Equilibrium with Multiple Objects Practice Problems

A crate is placed on a massless plank of 3 m in length and transported by two workers. One worker applies a 300 N vertical force at the left-hand end of the plank and the other one applies a 500 N vertical force at the right-hand end of the plank. Find i) the weight of the crate and ii) the position of the center of gravity.

A uniform pine plank of length 2 m and a mass of 15 kg is held by a carpenter and his son. The carpenter applies a vertical force of magnitude 40 N at the left end. Find i) the magnitude and ii) the point of application of the force that the son should exert to maintain the board stable. Start by drawing a free-body diagram of the plank.

A student glues a 45 g mass at the left extremity of a 1 m bar and a 15 g mass 10 cm from the right extremity. The small masses are considered point masses. The bar mass is 500 g, uniformly distributed along its length. The student is asked to balance the mass-bar combination horizontally on a pivot situated precisely below the combination center of gravity. At what distance from the right extremity must the pivot be placed?

The figure below depicts a hanging structure composed of interconnected massless rods and wires with suspended objects. Calculate the masses of objects R and S if the mass of Q is 0.954 kg.