Question

How far must I compress a spring with spring constant 573N/m to produce a force of 184N? Express your answer to the nearest hundredth

Answer 1

compressed0.32 meters

Step-by-step explanation

Step 1

The force exerted by a spring on objects attached to its ends is proportional to the spring's change in length away from its equilibrium length and is always directed towards its equilibrium position.

`F=-kx.`

so

let

`\begin{gathered} k=573\text{ }\frac{\text{N}}{m} \\ F=184\text{ N} \end{gathered}`

replace and solve for x

`\begin{gathered} F=-kx \\ 184=-573(N)/(m)\cdot x \\ divide\text{ both sides by 573 N/m} \\ (184)/(-573(N)/(m))=(-573(N)/(m)\cdot x)/(-573(N)/(m)) \\ -0.32\text{ m=x} \end{gathered}`

the negative symbol indicates the spring is compresed

so, the answer is

0.32 meters

I hope this helps you