Answer to Question #134129 in Mechanics | Relativity for adeola adegoke

Question #134129
the length of a spring is spring is 16cm when a load of 5n is attached to the spring is 20n the length is 19cm .calculate th
(i) force constant of the spring
(ii)original length of spring
1
Expert's answer
2020-09-21T08:28:08-0400

Explanations & Calculations


  • Take the force constant as "\\small k" and the original length as "\\small l_0".
  • Then considering the extensions & the equation : "\\small F=kx", followings can be written to calculate the needed data.

"\\qquad\\qquad\n\\begin{aligned}\n\\small l_0+e_1 &= \\small 0.16m \\,\\,\\,\\,\\to \\to \\,\\,\\,\\ e_1=0.16-l_0\\\\\n\\small ke_1 &= \\small k(0.16-l_0)=5N\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\cdots\\cdots(1)\\\\\n\\\\\n\\small l_0+e_2 &= \\small 0.19m \\,\\,\\,\\,\\to \\to \\,\\,\\,\\,e_2=0.19-l_0\\\\\n\\small ke_2 &= \\small k(0.19-l_0 ) =20N \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\cdots\\cdots(2)\n\\end{aligned}"


  • By (2) - (1),

"\\qquad\\qquad\n\\begin{aligned}\n\\small 15N &= \\small k(0.03m)\\\\\n\\small \\bold{k} &= \\small \\bold{500Nm^{-1}}\n\\end{aligned}"


  • From equation (1),

"\\qquad\\qquad\n\\begin{aligned}\n\\small 500Nm^{-1} \\times (0.16-l_0)&= \\small 5N\\\\\n\\small \\bold{l_0} &= \\small \\bold{0.15m} = \\bold{15cm}\n\\end{aligned}"


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Comments

Alfred Isaac
12.05.24, 18:59

Very helpful site

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