Is there an alternative to solving the equation for a bead on a hoop with friction?

in a physics laboratory a block x is balanced by a block Y of mass 200 kg,each are suspended from a balance of equal lever arms .the scale pan on X is at a height.H1=2 cm ,where as scale pan on Y is at height 1 cm above the floor.the error in weighing is (in gram)

consider the figure of a single riveted lap joint as follows

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cyclic heat engine operates between. temperature of 30 C. What is the least rate of heat rejection per kW net output of an engine. source temperature of 800 C and sink

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