Question

if PEs represents the potential energy stored in a spring in kg . m^2 /s2 ,and x represents the change in spring length from its equilbrium position in m , what is the unitfor the spring constant k in the formula PEs = 1/2 kx^2

Answer 1

We can do dimensional analysis in this particular problem. We do as follows:

PEs = 1/2 kx^2
kg . m^2 /s2 [=] k (m)²

The units in the left side should be the same units as the resulting units in the right side.

kg . m^2 /s2 [=] (kg/s²) (m)²

Therefore, the units of k should be kg/s².