A spring hangs freely with a hook at its end at rest at position, $y=0\mathrm{.}0.$ A $1kg$ mass is then. attached to the hook on the spring and the hook is now at $y=-0\mathrm{.}4m.$ The system is at rest.

a$.$ Calculate the spring constant.

b$.$ Calculate the mechanical energy stored in the spring.

An external force lowers the mass to position $y=-0\mathrm{.}5m$ and the mass is then released.

c$.$ Calculate the mechanical energy stored in the spring at the moment the mass is released

d$.$ Calculate the speed of the mass as it passes through the point $y=-0\mathrm{.}4m.$

e$.$ Calculate the maximum height reached by the mass.

f$.$ Calculate the acceleration of the mass at the monent it renches its maximun height.

A spring hangs freely with a hook at its end at rest at position, $y=0\mathrm{.}0.$ A $1kg$ mass is then attached to the hook on the spring and the hook is now at $y=-0\mathrm{.}4m.$ The system is at rest.

a$.$ Calculate the spring constant. $(k)=-$

b$.$ Calculate the mechanical energy stored in the spring.

An external force lowers the mass to position $y=-0\mathrm{.}5m$ and the mass is then released.

c$.$ Calculate the mechanical energy stored in the spring at the umoment the mass is released.

d$.$ Calculate the speed of the nuss as it passes through the point $y=-0\mathrm{.}4m.$

e$.$ Calculate the maximum height reached by the mass.

f$.$ Calculate the acceleration of the mass at the monent it renches its maximun height.