1Hey Nishant , Pls can u solve this complete sum ..........
Or can ANYONE ELSE SOLVE THIS SUM ...........???
An ornament for the courtyard at the world's fair is made up of four spheres each being identical and weighing 2√6N. The spheres are arranged such that the three of them forms the base and the fourth one lying on their top touching the other three!The bottom three are kept from separating by spot welds at the point of contact with each other. Allowing for the factor of safety of 3, how much tension should the spot welds withstand! The spheres are assumed to be friction less and the the fourth sphere is lying freely on the other three and is not welded with the other three!
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8 Answers
62dude this is simpler than u might think!!
actually the only thing is that u need to find the angles..
this is a triagular prism.. so u need to find the angle of triangular prism...
after than draw simple fbd... and find the tension the spot weld should withstand and then multiply it by three :)
to find R between the spheres..
3Rcosθ=mg (where cos theta is the angle the line joining the lower sphere's center to the top sphere makes with the vertical axis!
then draw the fbd of the lower sphere.. the unbalanced force in horizontal direction will give u the tension at the weld point.
u need to multiply it by 3
62factor of safety is for the extra safety measure taken...
for example if the maximum force that is applied in a string is 10N then we design the string for say k.10 N (where k is the factor of safety) so that even if it has extra force applied by chance.. it does not lead to an accident...
This is very important in practical world!
162dude.. i will tell u the steps..
1) find the angle the line of a triangular pyramid makes from the vertical
If u can get step 1.. u have solved 50% of the problem!
Tell me this answer.. then we will work together if u cant get to the next step :)
62try coordinate geometry with a little bit of vectors? .. it will be a piece of cake :)
62take the base as (0,0) , (1,0) , (0.5, √3/2)
and the top point as (a,b,c) what will it be? a,b are easy to find.. bcos they lie directly above the centroid of this triangle
also, c will e found using distance formula
62hey newton_reborn try to post ur results here.. so that it comes out as a continuous discussion (rather than in my scrap book :)
right?
ok so now find the vector of the top point to one of the points on the base..
the vertical line's equation is known (in terms of vector) (-k^)
so the dot product will give cosine of this angle.. this is what u had to find.... right?
