An object with a mass of #8 kg# is hanging from a spring with a constant of #9 kgs^-2#. If the spring is stretched by # 12 m#, what is the net force on the object?

Question

An object with a mass of #8 kg# is hanging from a spring with a constant of #9 kgs^-2#. If the spring is stretched by # 12  m#, what is the net force on the object?

Lily Adams · Accepted Answer

Total upward restoring force of the spring: #108N#.
Total downward gravitational force on the mass: #78.4N#
Net force on the mass: #29.6N upward# Kilogram per square second #(kgs^-2)# is an odd unit for the spring constant, #k#, of a spring. This is usually expressed in terms of newton per metre #(Nm^-1)# - for every additional metre a spring is stretched, it exerts a force of #k# newton. The two units are actually the same, as a dimensional analysis will show. The newton, #N#, is defined as a #kgms^-2#. If we multiply this by #m^-1# the #m# just cancels out and and we are left with #kgs^-2#. Why am I bringing this up so much? Because the answer to this question makes much more sense when the units are correct: "An object with a mass of #8 kg# is hanging from a spring with a constant of #9 Nm^-1#. If the spring is stretched by #12 m#, what is the net force on the object?" For each metre the spring is stretched, the force is increased by #9 N#, so a #12 m# stretch leads to a #12*9=108 N# increase in the force. This is an upward restoring force, pushing the mass back toward the spring's unstretched center position, but in order to determine the net force, we also need to account for the mass's downward gravitational force: #F = mg = 8*9.8 = 78.4 N# Since these forces are acting in opposite directions we subtract one from the other, and end up with a net upward force of #29.6 N#.

Emily Abbate · Answer

undefined The net force on the object is 96 N.