Chapter 14, Problem 103A

(a)

To determine

To calculate:

Spring constant.

Answer to Problem 103A

The spring constant for force $20\text{N}$ and displacement $0.5\text{m}$ is $40\text{N/m}$ .

Explanation of Solution

Given:

Force: $20\text{N}$

Spring is stretched: $0.5\text{m}$

Formula used:

For spring constant,

  $F=kx$

Where, $F$ stands for force, $k$ stands for spring constant and $x$ for displacement

Calculation:

Rearranging the equation,

  $\begin{array}{c}k=\frac{F}{x}\\ =\frac{20}{0.5}\\ =40\text{N/m}\end{array}$

Conclusion:

Hence, the spring constant for force $20\text{N}$ and displacement $0.5\text{m}$ is $40\text{N/m}$ .

(b)

To determine

To calculate:Amount of energy

Explanation of Solution

Given:

Force: $20\text{N}$

Spring is stretched: $0.5\text{m}$

Formula used:

Amount of energy needed to store in the spring can be given by,

  $P{E}_{sp}=\frac{1}{2}k{x}^{{}^2}$

Where, $P{E}_{sp}$ denotes potential energy of the spring, $k$ spring constant and $x$ displacement

Calculation:

Energy stored in the spring is the potential energy.

  $\begin{array}{l}=\frac{1}{2}\times (\text{40N/m}){(}^{\text{0}}\\ =5\text{J}\end{array}$

Conclusion:

Hence, $\text{5}\text{J}$ energy is stored in the spring.