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Home / Doubts and Solutions/ICSE/Class 11 Science/Physics

Draw a free body diagram of a ladder inclined to a wall.Obtain the condition for the ladder to be in equilibrium.

How can you show that Newton's third law of motion follows from the second law?

 

Asked by vijaygireesh 31st August 2019, 8:01 PM
Answered by Expert
Answer:
Figure shows the free body diagram of a ladder of length l  inclined to a smooth wall.
 
Forces acting on the ladder are
(1) weight W acting on centre of mass C of ladder, 
(2) Normal force NW acting at the contact point B of wall
(3) Normal force Ng acting at the contact point A with ground
(4) friction force f = μ Ng acting at A that opposes the motion of the ladder on the wall,
       μ is friction coefficient between ladder and ground
 
For equilibrium
(a) Sum of vertical forces is zero :-  W - Ng = 0            or  Ng = W  .....................(1)
(b) Sum of horizontal forces is zero :- NW - μ Ng = 0    or  NW = μ Ng .....................(2)
(c) Sum of clockwise moment = Sum of anticlockwise moment
 
Let us take moment of all forces about the point A. Let θ be the angle made by the ladder with horizontal.
 
Clockwise Moment :-  NW l sinθ
Anticlockwise moment :- W (l/2) cosθ
 
Hence as per equilibrium condition (c),     NW l sinθ = W (l/2) cosθ   ....................(3)
 
From eqn.(1) and (2), we get,  NW = μ W  .....................(4)
 
By substituting for NW from eqn.(4), eqn.(3) is simplified as,  tanθ = 1/(2μ)
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Only one question should be asked in one posting.
Hence only first question is answered
Answered by Expert 31st August 2019, 10:49 PM
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