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. An elephant has legs that stretch 2.3 from its shoulders to the ground. How much time is required for one leg to swing forward after completing a stride? What would you predict for this elephant's stride frequency? That is, how many steps per minute will the elephant take?

Answer 1

Answer:

 t = 6,485 s ,  t_step = 25.94 s

the elephant gives 2.3 step very minute

Explanation:

Let's approximate this system to a simple pendulum that has angular velocity

            w = √L / g

Angular velocity and period are related

           w = 2π / T

           T = 2π √g / L

Let's find the period

           T = 2π √9.8 / 2.3

           T = 12.97 s

Stride time is

           t = T / 2

           t = 12.97 / 2

           t = 6,485 s

Frequency is inversely proportional to period

            f = 1 / t

            f = 1 / 6,485

            f = 0.15 Hz

Since the elephant has 4 legs and each uses a time t, the total time for one step is

            t_step = 4 t

            t_step = 4 6.485

            t_step = 25.94 s

             f_step = 1/t_step =0.0385 s-1

Now let's use a proportion rule to find the number of steps in 60 s

           #_step = 60 / t_step

           #__step = 60 / 25.94

           #_step = 2.3 steps

So the elephant gives 2.3 step very minute