Intro to Springs (Hooke's Law) Video Lessons

Concept

# Problem: A vertical spring has a length of 0.225 m when a 0.25 kg mass hangs from it, and a length of 0.75 m when a 1.975 kg mass hangs from it.Find the spring constant k in N/m.

###### FREE Expert Solution

Hooke's law:

$\overline{){\mathbf{F}}{\mathbf{=}}{\mathbf{-}}{\mathbit{k}}{\mathbf{x}}}$

F1 = mg = (0.25)(10) = 2.5 N

Let L be the length of the unloaded spring.

x1 = (0.225 - L) m

k1 = F1/x1 = 2.5/(0.225 - L)

0.225k1 - k1L = 2.5

L = (0.225k1 - 2.5)/k1

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###### Problem Details

A vertical spring has a length of 0.225 m when a 0.25 kg mass hangs from it, and a length of 0.75 m when a 1.975 kg mass hangs from it.

Find the spring constant k in N/m.