Question

A cylinder of radius r = 1 m and mass m = 5 × 10³ kg is at rest on the edges of a structure as shown. Distance a is 0.5 m and b = √3/2 m. Reaction force on edges A and B are

• A. 24.6 kN, 24.6 Kn
• B. 42.6 kN, 42.6 Kn
• C. 42.6 kN, 24.6 kN
• D. 52.6 kN, 5.6 Kn

Answer 1

Answer: (C)

42.6 kN, 24.6 kN

Answer 2

sin α = $\frac { \mathrm { a } } { \mathrm { r } } = \frac { 0.5 } { 1 } = \frac { 1 } { 2 }$

or α = 30⁰

and sin β = $\frac { \sqrt { 3 } } { 2 } / 1$

or β = 60⁰

Then F₁ = mg cos α

= 5 × 10³ × 9.8 × cos 30

= 42.6 kN

and F₂ = mg cos β

= 5 × 10³ × 9.8 cos 60

= 24.5 kN.