Chapter 14, Problem 90A

To determine

The spring constant of spring.

Answer to Problem 90A

The spring constant of spring is $\text{2}\text{.6 }\text{N/m}$ .

Explanation of Solution

Given:

Mass of spring: $225\mathrm{g}$

Length of spring: $\text{9}\text{.4}\text{cm}$

Formula used:

The formula to calculate the spring constant,$k=\frac{F}{x}=\frac{mg}{x}$

Where,

  $k$ $=$ Spring constant

F$=$ Force

x$=$ Length of String$\text{g}$ $=$ acceleration due to gravity

Unit Conversions:

  $\text{1 cm =}\frac{1}{\text{100}}\text{ m}$

Hence, $\text{9}\text{.4 cm = 0}\text{.094}\text{m}$

  $\text{1g=}\frac{\text{1}}{\text{1000}}\text{kg}$

Hence, $\text{225 g = 0}\text{.025 kg}$

Calculation:

Put the values in the given formula

  $\begin{array}{c}k=\frac{\left(\text{0}\text{.025 }\text{kg}\right)\text{×}\left(\text{9}\text{.8 N/kg}\right)}{\left(\text{0}\text{.094 m}\right)}\\ \text{=2}\text{.6 }\text{N/m}\end{array}$

Conclusion:

Hence, the spring constant is $\text{2}\text{.6 }\text{N/m}$ .