Work done by a spring
Work done by pumping a
liquid
Work done by a
spring
HOOKES LAW
Hookes Law states that within the limits of elasticity the displacement
produced in a body is proportional to the force applied, that is,
F = kx,
where the constant k i
TOPIC
LENGTH OF AN ARC
and
AREA OF SURFACE OF REVOLUTION
LENGTHS OF CURVES
To find the length of the arc of the curve y = f (x) between x =
a and x = b let ds be the length of a small element of arc so
that:
2
ds
dy
2
2
2
ds dx dy thus 1
dx
dx
LENGT
PAPPUS THEOREM
S sd
2
dy
where s arc length 1 dx
dx
d C 2r
distance from the midpoint of the generating
line to the axis of rotation
d is the distance travelled by the curve' s geometric centroid
Thus,
S 2rs
The following table summarizes the surface
TOPIC
APPLICATIONS
CENTROIDS OF SOLIDS OF REVOLUTION
CENTER OF GRAVITY OF A SOLID OF REVOLUTION
The coordinates of the centre of gravity of a solid of
revolution are obtained by taking the moment of an
elementary disc about the coordinate axis and then su
TOPIC
VOLUME OF SOLIDS OF REVOLUTION
OBJECTIVES
At the end of the lesson, the student should be
able to:
define what a solid of revolution is.
find the volume of solid of revolution using disk
method.
find the volume of solid of revolution using the
washe