I saw this unfortunate incident on Instagram (I don't think it's funny at all)
https://www.instagram.com/reel/Cx21pCquu65/?igshid=MWFmMDEzMTdiNg==
and I thought to myself, how do I calculate the force of the blow the girl received on the head?
I don't have a background in Physics but I guess that the angle and the gravitational force exerted by the cabinet are some of the variables that need to be calculated.
Given that the object that hit her weighs, say 8 kg.
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1$\begingroup$ The kinetic energy mv²/2 and momentum mv say more than the force, since the force depends on the stiffness of the material. If a bullet hits you you also don't ask for its force but for its energy and momentum, that depends on its mass and velocity while the force also depends on the material and deformability of all involved objects. $\endgroup$– YukterezCommented Dec 17, 2023 at 18:14
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1 Answer
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From the collision between the two masses $~m~$ and $~M_H~$ you obtain the force $~F~$ . the mass $~m~$ hit the head mass $~M_H~$ with velocity $~v_m~$. (Figure II)
from here the force
$$F=\frac{M_H\,m}{M_H+m}\,v_m\,t_c\tag 1$$
where $~t_c~$ is the time that the collision accrue.
the velocity $~v_m~$ can be obtain from this differential equation. (Figure I)
$$m\,L_2^2\ddot\alpha=\tau_A=M\,g\,L_1\,\sin(\alpha)+m\,g\,L_2\,\cos(\alpha)\tag 2$$
solving equation (2) with the initial conditions $~\alpha(0)=\alpha_0~,\dot\alpha(0)=0~$ you obtain $~\alpha(t)~$. from here the velocity $~v_m~$
$$v_m=\dot\alpha(t=t_f)\,L_2$$
where $~t_f~$ is the time where $~\alpha(t)=\pi/2~$
Remark
for simplification the dynamics of the L-shape is describe with the mass $~m~$ and the distance $~L_2~$
