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.

#### Solution

Given : W_{1} = 100 N

W_{2} = 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

N_{2}sin45 - Rsin15 - Psin45 – W = 0

N_{2}sin45 - Psin45 = 122.4745 x 0.2588 + 50

N_{2}sin45 - Psin45 = 81.6987 ………..(1)

Applying conditions of equilibrium**ΣFx = 0**-N

_{2}cos45+Rcos15-Pcos45=0

N

_{2}cos45+Pcos 45=118.3013 ……(2)

Solving (1) and (2)

P=25.8819 N

**Magnitude of force P required = 25.8819 N**