How to dissolve this problem?

Question

You have two springs that are identical except that spring 1 is stiffer than spring 2 (k1>k2). On which spring is more work done...

(a) if they are stretched using the same force

(b) if they are stretched the same distance?

Answer 1

For my explanation, all capital letters represent a larger quantity than lowercase letters. For example, FORCE > force. Ok?

Work = Force * Distance

(a) For the two springs:

Spring 1: Force * distance = work

Spring 2: Force * DISTANCE = WORK

For the same amount of force, spring two moves further and thus you're doing more work since its a force over a larger distance.

(b) Again,

Spring 1: FORCE * Distance = WORK

Spring 2: force   *   Distance = work

It takes more force to move the stiffer spring, so work is larger.