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 give a certain amount of the beverage, and then placed on exercise wheels to observe their energy levels. D 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 hamsters wheels, and the speed of each hamster, from highest to lowest. Name Wheel Diameter(cm) Technician's Notes Archimidies 23.0 2 rotations in 1 s Bohr 16.0 7 rotations in 6 s Compton 13.0 25 rotations in 4 s Dirac 11.0 8 rotations in 3s Longest Speed Faster Shortest Slowest Archimedes Dirac Compton Bohr Archimedes Dirac Bohr Compton

Explanation / Answer

Archimedes...

Period = 2

Speed, d = vt

2pi(.115) = v(2)

v = .361 m/s

For Bohr

T = 7/6 = 1.16 s

Speed

2pi(.08) = 1.16v

v = .431 m/s

For Compton

T = 25/4 = 6.25 sec

Speed

2pi(.065) = 6.25v

v = .0653 m/s

For Dirac

T = 8/3 = 2.67 sec

Speed

2pi(.055) = 2.67v

v = .130 m/s

Thus, in order, Period...

Compton = Longest = 6.25 s

Dirac = 2.67 s

Archimedes = 2 s

Bohr = 1.16 s

Speed in order...

Bohr = .431 m/s

Archimedes = .361 m/s

Dirac = .130 m/s

Compton = .0653 m/s

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