Find the distance of weight ‘x’ from support:
The two weights C = 2000N and D = 1000N are located on horizontal beam AB as shown in the figure given below. Find the distance of weight 'C' from support 'A' that is, 'X' so that support reaction at A is twice that at point B. (May-00-01)
Sol.: As given that R_{A} = 2R_{B}
_{ }
∑H = 0
R_{A}_{H}_{ }_{= 0 ...(}i_{)}
∑V = 0
R_{A} + R_{B} - 2000 - 1000 = 0
R_{A} + R_{B }= 3000N
But R_{A} = 2R_{B}
That is
R_{B} = 1000N
...(ii)
R_{A }= 2000N
...(iii)
By taking moment about point A:
∑M_{A} = 2000 × x + 1000 × (x + 1) - R_{B} × 4 = 0
2000 × x + 1000 × (x + 1) -1000 × 4 = 0
2000x + 1000x + 1000 - 4000 = 0
3000x = 3000
x = 1m .......ANS