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?

1 Answer
Feb 7, 2016

#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).