A horizontal crane arm is mounted on a pivot point on the top of a vertical tower (the mass of the crane arm itself is negligible). A 500kg load is hanging from the right end of the arm, 30m to the right of the tower. Where on the arm must the 24,000kg counterweight be placed in order for the arm to be balanced (static equilibrium)?

Industrial processes often require the damping of vibrations. consider a workbench that uses four large ideal springs in place of traditional legs, with each spring supporting one corner of the workbench and exhibiting a force constant of 47500 n/m. this workbench is used when creating products that involve highly unstable chemicals. according to specifications, the acceleration of the manufacturing equipment must be held to less than 22.3 m/s2 for the manufacturing process to proceed safely. the amplitude of vibrations are expected to remain under 0.622 mm throughout. given that the workbench and maufacturing equipment combine to 6.05 kg, find the maximum acceleration expected of the equipment and workbench. (ignore the mass of the springs.)