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![[Post New]](/templates/default/images/icon_minipost_new.gif) 4 Mar 2008 20:23:39 IST
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A uniform ladder of length 10m and mass 16 Kg is resting against a vertical wall making an angle of 37 degree with it. The vertical wall is frictionles but the ground is rough. An electrician weighing 60 Kg climbs up the ladder. If he stays on the ladder at a point 8m from the lower end, what will be the normal force and the force of friction on the ladder by the ground? What should be the minimum coefficient of friction for the electrician to work safely?
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4 Mar 2008 22:56:50 IST
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hyp = 10 m
vertical abgle is 37 degrees ...which means ht is 8 m length is 6 m
sin(37) = 3/5
The forces acting are:
normal force by the wall (N1) to the left
normal force by the ground(N2) up
frictional force to the right
the wt of the ladder downwards (5 m) down
wt of the man (down)
conserving hori equilibrium
N1=f
conserving vertical equili.
N2=sum of two wts
= 160+600 = 760
net torque ..taking abt lowermost pt
N1*8 = 160*5*6/10 + 600*8*6/10
= 420
so the frictinal force will be 420 N
min coeff of friction is 420/760 = 21/38
pls correct me if wrong
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4 Mar 2008 22:58:09 IST
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since its a very lengthy procedure so i can tell u the method:
figure with all forces:a ladder-its weight acting downwards thru COM,weight of man( downwards),N1(frm vertical wall),N2 from d ground,friction(f)= N2.
since d ladder should be in horizontal n vertical equilibrium,net torque abt any pt. should be zero
mg+Mg=N2..put the values get d answer
put d condition(f=N1) 4 horizontal equilibrium also,u'll get d answer
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5 Mar 2008 07:24:29 IST
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Balancing torque about pt A ( figure below)
16g * 5 sin 37 + 60g * 8 sin 37 = N2* 10 cos 37
470.4 + 2822.4 =8N2
hence N2=411.6 N
Balancing horizontal and vertical forces --
friction =N2=411.6 N --------1
N1=(16+60)g=744.8N ---------2
for friction coefficient to be minimum(yet electrician works safely),
friction = N1
411.6 =  744.8
hence
=0.5526 --------3
1,2,3 give the answers
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5 Mar 2008 07:25:13 IST
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Re:ROTATIONAL MECHANICS
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5 Mar 2008 11:45:42 IST
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What do you mean by conserving torque????
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5 Mar 2008 11:54:53 IST
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sorry mate
it should be balancing
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