# Math Help - physics 3

1. ## physics 3

1.A spring has a length of L cm when a force of W N is applied to stretch it. When the force is increased to 6W N, the length of the spring increases to 2L cm. Find the percentage increase in the length of the spring from its original length when a force of W N is applied to stretch it.

2. Originally Posted by daphnewoon
1.A spring has a length of L cm when a force of W N is applied to stretch it. When the force is increased to 6W N, the length of the spring increases to 2L cm. Find the percentage increase in the length of the spring from its original length when a force of W N is applied to stretch it.
Let the unloaded length be $l_0$, then if $k$ is the spring constant when loaded with a force $w$ we have the length is:

$l(m)=l_0+k w$

Now we have:

$L=l_0+kW$

and:

$2L=l_0+k(6W)$

Subtract the first from the second to get:

$L=k(5W)$

Therefor a loading force of ... is needed to extend the spring by $L$.

CB

3. Originally Posted by CaptainBlack
Let the unloaded length be $l_0$, then if $k$ is the spring constant when loaded with a force $w$ we have the length is:

$l(m)=l_0+k w$

Now we have:

$L=l_0+kW$

and:

$2L=l_0+k(6W)$

Subtract the first from the second to get:

$L=k(5W)$

Therefor a loading force of ... is needed to extend the spring by $L$.

CB

You have sufficient information to work out the unloaded length (and the spring constant) in terms of $L$ and $W$. You will find that the initial length $l_0$ is just a multiple of $L$ form that you can work out the percentage extension when loaded with force $W$