# physics 3

• Nov 1st 2009, 12:14 AM
daphnewoon
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.
• Nov 1st 2009, 12:37 AM
CaptainBlack
Quote:

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 \$\displaystyle l_0\$, then if \$\displaystyle k\$ is the spring constant when loaded with a force \$\displaystyle w\$ we have the length is:

\$\displaystyle l(m)=l_0+k w\$

Now we have:

\$\displaystyle L=l_0+kW\$

and:

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

Subtract the first from the second to get:

\$\displaystyle L=k(5W)\$

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

CB
• Nov 1st 2009, 01:12 AM
daphnewoon
Quote:

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

\$\displaystyle l(m)=l_0+k w\$

Now we have:

\$\displaystyle L=l_0+kW\$

and:

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

Subtract the first from the second to get:

\$\displaystyle L=k(5W)\$

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

CB

hI, thanks for replying
i understand your working but what is the percentage then?
• Nov 1st 2009, 01:57 AM
CaptainBlack
Quote:

Originally Posted by daphnewoon
hI, thanks for replying
i understand your working but what is the percentage then?

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

CB