# An object with a mass of 4 kg is hanging from a spring with a constant of 3 (kg)/s^2. If the spring is stretched by  24 m, what is the net force on the object?

Jun 3, 2016

The net force will be $32.76$ N in the upward direction.

#### Explanation:

The forces acting on the mass are two: gravity and spring.
Gravity follows the equation

${F}_{g} = m g$

where $m$ is the mass and $g$ is the acceleration of gravity $g = 9.81$ m/s^2.

The force of a spring is a linear force with the length and it is represented by

${F}_{s} = k L$ where $k$ is the constant of the spring $k = 3 k \frac{g}{s} ^ 2$ and $L$ is the length of the stretched spring with respect to the rest position $L = 24$ m.

The two forces work one against the other because the gravity pulls the mass towards the ground while the spring is pulling in the other direction. We say that the gravity is in the positive direction, so we can write

$\setminus \Delta F = {F}_{g} - {F}_{s}$
$= m g - k L = 4 \cdot 9.81 - 3 \cdot 24$
$= 39.24 - 72$
$= - 32.76$ N

Because we said that the gravity is positive and our result is negative, it means that the mass will go upward.