# 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?

Feb 7, 2016

$46.8 N$ toward earth.

#### Explanation:

There are two forces acting on the object, the gravitational force on the object $\setminus \vec{{F}_{g}} = m . \setminus \vec{{g}_{}}$ towards earth and the spring force $\setminus \vec{{F}_{k}} = - k . \setminus \vec{{x}_{}}$. The net force is the vector sum of these two.

Defining UP as positive and DOWN as negative,
$\setminus \vec{{x}_{}} = - 1.0 m$; $\setminus \quad$ $\setminus \vec{{g}_{}} = - 9.8 m {s}^{- 2}$

$\setminus {\vec{{F}_{}}}_{N e t} = \setminus \vec{{F}_{k}} + \setminus \vec{{F}_{g}} = - k . \setminus \vec{{x}_{}} + m . \setminus \vec{{g}_{}}$,
$\setminus q \quad \setminus \quad$ $= - \left(12 k g {s}^{- 2}\right) \cdot \left(- 1 m\right) + \left(6 k g\right) . \left(- 9.8 m {s}^{- 2}\right)$,
$\setminus q \quad \setminus \quad$ $= \left(12 - 15.8\right) k g . m . {s}^{- 2} = - 46.8 N$,

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