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Unformatted text preview: PHYS2014 Fall 2010 Benton OSU Physics Dept. 81 Physics 2014: General Physics I Solutions to Homework Assignment 8 1. A solid stone grinding wheel of radius r = 20 cm and mass m = 25 kg is spinning at a frequency of 150 RPM. To sharpen a knife, you push the edge of the knife against the rim of the wheel with a constant force of 30 N at an angle of 60 with respect to the radius of the wheel. How long does it take for the wheel to stop spinning? Solution: If we find the torque on the wheel produced by pushing the knife blade against the wheels edge, we can find its angular acceleration. Then, based on the angular acceleration, we can use a kinematic equation to figure out how long the wheel will take to slow from an angular velocity equivalent to a frequency of 150 RPM down to zero. 2 sin sin 1 2 rF I rF I I Mr = = = = 2 2 sin 2 30N sin 60 rad 10.4 s 25kg 0.20m f F Mr = = = r ( ) 2 2 2 2 rev rad 1min 2 2 150 15.7 min 60s s rad 15.7 s 0.75s rad 2 10.4 s i i i i t t t f t = + = = = = = = = PHYS2014 Fall 2010 Benton OSU Physics Dept. 82 2. The effect of weightlessness on the human body (mostly in the form of bone and muscle loss) is considered one of the biggest obstacles to long term human habitation of space. One solution, first proposed nearly 100 years ago, is to design a space station in the form of a wheel and to spin that wheel at a frequency such that the centripetal acceleration at the rim of the wheel is equal to at least a significant fraction of the acceleration due to gravity at the Earths surface. Thus, spinning the space station on its axis effectively creates what is called artificial gravity. One design for a wheeltype space station is depicted above. It consists of an outer wheel that is 80 m in diameter and has a width of 3 m, an inner hub of 6 m diameter, and four thin pylons connecting the hub to the ring as depicted above. The outer wheel has a mass of 210,000 kg, the inner hub has a mass of 60,000 kg, and each pylon has a mass of 10,000 kg. If we approximate the outer wheel as a torus, the hub as a solid disk, and each pylon as a thin rod, what would be a) the moment of inertia, b) the angular momentum, and c) the centripetal acceleration of the space station if it was spinning at a frequency of 3.3 RPM? Solution: a) If we can think of the space station as being made up of discrete parts, each with its own moment of inertia, the total moment of inertia for the space station will be the sum of the moments of inertia of each of this discrete parts: 2 T n n n I I m r = = The wheel of the space station is a torus having an outer radius of 40 m, an inner radius of 37 m, and a mass of 210,000 kg. The moment of inertia of the wheel is then: ( ) ( ) ( ) 2 2 1 1 2 2 2 2 8 2 1 7 6 3 4 1 210,000kg 7 40.0m 6 40.0m 37.0m 3 37.0m 4 3.37 10 kg m t t t I M r rr r I I = + = + = N A S A N A S A N A S A N A S A PHYS2014...
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