TrojanPoem
  • TrojanPoem
Statics: A metal homogeneous opaque ball with radius r was fastened from a point on its surface with a robe and the other end was fastened on point (A) on a rough vertical wall, the ball stationed in balance and It was about to slip down the wall at point (B). If AB = sqrt(3) r and the friction coefficient between the ball and wall is 1/sqrt(3).Prove that the tan of the angle which the robe makes with the wall is sqrt(3)/2 notice that the the action line of the ball weight affects on it's center.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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dan815
  • dan815
what is the form for rotational intertia
dan815
  • dan815
you should have just drawn it :P
TrojanPoem
  • TrojanPoem
I though you'd prefer to draw it yourself :D

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More answers

TrojanPoem
  • TrojanPoem
|dw:1435161429650:dw|
TrojanPoem
  • TrojanPoem
I can't add the lengths or the drawing will be nasty.
dan815
  • dan815
woah okay, this is confusing drawing
dan815
  • dan815
where is the horizontal wall?
TrojanPoem
  • TrojanPoem
Notice that : Fg = weight of the ball Fb = force of pulling in the robe m = friction coefficient r = reaction of the wall
TrojanPoem
  • TrojanPoem
typo not horizontal but vertical.
dan815
  • dan815
okay lemme try drawing it and see if i got this right
dan815
  • dan815
|dw:1435161896312:dw|
dan815
  • dan815
okay so our normal force is Fb* sin theta
dan815
  • dan815
did you say the resistance force are both from the frictional + moment of intertia
TrojanPoem
  • TrojanPoem
When the ball tries to slip , friction force will be generated = reaction of the wall x friction coefficient it's similar to this : |dw:1435162343747:dw|
dan815
  • dan815
yes u also have to account for the resistive interial force, trying to remmber how to apply that again
dan815
  • dan815
both of these will aid in lowering FB
dan815
  • dan815
|dw:1435162483641:dw|
dan815
  • dan815
do u know it?
TrojanPoem
  • TrojanPoem
You are getting it slowly.
dan815
  • dan815
just need the basic concept here like how do u find the resistive inertial force for a simpler question
TrojanPoem
  • TrojanPoem
|dw:1435162643921:dw|
TrojanPoem
  • TrojanPoem
mr + FBCosH = Fg , FBSinH = r
TrojanPoem
  • TrojanPoem
The moment at any point = 0
dan815
  • dan815
okk thats what i want, are u sure its just mr?
dan815
  • dan815
u have to add frictional force too there dont u
TrojanPoem
  • TrojanPoem
m = friction coefficient , r = reaction. Just those
TrojanPoem
  • TrojanPoem
maximum friction force = mr . So as to ease things I add mr directly.
dan815
  • dan815
reaction force is sintehta Fb
TrojanPoem
  • TrojanPoem
FBSinH = r
dan815
  • dan815
we need this part too though|dw:1435162931881:dw|
dan815
  • dan815
|dw:1435162940154:dw|
dan815
  • dan815
im trying to remember, please clear the concept for me
TrojanPoem
  • TrojanPoem
Intertial force , Maybe up my grade level. Just ignore it.
dan815
  • dan815
what does moment of interia give us exactly??
dan815
  • dan815
isnt it a torque about that point
dan815
  • dan815
maybe we can just completely ignored it?? there will be no rotation?
TrojanPoem
  • TrojanPoem
Bro, if there is inertial force. The problem 'd mention it.
dan815
  • dan815
oh okayy alright then lets work now lol
dan815
  • dan815
|dw:1435163176004:dw|
dan815
  • dan815
|dw:1435163282223:dw|
dan815
  • dan815
gotta write an expression for the horizontal distance from point C first as a function of the radius of the circle
TrojanPoem
  • TrojanPoem
No need , just get the torque around (A).
dan815
  • dan815
oh i know, umm since its root3 r, we can figure out this angle
dan815
  • dan815
|dw:1435163481985:dw|
TrojanPoem
  • TrojanPoem
Did you notice that AC is unknown too ?
dan815
  • dan815
yeah
dan815
  • dan815
true, ugh just feels like root3 r is giving enough restrictions
TrojanPoem
  • TrojanPoem
Listen to me , Torque around (A) !
dan815
  • dan815
okayy howw
TrojanPoem
  • TrojanPoem
Fb, mr will be omitted
dan815
  • dan815
i dont really see how there can be any torque about A , should the tourque be about B
TrojanPoem
  • TrojanPoem
R * r sqrt(3) = FG * r so FG = sqrt(3)R R = FG/sqrt(3)
TrojanPoem
  • TrojanPoem
Solved.
dan815
  • dan815
nice, i still dont see how u did it
TrojanPoem
  • TrojanPoem
Get torque around (A), sum of forces up = 0 , sum of forces down = 0 , You get 4 equations with 4 unknowns solve and you will get tan ( I am using paper for ease :D)

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