Find out the centre of gravity of a right circular cone, Mechanical Engineering

Find out the centre of gravity of a right circular cone:

Find out the centre of gravity of a right circular cone of height H & the base radius a.

Solution

Refer to Figure, where radius of the circle is illustrated as a and semi vertical angle of the cone is α

∴ a = H tan α

377_Find out the centre of gravity of a right circular cone.jpg

Figure

At any level z from apex O, radius of thin slice of volume dV is specified by

x = z tan α.

As dz is very small thickness of the slice,

dV = π x 2  dz

= π z 2  tan 2  α dz

{Moment of dV about O }   = dV × z

By applying the theorem of moments around O, if G is the centre of gravity of cone where, OG =  z¯ ,

2355_Find out the centre of gravity of a right circular cone1.png

= π a2 × ( H/3) ( z¯ ) = π tan 2  α [H4/4]  

= π (tan 2  α H 2 ) ×  H2/4

= π a 2 ×  H2/4

z¯ =  (¾) H from apex O

∴          Location of G from base of Cone =  H/4

Posted Date: 1/29/2013 1:00:17 AM | Location : United States







Related Discussions:- Find out the centre of gravity of a right circular cone, Assignment Help, Ask Question on Find out the centre of gravity of a right circular cone, Get Answer, Expert's Help, Find out the centre of gravity of a right circular cone Discussions

Write discussion on Find out the centre of gravity of a right circular cone
Your posts are moderated
Related Questions
In this assignment you will apply what you have learned in previous training. Consider the part in figure, which constructed from a solid tube. The bracket is supported at surface

Explain the subtractive process of Rapid Prototyping

(Hydrostatic pressure on curved 3-D surfaces) A shark tank in the aquarium has a hemispherical glass viewing "bubble"  jutting into the water from the side wall. The radius of

Newer Approaches To On-Line Scheduling  The on-line scheduling has established to be superior option than off-line scheduling upon the shop floor. The on-line scheduling looks

(a) Write short note on following : (i) Ericsson cycle (ii) Diesel cycle (iii) Stirling cycle (b) The swept volume of a diesel cycle engine working on dual cycle is 0.0

Describe productivity. How do we calculate the productivity? Enumerate various factors effecting the productivity. Define various ways for the improvement of productivity.

Ductile mid brittle material: A material that can undergo large permanent deformation in tension, that is, it can be drawn into wires is called as ductile. A material which

Dry Saturated Steam - thermodynamics: A dry saturated steam is single phase medium. It does not have any water particle. It can be obtained on complete evaporation of water at

Q. Describe the term ‘Critical Insulation thickness'. What is its significance? Derive an expression for the critical insulation radius of a spherical system. A bar of square cr

Design Problem:  Design a pipeline and pump station to pump 100 MGD of water to the Mississippi river.  To reduce the required horsepower of the pumps, the flow will be pressurized