Question

What is the spring constant of a spring that compresses 0.27 m when a force of 589 N is applied to it? a. 160 N/m b. 21 N/m c. 2200N/m d. 3000 N/m​

Answer 1

• The distance of compression, x = 0.27 m

• Spring force, f = 589 N.

• Let k be the spring constant.

We know that,

Spring force, f = kx

$589 = k \times 0.27 \\ \\ k = \dfrac{589}{0.27} \\ \\ = \dfrac{589}{0.27} \times \dfrac{100}{100} \\ \\ = \dfrac{589 \times 100}{0.27 \times 100} \\ \\ = \dfrac{58900}{27} \\ \\ k = 2181.48 \: \dfrac{N}{m}$

The spring constant is 2181.48 N/m.

Approximately ,the value can be regarded as 2200N/m.

So the right option will be C.

Answer 2

Given:-

$\bigstar$The spring constant of a spring that compresses 0.27

$\bigstar$The force applied is 589 N

To Find:-

$\bigstar$The spring constant.

Solution:-

$\bigstar$Let spring constant be y

$\star{ \underline{ \boxed{ \sf{Spring \: Constant = \frac{Force}{Distance \: of \: compression} }}}}$

$\\ \longrightarrow \tt \: y \: = \frac{589}{0.27}$

$\\ \longrightarrow \tt \: y \: = 2181.48$

$\\ \longrightarrow \tt \: y \: = 2200_{(approx)}$

$\bigstar$The spring constant is 2200 N/m

$\bigstar$Hence,Option C is correct