physics 3

daphnewoon · #1 $Old$ November 1st, 2009, 01:14 AM

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.

CaptainBlack · #2 $Old$ November 1st, 2009, 01:37 AM

Quote:

Originally Posted by daphnewoon $View Post$

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

daphnewoon · #3 $Old$ November 1st, 2009, 02:12 AM

Quote:

Originally Posted by CaptainBlack $View Post$

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

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

CaptainBlack · #4 $Old$ November 1st, 2009, 02:57 AM

Quote:

Originally Posted by daphnewoon $View Post$

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 $L$ 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 $W$

CB