Recitation Worksheet M Solutions

Recitation Worksheet M Solutions - Worksheet M: Rigid body...

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Worksheet M: Rigid body motion (I) 1. Indiana Jones runs for his life escaping from a huge spherical rock of mass M = 5000 kg and radius R = 1.5 m that rolls down an inclined rectilinear cave. The rock started at rest at a height h = 4.0 m above the level of the access to the cave. Assume the rock rolls without slipping and neglect friction. a. Jones cannot run faster than 8 m/s. Will the archeologist be crushed by the rock? Let’s see what is the maximum speed of the rock, at the bottom of the cave. Using conservation of mechanical energy (the only force doing work on the rock is weight, a conservative force): 22 11 mgh mv I ω =+ where v is the speed of the center of mass and I is the moment of inertia of a uniform sphere about an axis through its center of mass, 2 2 5 sph I mR = . If the rock rolls without slipping, v=R ω and thus 2 2 2 2 5 10 10(9.8 m/s )(4.0 m) 7.5 m/s 77 v mgh mv mR R gh v == = Since the rock never moves faster than Jones, our hero can make it safely out of the cave.
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This homework help was uploaded on 03/27/2008 for the course PHYS 221 taught by Professor Herrera-siklody during the Fall '08 term at Iowa State.

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Recitation Worksheet M Solutions - Worksheet M: Rigid body...

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