Discussion_9_Rewrite

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Physics 1A Discussion Week 9 Due Wednesday 06/01/22 at 11:59pm on Gradescope Problem 1: Dart embedding on a hanging sphere A 20.00 kg lead sphere is hanging from a hook by a thin, massless wire 2.80 m long and is free to swing in a complete circle. Treat the sphere as a point mass. Suddenly it is struck horizontally by a 5.00 kg steel dart that embeds itself in the lead sphere. What must be the minimum initial speed of the dart so that the combination makes a complete circular loop after the collision? hint: think about what must be true about the tension at the top of the circle of motion in order for the mass to just barely swing in a complete circle. Problem 2: Measuring I As an intern at an engineering firm, you are asked to measure the moment of inertia of a large wheel for rotation about an axis perpendicular to the wheel at its center. You measure the diameter of the wheel to be 0.640 m. Then you mount the wheel on frictionless bearings on a horizontal frictionless axle at the center of the wheel. You wrap a light rope around the wheel and hang an 8.20 kg block of wood from the free end of the rope, as in the figure below. You release the system from rest and find that the block descends 12.0 m in 4.00 s. The rope does not slip on the rim of the wheel. What is the moment of inertia of the wheel for this axis? Problem 3 The pulley in the figure below has radius 0.160 m and moment of inertia 0.380 kg m 2 . The rope does not slip on the pulley rim. Use energy methods to calculate the speed of the 4.00 kg block just before it strikes the floor.
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