A regular platform $ABCD$ of weight $200N$ is smoothly hinged, along its edge $AB$, to a verical wall, The platform is kept horizontal by two parallel chains inclined at $45^o$ to the horizontal connecting the points $P$ and $Q$ of the wall to the points $D$ and $C$ respectively. $P$ and $Q$ are vertically above $A$ and $B$ respectively. A man of weight $850N$ stands on the edge of the platform midway between $C$ and $D$.
Find:
(a) the tension in each of the chains,
(b) the magnitude of the total force exerted o the hinge by the wall
I've already solved part a by using the moment and setting it equal to zero finding the tension $\approx 672N$
I have no idea how to approach the second question can someone help me out here
Best Answer
Let:
$L$ = width of platform
$T$ = combined tension in both chains
$V$ = upward force on platform at wall
$H$ = outward force on platform at wall
$mg$ = weight of platform (acting at centre of mass) = 200N
$Mg$ = weight of man = 850N
Then:
Balance of vertical forces: $V + T/\sqrt2 = mg + Mg$
Balance of horizontal forces: $H = T/\sqrt2$
Balance of moments about free edge of platform: $VL = mg \frac{L}{2}$
Therefore: $$ V = mg/2 = 100N \\T = \sqrt2 (mg - mg/2 + Mg) = 1343.50N $$ Tension in each chain $$ T/2 = 671.75N $$
Total force exerted by hinge on platform $$ \sqrt{V^2 + H^2} = \sqrt{(mg/2)^2 + T^2/2} = 955.25N $$