Physics
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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.
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 side of the warehouse. Given only compression and assuming a safety factor of 8, determine the number of columns required on each side of the warehouse and the spacing between each column. The compression strength for steel is 2.5×108 N/m2.