Q 7.22 As shown in Fig.7.40, the two sides of a step ladder and
are
long and
hinged at A. A rope ,
is tied half way up. A weight
is suspended from
a point ,
from
along the ladder
. Assuming the floor to be frictionless
and neglecting the weight of the ladder, find the tension in the rope and forces
exerted by the floor on the ladder. .
(Hint: Consider the equilibrium of each side of the ladder separately.)
The FBD of the figure is shown below :
Consider triangle ADH,
(AD and DH can be found using geometrical analysis.)
Now we will use the equilibrium conditions :
(i) For translational equilibrium :
......................................(i)
(ii) For rotational equilibrium :
or
or ............................................................(ii)
Using (i) and (ii) we get :
and
Now calculate moment about point A :
Solve the equation :