Physics spring constant

Question

1. Our system is a block attached to a horizontal spring on a frictionless table. The spring has a spring constant of 4.0 N/m and a rest length of 1.0 m, and the block has a mass of 0.25 kg.  

Compute the PE when the spring is compressed by 0.50 m. 

Answer 1

The equation for potential energy on a frictionless surface only depends on 2 things, the spring constant and the displacement. In the case of only needing to calculate the PE, the mass of the spring is unnecessary.

PE=0.5*k*x^2

where k is the spring constant and x is the displacement from equilibrium.

so for this particular question

PE=0.5*4.0 N/m*(0.5m)^2

=2.0*0.25 N/m *m^2

=0.50 N*m or 0.50 J

a joule (J) is the SI unit of energy and N*m=J, so that is a way you can check you did the math right. keeping track of your unit and doing dimensional analysis.