Answer:
0.1164 m
0.49387 m
Explanation:
m = Mass = 5 kg
g = Acceleration due to gravity = 9.81 m/s²
h = Height from which brick falls = 12 m
k = Spring constant = 8 kN/m
a) Potential energy of the brick
[tex]PE=mgh\\\Rightarrow PE=5\times 9.81\times 12\\\Rightarrow PE=588.6\ J[/tex]
Potential energy in spring
[tex]PE=\frac{1}{2}\times kx^2\\\Rightarrow x=\sqrt{\frac{PE\times 2}{k}}\\\Rightarrow x=\sqrt{\frac{588.6\times 2}{8000}}\\\Rightarrow x=0.3836\ m[/tex]
The compression of spring = 0.5-0.3836 = 0.1164 m
b) Weight of the brick
[tex]F=5\times 9.81\\\Rightarrow F=49.05\ N[/tex]
[tex]F=kx\\\Rightarrow x=\frac{F}{k}\\\Rightarrow x=\frac{49.05}{8000}\\\Rightarrow x=0.00613\ m[/tex]
The final length of the spring = 0.5-0.00613 = 0.49387 m
