An elephant\'s legs have a reasonably uniform cross section from top to bottom,

Question

An elephant's legs have a reasonably uniform cross section from top to bottom, and they are quite long, pivoting high on the animal's body. When an elephant moves at a walk, it uses very little energy to bring its legs forward, simply allowing them to swing like pendulums. For fluid walking motion, this time should be half the time for a complete stride; as soon as the right leg finishes swinging forward, the elephant plants the right foot and begins swinging the left leg forward.

A)An elephant has legs that stretch 2.3 m from its shoulders to the ground. How much time is required for one leg to swing forward after completing a stride?

B) What would you predict for this elephant's stride frequency? That is, how many steps per minute will the elephant take?

Explanation / Answer

The question tells us that the elephant's gait serves as a simple pendulum. From this information we can find the period of the stride in seconds/cycle.
Part 1:

T(Period)=2pvL/g
T=2pv2.3m/9.8m/s^2
T=3.04 seconds/cycle

--The question is a little ambiguous, I think. If it wants the time to complete a full stride, then the answer is 3.04seconds. If it want's the time the half step, the question says this should be half of a complete cycle, so 3.04s/2=1.52seconds.

Part 2:

To determine the frequency, we use this equation:

f=v(g/L)/2p
f=v(9.8m/s^2/2.3m)/2p
f=.82Hertz=.82cycles/second

The question asks how many steps the elephant will take in a minute, so convert the seconds to minutes:
0.82*cycles/second*60seconds/minute

To cancel the seconds:

.82(60)cycles/1minute=49.2cycles/minute

So, for every minute, the elephant will complete 49.2 cycles.

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