Chapter 14, Problem 1STP

To determine

To Choose: The correct option.  

Answer to Problem 1STP

Option D

Explanation of Solution

Given:

Potential energy: $8.67J$

Length: $247\text{mm}$

Unit conversion:

  $1\text{mm}={10}^{-3}\text{m}$

Formula Used:

The following expression is used to find spring constant:

  $P.E=\frac{1}{2}k{x}^2$

Where,

  $P.E$ : Potential energy.

  $k$ : spring constant.

  $x$ : length

Calculation:

The spring constant is calculated by using following expression:

  $P.E=\frac{1}{2}k{x}^2$

Put the values from given data:

  $\begin{array}{l}P.E=\frac{1}{2}k{x}^2\\ 8.67=\frac{1}{2}k\left({0.247}^2\right)\\ 8.67=\frac{1}{2}k\left(0.061009\right)\\ 8.67=k\left(0.03050\right)\\ k=284\text{N/m}\end{array}$

Conclusion:

Thus, the option D is correct.