A snake lying on the floor starts to rise with vertical velocity $v$. Find the pressure force on the floor if the snake is homogeneous, its mass is $m$, length $l$
Decision:
The length of the part of the snake that has risen in time $t$ is $x = vt$. This part of the snake has velocity $v$, while the rest of the length $l-x$ is at rest. It follows that the velocity of the center of mass
$u = \frac{vx}{l} = \frac{v^{2}t}{l}$.
We see that this velocity depends linearly on time, hence the acceleration of the center of mass is upward and equal to $a = \frac{v^{2}}{l}$.
The sum of the gravity force $mg$ and the support reaction force $N$ must be equal to $ma$. The equality of these quantities in projection to the vertical direction is as follows
$N - mg = ma = \frac{mv^{2}}{l}$.
According to Newton's III law of motion, the force of the snake's pressure on the floor $(P)$ is equal in magnitude to the force of the support reaction $N$:
$P = N = mg + \frac{mv^{2}}{l}.$
Decision:
The length of the part of the snake that has risen in time $t$ is $x = vt$. This part of the snake has velocity $v$, while the rest of the length $l-x$ is at rest. It follows that the velocity of the center of mass
$u = \frac{vx}{l} = \frac{v^{2}t}{l}$.
We see that this velocity depends linearly on time, hence the acceleration of the center of mass is upward and equal to $a = \frac{v^{2}}{l}$.
The sum of the gravity force $mg$ and the support reaction force $N$ must be equal to $ma$. The equality of these quantities in projection to the vertical direction is as follows
$N - mg = ma = \frac{mv^{2}}{l}$.
According to Newton's III law of motion, the force of the snake's pressure on the floor $(P)$ is equal in magnitude to the force of the support reaction $N$:
$P = N = mg + \frac{mv^{2}}{l}.$