Prob0108s

Prob0108s - PHYS1417 Basics Physics Problem set 1 Due Date 5:00 p.m March 9 2009 Answer all questions in this problem set 1 A river with a water

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PHYS1417 Basics Physics Problem set 1 Due Date: 5:00 p.m., March 9, 2009 Answer all questions in this problem set. 1. A river with a water current running at 4 km/hr is 0.25 km wide between parallel banks. A boat whose speed in still water is 6 km/hr wishes to cross. In what direction should it be headed so as to cross the stream 6 km/hr in still water 0.25 km Water current Boat 4 km/hr (a) in the least possible time, (b) to a point directly opposite its starting point? (c) Find the time in each case and the distance moved downstream in case (a). 2. Three uniform thin rods, each of length L , are arranged in an inverted U , as shown in the figure. The two rods on the arms of the inverted U each has mass M ; the third rod has mass 3 M . (a) Where is the center of mass of the system? Give your answer with respect to the reference point at O . O L L M 3M L M L M 3M L L M (b) Find the moment of inertia about an axis passing through the center of the 3 M rod. The moment of inertia of a rod of mass m and length l is 2 1 12 ml when it is rotating about an axis normal to the rod and passing through its center. 1
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3. A man throws a disk of radius R down a table at O as shown in figure (a). The disk slides on the plane with initial speed v 0 and initial angular speed ω 0 , where R 0 >> v 0 . The coefficient of kinetic friction between the disk and the table is µ . The disk slides for a while and then rolls smoothly. The moment of inertia of the disk about its center is given as 2 2 1 MR , where M is the mass of the disk. The gravitational acceleration is labeled as g . v 0 0 O . v 0 0 O . Figure (a) Figure (b) (a) Sketch figure and point out the direction of kinetic friction, which acts on the sliding disk. (b) Describe in a few words the motion of the disk when it is sliding. Is the speed of disk increasing or decreasing? Is the angular speed increasing or decreasing? (c)
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This note was uploaded on 09/06/2010 for the course BSC PHY1417 taught by Professor Prof during the Spring '08 term at HKU.

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Prob0108s - PHYS1417 Basics Physics Problem set 1 Due Date 5:00 p.m March 9 2009 Answer all questions in this problem set 1 A river with a water

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