Calculate pressure on each side of spherical ball , Mechanical Engineering

Calculate pressure on each side of spherical ball :

Heavy spherical ball of weight W rests in V shaped trough whose sides are inclined at the angles and to the horizontal. Find pressure on each side of trough. If second ball of equal weight be placed on side of inclination, so as to rest above the first, find pressure of the lower ball on side of inclination.

Sol.: Let

 

2042_calculate pressure on each side of spherical ball.png

R1  = Reaction of inclined plane AB on                                                       

the sphere or required pressure on AB                           

R2  = Reaction of inclined plane AC on

the sphere or required pressure on AC

The O is in equilibrium under the action of

following three forces: W, R1, R2

Case - 1:

Apply lami's theorem at point O               

R1/sinß = R2/sin(180 -α  ) = W/sin(α   +β   )

or                       R1 = Wsinβ  /sin(α   +β   )           .......ANS                                            

and                     R2 = Wsinα  /sin(α                        + β  )                                             .......ANS        Fig 6.74

Case - 2: Let

R3  = Reaction of inclined plane AC on the bottom sphere or required pressure on AC

As the two spheres are equal, the center line O1O2  is parallel to plane AB.

When the two spheres are considered as single unit, the action and reaction between them at the point of contact cancel each other. Considering equilibrium of the two spheres taken together and resolving the forces along Line O1O2, we get

2064_calculate pressure on each side of spherical ball1.png

R3cos{90° - (α  +β   )} = Wsinα  + Wsinα

R3sin(α + β ) = 2Wsinα

Or, R3 = 2Wsin α /sin(α + β   )    .......ANS

 

 

Posted Date: 10/16/2012 5:58:26 AM | Location : United States







Related Discussions:- Calculate pressure on each side of spherical ball , Assignment Help, Ask Question on Calculate pressure on each side of spherical ball , Get Answer, Expert's Help, Calculate pressure on each side of spherical ball Discussions

Write discussion on Calculate pressure on each side of spherical ball
Your posts are moderated
Related Questions
Objectives After studying this unit, you should be able to describe how a motorcycle works, identify the transmission system and its various part, explain abo

derivation of elongation of bar due to its self weight

Plant layouts shall provide for a maximum of safety and exposure protection from the spread of fire, with ease of operation and maintenance consistent with economical design. Requi

STORAGE AND HANDLING OF ELECTRODES It is recommended that the electrodes should be stored in a warm and dry place. Generally, conditions of storage in the shop are not very condu


The grouping of the words turbine and propeller in techno jargon will give you the word "turboprop". A turboprop engine is a turbojet (gas turbine) engine, which powers the propell

What is the tesisting force

Theore m of perpendicular axis It states that if I X X and I Y Y   be the M.I. of plane section about the two mutually perpendicular axes meeting at a point. Th

Cemented Carbide These are minute pieces along with cutting edges and mechanically jointed or brazed to tool shank. This Carbide tool tips are generated by process of powder m

A 16-bit A/D board is arranged to accept voltage signals ranging from -5V to +5V.  The A/D board is used to monitor the output from the Wheatstone bridge shown below.  The strain g