The smooth disks D and E have a weight of 200 lb and 100 lb, respectively. If a horizontal...
The smooth disks D and E have a weight of 200 lb and 100 lb, respectively. If a horizontal force of P = 200 lb is applied to the center of disk E, determine the normal reactions at the points of contact with the ground at A, B, and C.
Step-by-Step Solution
Draw the free body diagram.
Consider 
, 
, and 
to be the reaction forces at 
, 
, and 
respectively.
Calculate the angle 
.
Calculate the horizontal distance between the two circle centers by using Pythagoras theorem.
Consider the force equilibrium equation in the 
direction.
Here, 
is the applied force.
Substitute 
for 
.
Therefore, the normal reaction at 
is 
.
Consider the force equilibrium equation in the 
direction.
Here, 
and 
are the weights of the disks 
and 
respectively.
Substitute 
for 
, 
for 
, and 
for 
.
…… (1)
Consider the moments about point 
.
Substitute 
for 
, 
for 
, 
for 
, and 
for 
.
Therefore, the normal reaction at 
is 
.
for 
in equation (1). 
Therefore, the normal reaction at 
is 
.
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