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Mathinline
body--uriencoded--Fr = \frac%7Bv2%7D%7BgL%7Dfrac%7Bv%5e2%7D%7BgL%7D

where 

Mathinline
bodyv
 = the speed of movement (in m/s)

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(a) Using the simple inverted pendulum model from the previous question, explain why the walk-run transition theoretically occurs at 

Mathinline
bodyFr = 1
. (Note: the model is redrawn below with the linear speed speed 
Mathinline
bodyv
and gravitational acceleration
Mathinline
bodyg
 
shown.)



(b) Dr. Evil (a somewhat normal adult male with a leg length of 0.9m) and Mini-Me (an exact 1/8 replica of Dr. Evil) need to go to the other side of their secret lair in Nevada to feed their sharks and repair some laser beams. Dr. Evil demands that Mini-Me hold his hand so they can remain side-by-side as they travel to the shark tank. Dr. Evil walks to the shark tank at optimum walking speed (Fr = 0.25). Once arriving at the destination, Mini-Me says that he is too tired from running to keep up with Dr. Evil to feed the sharks. How can you explain this?

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