Respuesta :
` You can consider T to be in units of seconds/step. Frequency is the inverse of period, so
1/T = frequency and has units of steps per second. There will be 60 times as many steps in a minute.
1/T = frequency and has units of steps per second. There will be 60 times as many steps in a minute.
The number of steps taken by the elephant per minute inside water is [tex]\boxed{97\,{{{\text{steps}}}\mathord{\left/{\vphantom{{{\text{steps}}}{{\text{min}}}}}\right.\kern-\nulldelimiterspace}{{\text{min}}}}}[/tex] .
Further Explanation:
The long legs of the Elephant are considered to be the rods and the center of mass of the rod lies at the half length of the rod.
Therefore, the elephant’s legs acts as the physical pendulum whose time period of oscillation is expressed as:
[tex]\boxed{T=2\pi\sqrt{\frac{I}{{mgh}}}}[/tex]
Here, [tex]T[/tex] is the time period of the swing, [tex]I[/tex] is the moment of inetia of the elephant’s leg and [tex]h[/tex] is the height of the center of mass from the fixed point.
The moment of inertia of a rod (elephant’s leg) about the fixed point (shoulder) is:
[tex]I=\frac{1}{3}m{L^2}[/tex]
Substitute the value in above expression.
[tex]\begin{aligned}T&=2\pi\sqrt{\frac{{\frac{1}{3}m{L^2}}}{{mg\frac{L}{2}}}}\\&=2\pi\sqrt{\frac{{2L}}{{3g}}}\\\end{aligned}[/tex]
Substitute the value of length and the acceleration due to gravity.
[tex]\begin{aligned}T&=2\pi\sqrt{\frac{{2\times2.3}}{{3\times9.8}}}\\&=6.28\times0.394\\&\approx2.48\,{\text{s}}\\\end{aligned}[/tex]
The time taken by the elephant to make its leg move forward will be half of the time taken in one complete oscillation.
[tex]\begin{aligned}t&=\frac{T}{2}\\&=1.24\,{\text{s}}\\\end{aligned}[/tex]
This means that the elephant takes [tex]1.24\,{\text{s}}[/tex] to complete one step and in one second it complete 2 steps by using a pair of leg at a time.
Now, the number of steps taken by the elephant in one min will be:
[tex]\begin{aligned}N&=2\times\frac{{60}}{t}\\&=2\times\frac{{60}}{{1.24}}\\&=2\times48.38\\&\approx97\,{\text{steps}}\\\end{aligned}[/tex]
Thus, the number of steps taken by the elephant per minute inside water is [tex]\boxed{97\,{{{\text{steps}}}\mathord{\left/{\vphantom{{{\text{steps}}}{{\text{min}}}}}\right.\kern-\nulldelimiterspace}{{\text{min}}}}}[/tex].
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Answer Details:
Grade: Middle School
Subject: Physics
Chapter: Oscillations
Keywords:
Elephant’s stride frequency, steps per minute, swings like pendulum, legs that stretch, physical pendulum, moment of inertia, shoulders to the ground.
