Answer to Question #101921 in Mechanics | Relativity for jude

Question

A 15m wide horizontal platform is suspended by ropes at each end, each capsule of withstanding tension of 112KN. The uniform concrete platform has mass 1500kg.
a) Calculate the maximum load that can be added to the centre of the platform
b) Calculate the maximum load that can be added to the extreme ends of the platform
c) Explain why these two calculations produce different values
d) Suggest a value for the maximum safe recommended load for the platform and justify

Answer 1

Length of the platform=15m

Maximum tension can be beard by the the string=122KN

Mass of the concrete platform=1500Kg

a) Let the maximum load at the center of the platform=m1=m_1=m1 kg and tension in the rope=T

Upward force=downward force

$T+T=(m+m1)g$

$⇒2T=(1500+m1)\Rightarrow 2T=(1500+m_1)⇒2T=(1500+m1) g$

$⇒2×122000=(1500+m1)g\Rightarrow 2\times 122000=(1500+m_1)g$

$⇒2×122000=(1500+m1)g$

$⇒m1=2×1220009.8−1500\Rightarrow m_1=\dfrac{2\times 122000}{9.8}-1500$

$⇒m1=9.82×122000−1500$

$⇒m1=24897.95−1500=24898−1500=23398kg$

$\Rightarrow m_1=24897.95-1500=24898-1500=23398kg$

b) Now, taking torque about the one end of the platform,

$T×0−1500g×7.5+T×15−m1g×15T\times0-1500g\times 7.5+T\times 15-m_1g\times15T×0−1500g×7.5+T×15−m1g×15$$⇒m1g×15=−1500g×7.5+122000×15$

$\Rightarrow m_1g\times15=-1500g\times 7.5+122000\times 15⇒m1g×15=−1500g×7.5+122000×15$ $⇒m1=122000×15−1500g×7.515×9.8$

$\Rightarrow m_1=\dfrac{122000\times 15-1500g\times 7.5}{15\times9.8}$

$⇒m1=15×9.8122000×15−1500g×7.5$

$m1=12448.97−750=12449−750=11699kg$

c) It is producing different values, because when the platform is loaded at one end, then the torque on the one side of the string large, with respect to other side of the bridge, due to which one side rope load is getting increase to the maximum bearable limit, by which string can withstand, but when we are loading the platform at the middle, then the load on the platform is distributed on the both rope, due to which it's loading efficiency is getting increase.

d) The maximum safe recommended load will be 11699kg because, it can withstand the maximum load in the string and balance the torque.