Chapter 11, Problem 18SP

A small metal sphere weighing 10.0 N is hung from a vertical spring, which comes to rest after stretching 2.0 cm. Determine the spring constant.

To determine

The spring constant considering a small metal sphere of weight of $10\text{ N}$ is hung from the vertical springthatcomes to rest after stretching $2.0\text{ cm}$.

Answer to Problem 18SP

Solution: $500\text{ N/m}$

Explanation of Solution

Given data:

The weight of the metal sphere is $10\text{ N}$.

The spring is stretched vertically by $2.0\text{ cm}$ due to the hanging of the metal sphere.

Formula used:

Therestoring force in a spring is expressed as,

$F=kx$

Here, $k$ is the elastic spring constant, $F$ is the applied force, and $x$ is the deflection or change in length of the spring on application of force $F$.

Explanation:

Consider the expression for applied force in the spring

$F=kx$

Substitute $10\text{ N}$ for $F$ and $2.0\text{ cm}$ for $x$

$\begin{array}{c}10\text{ N}=k\left(2.0\text{ cm}\right)\\ 10\text{ N}=k\left(2.0\text{ cm}\right)\left(\frac{0.01\text{ m}}{1\text{ cm}}\right)\\ k=\frac{10\text{ N}}{\left(2.0\text{ cm}\right)\left(\frac{0.01\text{ m}}{1\text{ cm}}\right)}\\ k=500\text{ N/m}\end{array}$

Conclusion:

The spring constant for the spring is $500\text{ N/m}$.