Sardar Patel Institute of Technology, AndheriENGINEERING
CURVES1. Points A, B and P lie on a line in order. AB = 60mm, AP =
80mm. A and B are fixed and P starts moving such that AP + BP
remains always constant and when they form an isosceles triangle,
AP = BP = 50mm. Draw the path traced out by point P from the
commencement of its motion back to its initial position.2. The
concrete arch for a water channel of a railway bridge is
semi-elliptical in shape with major axis 2.5 meters and minor axis
1.5 meters. Draw the boundary of concrete arch to suitable scale.
(Use arcs of circle method for one half and directrix-focus method
for the other half.) Determine eccentricity.3. A plot of ground is
in the shape of a parallelogram, 5000m by 1000m. The angle between
the sides is 60 degrees. Inscribe an elliptical flower bed in it.
Select suitable scale. Find major and minor axis.4. Draw the path
of a point moving in a plane in such a way that the ratio of its
distance from fixed straight line to its fixed point is 5:7. The
fixed point is situated at a distance of 20 mm from the vertex.
Name the curve.5. The major axis of an ellipse is 120mm long and
the minor axis is 80mm long. Draw half of the ellipse by rectangle
method and the other half by concentric circles method.6. A motor
car head lamp parabolic reflector has an opening of 175mm and a
depth of 135mm. Draw the shape of the reflector.7. A stone is
thrown from a building 7 meters high and its highest point of
flight just crosses a palm tree 14 meters high. Draw the path of
the stone till it touches the ground if the distance between the
building and the palm tree is 3.5 meters. Take suitable scale.8.
For a perfect gas, the relation between the pressure P and the
volume V is isothermal expansion which is given by PV = constant.
Draw the curve of isotherman expansion of an enclosed volume of gas
if 0.056684m3 of the gas corresponds to a pressure of
0.8515kg/cm2.9. Draw right angled triangle BAC where A is the right
angle. BA = 50mm and AC=60mm. If B is the vertex of the parabola,
BA is the axis, and C is a point on the curve, draw this
parabola.10. Construct a parabola with a base of 100mm and axis
height of 50mm by tangent method.11. A point F is 60mm from line
AB. Draw the locus of a point P moving in the plane of AB and F in
such a way that the ratio of its distance from the line AB and
point F is equal to . Draw the curve and name it. Locate minimum
ten points on the curve.12. Draw a hyperbola passing through point
P if its asymptotes make an angle of 70 degrees with each other.
The point P is 40mm away from one asymptote and 45mm away from the
other. Draw the normal and tangent through point M on the curve,
which is 25mm away from one asymptote.13. An equilateral triangle
PQR of side 60mm inscribed in a circle rolls without slipping along
a straight line at 30 degrees to the horizontal. Trace the path of
vertices P, Q, and R for one complete revolution. Assume initial
position of vertex P is in contact with the horizontal line (ie,
tangent line).14. A circle of 60mm diameter rolls on a horizontal
line for half a revolution and then on a vertical line for another
half revolution without slipping. Draw the curve traced by point P
on the circumference of a circle considering initial position of
point P on the top of the rolling circle.15. Two lines OX and OY
are inclined at 130 degrees to each other. Point P is 30mm from OX
and 40mm from OY. Draw a hyperbola through P.16. A circle of 40mm
diameter rolls along a straight line without slipping. Draw the
curve traced by a point on the circumference for one complete
revolution of the circle. Name the curve. Draw a tangent and normal
to the curve at a point on it, 30mm above the straight line.17.
Draw the curve traced by the end of a straight line AB (120mm long)
when it rolls without slipping on a semicircle (diameter AC =
80mm). Assume line AB to be vertical and tangent to the semicircle
initially.18. Draw a circle with diameter AB = 65mm. Draw line AC
tangent to the circle at A and of length 135mm. Trace the path of
end A of line AC when it rolls on the circle without slipping. Name
the curve. Draw a tangent and normal to the curve at a point 100mm
from the centre of the circle.19. A rod PQ, 99mm long, is resting
horizontally on the circumference of a circular disc of 68mm
diameter at the midpoint. Rod PQ rolls without slipping on the
circumference to the full extent on both sides. Draw loci of P and
Q.20. One end Q of an inelastic string PQ, 150.5mm long, is
attached to the circumference of a half circular, half hexagonal
disc of 49mm diameter. Draw the curve traced out by the other end
of the string P when it is completely wound around the
circumference of the disc, keeping the string always tight. Take
initial position of the string tangent at the midpoint Q of the
circular portion.21. The string PQ is wound around the semicircle
in clockwise direction. Draw locus of Q.
R302013020PQ
22. A pole (shown in figure) is to be wrapped by means of thread
AB by keeping the thread always tight. Draw the locus of point B if
the end A is fixed at the position shown.
ABPSROQ30o150oQS = 25mmOS = OQ = ORAB = 100mmAP = 10mm23. A
circular disc of 62mm diameter rolls along the perimeter of an
equilateral triangle ABC (side 65mm). Draw the locus of point P
lying on the circumference of a circle whose initial position is at
midpoint of AB.
