Archie designs an arch of a certain width and height to serve as an outdoor sculpture in a park. To achieve the size and shape for the strongest possible arch, he suspends a chain from two equally elevated supports as far apart as the arch is wide and allows the chain to hang as low as the arch is high. He then designs the arch to have exactly the inverted shape of the hanging chain. Explain why.

After an unfortunate accident occurred at a local warehouse, you were contracted to determine the cause. A jib crane collapsed and injured a worker. An image of this type of crane is shown in the figure. The horizontal steel beam had a mass of 90.20 kg per meter of length, and the tension in the cable was T = 12820 N. The crane was rated for a maximum load of 500 kg. The acceleration due to gravity is g = 9.810 m/s². 2.250 m, 0.594 m, x = 1.250 m, and h = If d = 5.290 m, s = what was the magnitude of W₁ (the load on the crane) before the collapse? What was the magnitude of force Fp at the attachment point P? h W₁ = Fp = d 0 W₁ L 1 N N

45° Tz T2 T. A cat burglar is planning a daring heist. He will lower himself from a beam as shown in the figure on the left. The burglar weighs 150 lbs. He plans to use a long rope that can withstand a tension of 100 lbs to suspend himself from a shorter rope, reasoning that each segment of the longer rope will only need to support half his weight. (The short rope segment is Kevlar and can easily support the burglar's full weight.) (a) Despite your moral outrage, you decide to set the burglar straight. Compute the tensions T1, T2, and T3 and explain why the plan will not work. (b) As a strictly intellectual exercise, you design an alternative arrangement of ropes that will support the burglar's weight using the same long rope from part (a). In the configuration on the right, what is the maximum angle 0 that will result in a tension of less than 100 lbs in each segment of rope? You may ignore the mass of the rope in parts (a) and (b).

As a hiker in Glacier National Park, you are looking for a way to keep the bears from getting at your supply of food. You find a campground that is near an outcropping of ice from one of the glaciers. Part of the ice outcropping forms a slope of angle ? up to a vertical cliff. You decide that this is an ideal place to hang your food supply, as the cliff is too tall for a bear to reach it. You put all of your food into a burlap sack, tie an unstretchable rope to the sack, and tie another bag full of rocks to the other end of the rope to act as an anchor. The mass of rocks that you put into the anchor bag is equal to the mass of food in the other bag. What will be the acceleration ? of the food bag when you let go of the anchor bag? Assume that the weight of the rope is negligible, and that the ice can be considered frictionless. Express the resulting acceleration ? of the food bag in terms of ? and ?, the acceleration due to gravity. Let the positive direction for this bag be downwards.

A horizontal uniform meter stick supported at the 50-cm mark has a mass of 0.50 kg hanging from it at the 20-cm mark and a 0.30 kg mass hanging from it at the 60-cm mark. Determine the position on the meter stick at which one would hang a third mass of 0.60 kg to keep the meter stick balanced.   Question 14 options:   74 cm   65 cm   62 cm   70 cm   86 cm