Question

Two cylinders 1 and 2 are connected by a rigid bar of negligible weight hinged to each cylinder and left to rest in equilibrium in the position shown under the application of force P applied at the center of cylinder 2.
Determine the magnitude of force P.If the weights of the cylinders 1 and 2 are 100N and 50 N respectively.

Answer 1

Given : W₁ = 100 N
W₂ = 50 N
Cylinders are connected by a rigid bar
To find : Magnitude of force P
Solution :
Consider cylinder I

Applying Lami’s theorem :

`R/(sin(90+30))=W/sin(60+75)=N_1/sin(90+15)`
R=`(100)/(sin135)Xsin120`
R = 122.4745 N
Cylinder 2 is under equilibrium

Applying conditions of equilibrium
ΣFy = 0
N₂sin45 - Rsin15 - Psin45 – W = 0
N₂sin45 - Psin45 = 122.4745 x 0.2588 + 50
N₂sin45 - Psin45 = 81.6987 ………..(1)
Applying conditions of equilibrium
ΣFx = 0
-N₂cos45+Rcos15-Pcos45=0
N₂cos45+Pcos 45=118.3013 ……(2)
Solving (1) and (2)
P=25.8819 N
Magnitude of force P required = 25.8819 N