Another connection between force and potential energy

Joe attaches a spring to a post in his backyard. The spring is free to rotate around the post. The force constant of the spring is k = 20 N/m. He makes a map of several locations in his yard, using a scale of 1:100.

• What is the rest length of the spring?

Joe tries moving the end of the spring to different locations.

            distance from     spring must        SPE
location      post (m)       stretch by (m)      (J)
---------------------------------------------------------
   A        
   B
 
   C
   D

   E
   G
----------------------------------------------------------

Suppose that Joe moves from one location to another. What is the change in SPE as he moves?

                   change in   
from       to       SPE (J)     
------------------------------------
  A        B
 
  D        E

  G        C
------------------------------------

Joe compares the change in SPE to his displacement from one point to another. He decides to compute a quantity he calls Q

           change in SPE  (J)
   Q  =  --------------------
           displacement (m)

What are the units of this combination?

Compute this quantity for each of the following:

from    to       change in SPE     displacement      Q
                     (J)              (m)           
--------------------------------------------------------
  G      C           

  A      D
--------------------------------------------------------

Use positive numbers to mean "away from the post" and negative numbers to mean "towards the post" in the following.

1. What is the force exerted by the spring when Joe stands at G?
2. What is the force exerted by the spring when Joe stands at C?
3. What is the force exerted by the spring when Joe stands halfway between G and C?