Question

An object with a mass of `6 kg` is hanging from a spring with a constant of `12 (kg)/s^2`. If the spring is stretched by `1 m`, what is the net force on the object?

Answer 1

`46.8 N` toward earth.

Explanation:

There are two forces acting on the object, the gravitational force on the object `\vec{F_g} = m. \vec{g_{}}` towards earth and the spring force `\vec{F_k} = -k.\vec{x_{}}`. The net force is the vector sum of these two.

Defining UP as positive and DOWN as negative,
`\vec{x_{}} = -1.0m`; `\quad` `\vec{g_{}} = -9.8 ms^{-2}`

`\vec{F_{}}_{Net}=\vec{F_k}+\vec{F_g} = -k.\vec{x_{}}+m.\vec{g_{}}`,
`\qquad\quad` `=-(12kgs^{-2})*(-1m)+(6kg).(-9.8ms^{-2})`,
`\qquad\quad` `=(12-15.8)kg.m.s^{-2} = - 46.8N`,

A negative Net force means it points downward (toward earth).