Check the solution to "An elastic cord is 61 cm long when..."

College
Physics
Advanced Physics

Adrianna Esparza

Answered question

2023-01-18

An elastic cord is 61 cm long when a weight of 75 N hangs from it but is 85 cm long when a weight of 210 N hangs from it. What is the "spring" constant k of this elastic cord?

Answer & Explanation

Layne Vaughn

Beginner2023-01-19Added 8 answers

Let the length of the elastic cord at rest

= l m

Then,
In the first case,

k = \frac{F_{1}}{Δ x_{1}} = \frac{75}{0.61 - l}

In the second case,

k = \frac{F_{2}}{Δ x_{2}} = \frac{210}{0.85 - l}

There are 2 unknowns in our 2 equations.

\frac{75}{0.61 - l} = \frac{210}{0.85 - l}

75 (0.85 - l) = 210 (0.61 - l)

210 l - 75 l = 210 \cdot 0.61 - 75 \cdot 0.85

135 l = 64.35

l = \frac{64.35}{135} = 0.48

So,

k = \frac{75}{0.61 - 0.48} = 576.9 N m^{- 1}

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