Answer to Question #280504 in Physics for Faith

Question

In his garage, Rick conducted an experiment to teach Morty how to calculate a spring's force constant. He attached an air track glider to the end of an ideal spring of neglible mass and set it to oscillate.He then asked Morty to measure the time it takes to pass through the equilibrium point and then the second time it pass through the same point. Below are the data gathered by Morty.

• m= 0.53
• t=1.2

Based on the above observation, what is Morty's calculation of spring's force constant?

Answer 1

The period of the ideal spring oscillator is given as follows:

$$T = 2\pi \sqrt{\dfrac{m}{k}}$$

where $k$ is the spring constant. Expressing $k$ and substituting $m = 0.53 kg, T = 1.2s$, find:

$$k = \dfrac{4\pi^2m}{T^2} = \dfrac{4\pi^2\cdot 0.52kg}{(1.2s)^2} \approx 14N/m$$

Answer. 14 N/m.