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<title>With what force does the cobra press on the ground when it is preparing to jump, rises vertically upwards at a constant speed v? The mass of the snake is m, its length is l.</title>
$2.2.42.$ With what force does the cobra press on the ground when it is preparing to jump, rises vertically upwards at a constant speed $v$? The mass of the snake is $m$, its length is $l$.
</p>
<h3>Solution</h3>
<p>
</p>
<center>
<figure>
<img src="2.2.42.jpg"
loading="lazy" width="230" />
<figcaption>
Forces acting on cobra
</figcaption>
</figure>
</center>
<p>
Let's consider small part of cobra with the length $\Delta x$ and mass $\Delta m$:
\begin{equation*}
\Delta P = \Delta m \cdot v
\end{equation*}
Since the snake is homogeneous
\begin{equation*}
\Delta m = \frac{m}{L} \cdot\Delta x
\end{equation*}
By newton's second law:
\begin{equation*}
F=\frac{\Delta P}{\Delta t} = \frac{\Delta m}{\Delta t} \cdot v
\end{equation*}
$$F = \frac{m}{L}\cdot\frac{\Delta x}{\Delta t}\cdot v = \frac{mv^2}{L}$$
By definition of speed
\begin{equation*}
\frac{\Delta x}{\Delta t} = v
\end{equation*}
Whence the force associated with the acceleration of the centre of mass
\begin{equation*}
F = \frac{\Delta P}{\Delta t} = \frac{mv^2}{L}
\end{equation*}
Let's take everything together and find the support reaction force
\begin{equation*}
N = mg + \frac{mv^2}{L} = m\left(g + \frac{v^2}{L}\right)
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
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<meta property="og:description" content="With what force does the cobra press on the ground when it is preparing to jump, rises vertically upwards at a constant speed v? The mass of the snake is m, its length is l.">
<meta property="og:description" content="With what force does the cobra press on the ground when it is preparing to jump, rises vertically upwards at a constant speed v? The mass of the snake is m, its length is l.">
<title>With what force does the cobra press on the ground when it is preparing to jump, rises vertically upwards at a constant speed v? The mass of the snake is m, its length is l.</title>
<title>With what force does the cobra press on the ground when it is preparing to jump, rises vertically upwards at a constant speed v? The mass of the snake is m, its length is l.</title>
$2.2.42.$ With what force does the cobra press on the ground when it is preparing to jump, rises vertically upwards at a constant speed $v$? The mass of the snake is $m$, its length is $l$.
$2.2.42.$ With what force does the cobra press on the ground when it is preparing to jump, rises vertically upwards at a constant speed $v$? The mass of the snake is $m$, its length is $l$.
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="2.2.42.jpg"
<img src="2.2.42.jpg"
loading="lazy" width="230" />
loading="lazy" width="230" />
<figcaption>
<figcaption>
Forces acting on cobra
Forces acting on cobra
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
Let's consider small part of cobra with the length $\Delta x$ and mass $\Delta m$:
Let's consider small part of cobra with the length $\Delta x$ and mass $\Delta m$:
\begin{equation*}
\begin{equation*}
\Delta P = \Delta m \cdot v
\Delta P = \Delta m \cdot v
\end{equation*}
\end{equation*}
Since the snake is homogeneous
Since the snake is homogeneous
\begin{equation*}
\begin{equation*}
\Delta m = \frac{m}{L} \cdot\Delta x
\Delta m = \frac{m}{L} \cdot\Delta x
\end{equation*}
\end{equation*}
By newton's second law:
By newton's second law:
\begin{equation*}
\begin{equation*}
F=\frac{\Delta P}{\Delta t} = \frac{\Delta m}{\Delta t} \cdot v
F=\frac{\Delta P}{\Delta t} = \frac{\Delta m}{\Delta t} \cdot v
\end{equation*}
\end{equation*}
$$F = \frac{m}{L}\cdot\frac{\Delta x}{\Delta t}\cdot v = \frac{mv^2}{L}$$
$$F = \frac{m}{L}\cdot\frac{\Delta x}{\Delta t}\cdot v = \frac{mv^2}{L}$$
By definition of speed
By definition of speed
\begin{equation*}
\begin{equation*}
\frac{\Delta x}{\Delta t} = v
\frac{\Delta x}{\Delta t} = v
\end{equation*}
\end{equation*}
Whence the force associated with the acceleration of the centre of mass
Whence the force associated with the acceleration of the centre of mass
\begin{equation*}
\begin{equation*}
F = \frac{\Delta P}{\Delta t} = \frac{mv^2}{L}
F = \frac{\Delta P}{\Delta t} = \frac{mv^2}{L}
\end{equation*}
\end{equation*}
Let's take everything together and find the support reaction force
Let's take everything together and find the support reaction force
\begin{equation*}
\begin{equation*}
N = mg + \frac{mv^2}{L} = m\left(g + \frac{v^2}{L}\right)
N = mg + \frac{mv^2}{L} = m\left(g + \frac{v^2}{L}\right)
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
