Question 161986
A weight of 250g stretches a spring to a distance of 9.5 cm. If the distance stretched is directly proportional to the attached weight, what weight will stretch the spring to 5.7cm?
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The vertical spring formula is

{{{W = kx}}}

where {{{W}}} = the weight placed on the spring,
      {{{k}}} = the spring constant
      {{{x}}} = the distance in cm the spring stretches when
a weight of {{{W}}} grams is placed on it.

We don't know the spring constant.  We find it from

>>...A weight of 250g stretches a spring to a distance of 9.5 cm...<<

So we substitute {{{W=250}}} and {{{x=9.5}}} into {{{W = kx}}}:

{{{W = kx}}}
{{{250 = k(9.5)}}}
Divide both sides by 9.5
{{{250/9.5=k}}}
{{{26.31578947=k}}}

Now we substitute {{{k=26.31578947}}} into the spring formula:

{{{W=kx}}}

{{{W=26.31578947x}}}

Now our formula is complete and we can now solve the problem
asked for:

>>...what weight will stretch the spring to 5.7cm?...<<

Substitute {{{x=5.7}}} into the complete formula {{{W=26.31578947x}}}

{{{W=26.31578947x}}}
{{{W=26.31578947(5.7)}}}
{{{W=150grams}}}

Edwin</pre></b></font>