Question

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

Answer 1

889869119.99 N/m²

Step-by-step 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

`v^2-u^2=2gs\\\Rightarrow v=√(2gs+u^2)\\\Rightarrow v=√(2* 9.81* 1.43+0^2)\\\Rightarrow v=5.29684\ m/s`

Force is given by

`F=(m(v-u))/(t)\\\Rightarrow F=(4.2(5.29684-0))/(1* 10^(-3))\\\Rightarrow F=22246.728\ N`

Pressure is given by

`P=(F)/(A)\\\Rightarrow P=(22246.728)/(0.25* 10^(-4))\\\Rightarrow P=889869119.99\ Pa`

The pressure on the temple was 889869119.99 N/m²