vivek asked 1 year ago
Three cylinders weighting 100 N each and of 80 mm diameter are placed in a channel of 180 mm width as shown in Fig. below. Determine the pressure exerted by (i) the cylinder A on B at the point of contact (ii) the cylinder B on the base and (iii) the cylinder B on the wall.
Sazid Ahmad answered 1 year ago
Given,
weight of each cylinder=100N
Diameter of each cylinder=80mm
(i) Pressure exerted by cylinder A on B:
PQ=180-2r = 180-80=100
PS = 100/2= 50 mm
sin θ = PS/PR = 50/80
sinθ=0.625
θ=38.7
From lami’s theorem,
R1/sin(180-θ)=100/sin 2θ=R2/sin(180-θ)
R1sin/(180-38.7)=100/sin 2(38.7)
R1/0.625=100/0.9759
R1= 64N
Similarly, R2=64N because of same equation
(ii)Pressure exerted by cylinder B on base
Rw: Reaction of B on vertical wall
Rb:Reaction of B on base
From free body diagram,
∑Fy = 0 = -R1cosθ + Rb=0
Rb=64 cos 38.7
Rb=50 N
(iii) Pressure exerted by B on wall :
∑Fx = 0
=-R1sinθ + Rw=0
Rw=64 sin 38.7
Rw=40N
S gill answered 1 year ago
Consider pressure at the point of contact between cylinder A, B, and C is
.
Draw the free-body diagram of cylinder B showing the external forces.
Calculate the angle between the forces.
Here, point A, B, and C represents cylinder centers.
Substitute the value 
for
and 
for
.
Calculate the contact pressure 
acting on the cylinder B.
Substitute, 
for 
and 
for W in the equation (1).
Hence, pressure exerted by cylinders
and
at the point of contact is 