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Rank the three disks in the order in whichthey finish the race. Rank from larges

ID: 1722127 • Letter: R

Question

Rank the three disks in the order in whichthey finish the race. Rank from largest to smallest timefor the race. To rank items as equivalent, overlap them. Rank the three disks in the order in whichthey finish the race. Rank from largest to smallest timefor the race. To rank items as equivalent, overlap them. A three disks are released at the same time at the top of aninclined plane. Let disk 1 have a mass {M} and a radius R,disk 2 have a mass {M} and a radius 2R,and disk 3 have a mass 2{M} and a radius R. Rank the three disks in the order in whichthey finish the race. Rank from largest to smallest timefor the race. To rank items as equivalent, overlap them.

Explanation / Answer

Assuming that all three disks are uniform, they will all havethe same linear speed all the way down and will finish the race atthe same time. This can be seen by: .     initial potential energy = final kinetic energy of translation + kinetic energy ofrotation .               m g h          = (1/2) m v2    + (1/2) I2 .              m gh           = (1/2) m v2    + (1/2) [ (1/2)m r2 ] (v/r)2 .             m g h          =   (1/2) m v2     + (1/4) m v2 .             g h =      (3/4) v2 .           v = (4/3)gh             notice that the final speed does not depend on the mass or radiusof the disk, so they all have the same final speed. .           v = (4/3)gh             notice that the final speed does not depend on the mass or radiusof the disk, so they all have the same final speed.