A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle 0, as shown in the figure. How should e be chosen (in radians) so that the gutter will carry the maximum amount of water? E 10 cm → 10 cm → 10 cm e = 0.5235 X radians Need Help? Read It
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- B1Please help meA solid sphere, made of acrylic plastic with a density of 1.1 g/cm3,1.1 g/cm3, has a radius of 5.0 cm.5.0 cm. A very small "eyelet" is screwed into the surface of the sphere and a horizontal support rod is passed through the eyelet, allowing the sphere to pivot around this fixed axis, as shown in the figure. If the sphere is displaced slightly from equilibrium on the surface of Earth, determine the period ?T of its harmonic motion when it is released.
- To get up on the roof, a person with a mass m = 71 kg leans an aluminum ladder (mass 10.5 kg and length 6.0 m) against the house on a concrete pad with the base of the ladder 2.00 m from the house. The ladder just overhangs a plastic rain gutter, which we can assume to be frictionless, so the force from the gutter on the ladder acts perpendicularly to the ladder. As a result, the top of the ladder experiences a normal force at an angle, while the bottom of the ladder experiences both a vertical normal force and a horizontal friction force. The center of mass of the ladder is 2 m from the bottom. The person is standing 3 m from the bottom. a.) What is the magnitude of the net force on the ladder at the top? Give your answer in newtons b.) What is the magnitude of the net force on the ladder at the bottom? Give your answer in newtonsA ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass md = 2.7 kg and radius R = 0.25 m. The rods each have mass m, = 1.2 kg and length L = 0.86 m.In the figure, a lead brick rests horizontally on cylinders A and B. The areas of the top faces of the cylinders are related by Aa= 2.4 Ag: the Young's moduli of the cylinders are related by EA 1.6 Ea. The cylinders had identical lengths before the brick was placed on them. What fraction of the brick's mass is supported (a) by cylinder A and (b) by cylinder B? The horizontal distances between the center of mass of the brick and the centerlines of the cylinders are d,for cylinder A and dg for cylinder B. (c) What is the ratio d,/dg? com of brick