Equilibrium with Multiple Supports Practice Problems

A base jumper athlete carrying a parachute stands at the free end of a 4.0 m long homogenous board placed at the top of a skyscraper. The board is fixed on the left end and lies on support, P, at a distance d = 1.5 m from the left-hand end, as shown in the image. If the jumper weighs 650 N (with the parachute) and the board 300 N, determine the force at the support point.

Two cables connect, vertically, each extremity of a uniform horizontal wooden board of 15 kg mass to the ceiling of a living room. The length L of the board is 1 m. The left and right cables can withstand maximum tensions of 200 N and 300 N, respectively. You want to place a flower pot on the board. What is the maximum weight you can place without breaking either cable and where should you place it?

A 35 kg dog begins to cautiously tread on a 6.2 meter long, 58 kg wooden plank that is supported by two support beams. With safety in mind, determine the nearest distance the dog can approach the right end of the wooden plank without causing it to topple over.

A group of amateur engineers wants to find the center of mass of a person using a simple experiment. They set up a 3-meter-long, 6 kg wooden plank horizontally, placing one end on a scale and the other end on a support. A 55 kg participant lays down on the plank, positioning their feet above the support. The engineers read the scale and observe that it measures a mass of 22 kg. Determine the distance from the participant's feet to their center of mass.

Find the tension in the support cable angled at 36.0° and the horizontal and vertical forces that the hinge exerts on the beam at the wall, given that a cafe's outdoor sign weighing 216 N is affixed to the end of a uniform 156-N beam.

A flagpole 2.7 m high is stabilized by two cables. These cables are fixed to the ground 2.1 m away from each other and each 2.1 m from the base of the pole. Each cable experiences a force of 116 N. Assuming the flag attached at the top of the pole is perfectly horizontal, what is the force exerted on the flag due to the tension in the cables?

Determine the tension F_T​ in the support cable and the force F_A​ at pin A for a cantilever truss supporting a 65.0 kN billboard at point E, neglecting the weight of the truss itself.

A warehouse has dimensions of 20 meters by 30 meters and a roof with a total mass of 1.5×10⁴ kg. The roof is to be supported by vertical steel columns, each with a square cross-section of 20 cm by 20 cm. These columns will be evenly distributed along the longer sides of the warehouse. Given only compression and assuming a safety factor of 8, determine the number of columns required on each longer side of the warehouse and the spacing between each column. The compression strength for steel is 2.5×10⁸ N/m².

Two springs, both have a stiffness constant of 230 N/m, and support a horizontal thin aluminum platform uniformly, which has a mass of 0.700 kg. Determine the natural lengths of each spring, considering that the platform is maintained in a perfectly horizontal position.

Hint: Note that while one spring is extended, the other is compressed from its natural length.