Question

The natural length of a spring is $60cm$ and its spring constant is $4000\frac{N}{m}$. A mass of $20kg$ is hung from it. The extension produced in the spring is (Take g = $9.8m/s^2$)

Answer 1

Step 1: Given

Length of spring$\left(l\right)=60cm=60\times {10}^{-2}m$

Spring constant ($k$) = $4000\frac{N}{m}$

Acceleration due to gravity ($g$) =$9.8m/s^2$

Mass (m) = $20kg$

Step 2: Formula used

The force on string $F_k=-kx$, where $k$is the spring constant and $x$ is the elongation in the spring.

Step 3: Find the extension produced in the spring

Weight hung to spring

$$\begin{gathered} =mg \\ =20kg\times 9.8m/s^2 \\ =196N \end{gathered}$$

The force of string $F_k=-kx$ (negative sign only as per sign convention and not for calculation). On balancing the forces:

Force applied on string = Downward force on the string

$kx=mg$

$$\begin{gathered} 4000x=196 \\ x=\frac{196}{4000}=0.049m=4.9cm \end{gathered}$$

The extension produced in the string is equal to $0.049m$ or $4.9cm$.