A police crime lab is trying to determine whether someone was murdered or died as a result of an accident. He was struck in the temple by a 4.20 kg sculpture that is alleged to have fallen off a bookcase. The sculpture presumably fell a distance of 1.43 m and the corner that struck him had an area of 0.250 cm 2. If the time for the sculpture to stop was 1.00 ms, the pressure on his temple, in N/m 2, was

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boffeemadrid boffeemadrid · Answer 1 · 2019-12-20T06:45:55+01:00

Answer:

889869119.99 N/m²

Explanation:

t = Time taken to stop = 1 ms

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

g = Acceleration due to gravity = 9.81 m/s²

m = Mass of statue = 4.2 kg

Equation of motion

[tex]v^2-u^2=2gs\\\Rightarrow v=\sqrt{2gs+u^2}\\\Rightarrow v=\sqrt{2\times 9.81\times 1.43+0^2}\\\Rightarrow v=5.29684\ m/s[/tex]

Force is given by

[tex]F=\dfrac{m(v-u)}{t}\\\Rightarrow F=\dfrac{4.2(5.29684-0)}{1\times 10^{-3}}\\\Rightarrow F=22246.728\ N[/tex]

Pressure is given by

[tex]P=\dfrac{F}{A}\\\Rightarrow P=\dfrac{22246.728}{0.25\times 10^{-4}}\\\Rightarrow P=889869119.99\ Pa[/tex]

The pressure on the temple was 889869119.99 N/m²