A lab technician is testing new energy drink formulations on a series of hamster

Question

A lab technician is testing new energy drink formulations on a series of hamsters. The hamsters are given a certain amount of the beverage, and then placed on exercise wheels to observe their energy levels. Due to poor planning, however, each exercise wheel is a different size. The names of the hamsters, the diameter of each of their wheels, and the technician's notes are in the table below. Rank the period of rotation of each hamster's wheels, and the speed of each hamster, from highest to lowest.

Explanation / Answer

Name Wheel Diameter(cm)         Technician's Notes

Archimedes              14.0                              3 rotations in 5 seconds

Bohr       22.0                 8 rotations in 3 seconds

Compton                  15.0                     7 rotations in 5 seconds

Dirac                        19.0               14 rotations in 5 seconds

Period:

T_Archimedes = 1.667 s

T_Bohr = 0.375 s

T_Compton = 0.7143 s

T_Dirac = 5/14 = 0.3571 s

Archimedes > Compton > Bohr > Dirac

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Speed:

v = 2r/T

v_Archimedes = 2*3.14*0.14/1.667 = 0.527 m/s

v_Bohr = 2*3.14*0.22/0.375 = 3.68 m/s

v_Compton = 2*3.14*0.15/0.7143 = 1.32 m/s

v_Dirac = 5/14 = 2*3.14*0.19/0.3571 = 3.34 m/s

Bohr > Dirac > Compton > Archimedes

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