# Work done by variable force

kallied

## Homework Statement

if a 10-N force is used to compress a spring with a spring constant of 4.0x10^2N/m, what is the resulting spring compression?

## Answers and Replies

dikmikkel
The spring constant tells you something about how great a force is needed to compress the spring 1 m so see if the units give you a hint. It is just a ratio.
I think the problem is about finding the dx (The displacement). Alternativly use newtons 1. law to see where it stands still, and the force seems constant to me:
Fhook - Fpress = 0 => kx - Fpress = 0 <=> x = Fpress/k
Do you get the idea?

kallied
no not really :(

Nessdude14
What the spring constant says is: for each meter the spring is compressed, the spring will push back with 400 Newtons more force. The spring in your problem will push back with 400x Newtons of force, where x is the distance you compress it in meters. To get your answer, you must find the compression (x) where this spring exerts 10 Newtons of force.

dikmikkel
Try imangining you compressing a spring. If you pressed with 10 N, then the spring would try to oppose it(You can feel it trying). If you pressed it until it was half as wide as initially, and stood still there, then the acceleration of the spring equals zero(a=0). Then newtons first law of motion states:
$\sum F = 0$
The two forces are in opposite directions(you pressing and the spring pressing against)
$Fhook-Fpress = 0 \,\Leftrightarrow \\ kx -10N = 0\\ kx = 10N$