In a supermarket,you place a 22.3-N (around 5 lb)bag of oranges on a scale,and the scale starts to oscillate at 2.7 Hz.What is the spring constant of the spring of the scale?

Question

Quizplus · Accepted Answer

The spring constant $k$ can be found using the formula for the period of oscillation of a mass-spring system, $T = 2\pi\sqrt{\frac{m}{k}}$, where $T$ is the period, $m$ is the mass, and $k$ is the spring constant. Given the frequency $f = 2.7 \, \text{Hz}$, we can find the period $T = \frac{1}{f} = \frac{1}{2.7} \approx 0.37 \, \text{s}$. The mass $m$ can be found from the weight $W = mg$, giving $m = \frac{W}{g} = \frac{22.3}{9.8} \approx 2.27 \, \text{kg}$. Substituting $T$ and $m$ into the formula and solving for $k$ gives $k \approx 650 \, \text{N/m}$.

In a Supermarket,you Place a 22