Question

An apple is falling down from a height of 20m and then hit a

person. Assume that the mass of the apple is 200g. The

duration of impact is 0.001 sec and that the area of the

bone is 1 cm². (a) Calculate the impulsive force applied to

the person. (b) If the rupture strength for body tissue is

about 5 X 10⁶ dyn/cm² will the impact force lead to serious

injury for the person?

Answer 1

$h = 20m\newline m =200g =0.2kg\newline \Delta t = 0.001s\newline S =1cm^2\newline p_{max}= 5*10^6\frac{dyn}{cm^2}=50\frac{N}{cm^2}$

$g = 9.8\frac{m}{s^2}$

$\text{Apple speed at the end of the fall:}$

$v =\sqrt{2gh}=\sqrt{2*9.8*20}\approx19.8\frac{m}{s}$

$\text{Apple's impulse at the end of the fall:}$

$J = mv =0.2*19.8=3.96\ kg\frac{m}{s}$

$\text{The force of the apple on the body:}$

$J= F\Delta t$

$F = \frac{J}{\Delta t}= \frac{3.96}{0.001}=3960N$

$\text{The pressure of the apple on the body during the impact:}$

$p = \frac{F}{S}=\frac{3960}{1}=3960\frac{N}{cm^2}$

$p>p_{max}\text{ hence }$

$\text{impact force will cause human trauma}$

$\text{Answer:}$

$a)F =3960N$

$b)\text{impact force will cause human trauma}$