Question Number 185947 by aurpeyz last updated on 30/Jan/23
Answered by mr W last updated on 30/Jan/23
$${assume}\:{w}\:{is}\:\downarrow. \\ $$$${W}={w}×\mathrm{5}=\mathrm{2}.\mathrm{5}×\mathrm{5}=\mathrm{12}.\mathrm{5}\:{N} \\ $$$${HA}=\mathrm{0} \\ $$$$\Sigma{M}_{{B}} =\mathrm{0}: \\ $$$${VA}×\mathrm{10}+\mathrm{7}×\mathrm{9}−\mathrm{12}.\mathrm{5}×\mathrm{5}.\mathrm{5}+\mathrm{8}×\mathrm{2}=\mathrm{0} \\ $$$$\Rightarrow{VA}=−\mathrm{1}.\mathrm{025}\:{N} \\ $$$$\Sigma{M}_{{A}} =\mathrm{0}: \\ $$$${VB}×\mathrm{10}+\mathrm{7}×\mathrm{1}−\mathrm{12}.\mathrm{5}×\mathrm{4}.\mathrm{5}+\mathrm{8}×\mathrm{8} \\ $$$$\Rightarrow{VB}=−\mathrm{1}.\mathrm{475}\:{N} \\ $$$${controll}: \\ $$$${VA}+{VB}=−\mathrm{1}.\mathrm{025}−\mathrm{1}.\mathrm{475}=−\mathrm{2}.\mathrm{5}\:{N} \\ $$$$\mathrm{7}−\mathrm{12}.\mathrm{5}+\mathrm{8}=\mathrm{2}.\mathrm{5}\:{N}\:\checkmark \\ $$