Answer:
The maximum height the box will reach is 1.72 m
Explanation:
F = k·x
Where
F = Force of the spring
k = The spring constant = 300 N/m
x = Spring compression or stretch = 0.15 m
Therefore the force, F of the spring = 300 N/m×0.15 m = 45 N
Mass of box = 0.2 kg
Work, W, done by the spring = [tex]\frac{1}{2} kx^2[/tex] and the kinetic energy gained by the box is given by KE = [tex]\frac{1}{2} mv^2[/tex]
Since work done by the spring = kinetic energy gained by the box we have
[tex]\frac{1}{2} mv^2[/tex] = [tex]\frac{1}{2} kx^2[/tex] therefore we have v = [tex]\sqrt{\frac{kx^2}{m} }[/tex] = [tex]x\sqrt{\frac{k}{m} }[/tex] = [tex]0.15\sqrt{\frac{300}{0.2} }[/tex] = 5.81 m/s
Therefore the maximum height is given by
v² = 2·g·h or h = [tex]\frac{v^2}{2g}[/tex] = [tex]\frac{5.81^{2} }{2*9.81}[/tex] = 1.72 m
