(ii) Show by integration that the centroid of a uniform semi-circular lamina of radius a from the center is 4a 3m

International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter7: Dry Friction
Section: Chapter Questions
Problem 7.49P
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(i) A uniform ladder of weight W and length 2a rests in limiting equilibrium with one end on a rough
horizontal ground and the other end on a rough vertical wall. The coefficients of friction between
the ladder and theground and between the ladder and the wall are U and A respectively.
if the ladder makes an angle O with the ground, where tan 0 =
(a) show that 5p + 64g-6-0,
(b) find the values of u and i, given that iu = %
(ii) Show by integration that the centroid of a uniform semi-circular lamina of radius a from
the center is
4a
3m
Transcribed Image Text:(i) A uniform ladder of weight W and length 2a rests in limiting equilibrium with one end on a rough horizontal ground and the other end on a rough vertical wall. The coefficients of friction between the ladder and theground and between the ladder and the wall are U and A respectively. if the ladder makes an angle O with the ground, where tan 0 = (a) show that 5p + 64g-6-0, (b) find the values of u and i, given that iu = % (ii) Show by integration that the centroid of a uniform semi-circular lamina of radius a from the center is 4a 3m
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