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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

H_Hassan
  • 807

1 Answers1

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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 $$ \sqrt{V^2 + H^2} = \sqrt{(mg/2)^2 + T^2/2} = 955.25N $$

MartinG
  • 978