sliding down. 
3. A B is a uniform rod of given weight (100 lbs.) capable of 
turning round a hinge A ; the end B is fastened by a thread to a 
point C vertically over A ; the lengths of the rod and thread are 
such that B C is horizontal, and A B at an angle of 60° to the 
horizon ; find (by construction or calculation) the tension of the 
thread, and the magnitude and direction of the pressure on the hinge. 
4. State (without proof) the relation between the power and the 
weight in a common screw press working without friction. 
The pitch of the screw is 1 in. and the length of the power arm 
21 in., what power would be required to lift a ton weight, if the 
machine worked without friction ? If it were found that in point of 
fact a power of 100 lbs. was required, what part of the power would 
be expended on friction (Ttt = 22) ? 
5. When a body of considerable size is moved, how is the work 
done against gravity calculated? 
A rectani;ular block, whose base is 4 feet square and length 20 feet, 
lies horizontally on one side ; how many foot-pounds of work are 
done against gravity when it is placed upright on its base, one cubic 
foot of the material weighing 150 lbs. ? 
6. State (without proof) a formula for determining the distance 
described in a given time by a body whose velocity undergoes a 
constant acceleration. 
If a body's velocity undergoes a constant acceleration, what infer- 
ence can you draw as to the force which produces the motion ? 
VOL. XXII. — S. S. h 
