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pink_ele

a ladder of length L rests against a roller on a frictionless surface.FIND THE COEFFICIENT OF FRICTION FOR MINIMUM ANGLE

which it makes with the ground height of the wall is, h..(hcv prob)

pink_ele

my answer has been delayed sir

shubham_sachdeva

here is the soln.

let the normal force offered by ground be r2 in upward dir. & by roller in prependicular dir. to the roller r1 & frictional force

r2 in right

eqns

r2+r1cos theta=mg-------1

r2 =r1sin theta-------------2

taking moment about a

r1 X x =mgcos theta X l/2 ( where x=lenth of ladder b/w roller & the ground)

r1 X h/ sin theta=mgcos theta X l/2-----------------------3

dividing 2 by 3 we get

r2=sin^ 2 theta X cos theta X mgl/ 2

h

similarily r1=

r2 / sin theta

put values of r1 & r2 in eqn. 2 u will get

= sin^2 theta cos theta l/2h-lsin theta cos^2 theta

that's the required amswer given at the end of hcv

vaisa how was the answer it was long but was a good qn.

cheers!!!!!!!!

Moderator

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~ forum moderator

deepak_agarwal

hello pink-el...

please rewrite the question in the exact form as given.....i am a bit confused since for me it makes two meanings.....friction can be between roller and ladder...ladder and wall and ladder and groud...ground u hav said is frictionless...what abt the other two....sorry for the delay but please mak it clear.

shubham_sachdeva

hi!!!!! deepak qn. was

a uniform rod of length l rests against a smooth roller . find the friction coefficient b/w the ground & the lower end if the minimum angle that the rod can make with horizontal is

.

please tell me whether i m correct or not

CHEERS!!!

deepak_agarwal

thank u very much shubham for rewriting the ques....now its absolutely clear....

draw a rod abtouch roller(circle) at b and ground at a...ab=L...

draw the free body diagram...N1 and N2 be normals at a and b perpendicular to ground and circle respectively....

eqns are as follows..

N1+N2cos(theta)=mg

uN1=N2sin(theta)

N2L=(mgL/2)cos(theta).....

where u is the coeff of friction..

from third get N2 and substitute in 2 to get N1...now put both of them in 1 to get u=sin(theta)cos(theta)/(2-cos^2(theta))....

.

shilps

good answers....it solve mu doubts..

nishantsingh89

solved the same question here, have a look:)

http://www.goiit.com/posts/list/mechanics-hcv-ques-rotational-motion-rates-assured-30626.htm#157645

shubham_sachdeva

nishant see the date of above topic..above is solved in jan...so long before..:))

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