142 ROYAL SOCIETY OF CANADA 
MECHANICS. 
[Time, 7 hours ; 7 a.m.-2 p.m.] 
A kite of weight ? is subject to normal action by the wind, repre- 
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1 oO 
sented by a force —— P. In its position of equilibrium it is inclined 
= 
at an angle of 30° to the horizon; it has an axis of symmetry on which 
is its centre of gravity G and the centre O of the push of the wind; O 
is above Gand OG equals 4 centimetres. 
Ata point A of the axis, below G, 40 centimetres, is attached a 
string of length 7; two other strings of length / are attached in two 
points B and C symmetrical with respect to the axis, the line BC, equal 
to 24 is 29 centimetres above G. In the position of equilibrium these 
three strings, flexible, inextensible and without mass are tight and 
united in a point #7 at which is attached the string which holds the kite. 
1°. Find the relation which connects /, /’ and 4; supposing these 
lengths known calculate the tensions of the three strings. 
2°. The point 47 being 30 metres above the earth's surface, what 
is the tension of the other extremity Æ of the string supposed fixed on 
the earth, flexible, inextensible and of weight ~ per unit of length; 
determine p such that the tangent at Æ is horizontal (action of wind on 
the string is to be neglected). 
3°. Under these conditions, suppose that the string, lengthened 
from &, unroll with friction of coefficient f along a helix traced on a 
fixed cylinder of revolution, of which the axis is perpendicular to the 
plane of the string, the radius of the cylinder being 7 and the pitch of 
the helix 2; what will be the necessary force to maintain equilibrium, 
this force being applied at the new free extremity of the string supposed 
unrolled for a complete spiral? (The weight of the part unrolled is to 
be neglected). 
4°. The string holding the kite having the form found above (2°) 
and being supposed indeformable, place at the extremity situated on 
the earth a runner [pos/llon] subject to a force, the resultant of the 
weight of the runner and of the action of the wind; this force is constant 
and is in the plane of the string; what condition must be fulfilled that 
the runner move, supposing that there is a coefficient of friction 1 ? 
Study the movement of the runner in the case where the force is 
horizontal. (It is supposed that the runner is a material point moving 
with coefficient of friction 1 on the material curve represented by the 
string which is supposed indeformable. 
6 July. 
