## Related questions with answers

A sewing machine needle moves with a rapid vibratory motion, rather like SHM, as it sews a seam. Suppose the needle moves 8.4 mm from its highest to its lowest position and it makes 24 stitches in 9.0 s. What is the maximum needle speed?

Solutions

Verified**Given Data:**

Distance between two extreme positions, $\text{d}=8.4\ \text{mm}$.

Number of stitches $= 24$

Time is taken to complete the stitches, $\text{t}=9.0\ \text{s}$

**To Find:**

We need to find the maximum needle speed.

$\textbf{Concepts: }$

Simple harmonic motion is defined as the vibratory motion that occurs when the restoring force is proportional to the displacement from equilibrium. The net force on the object is given by

$\begin{align*} F_{x} &= - k x \end{align*}$

Where, $k$ is the spring's constant. In order to evaluate the elastic potential energy of the spring, We use the following relation:

$\begin{align*} U &= \dfrac{1}{2} k x^{2} \end{align*}$

Where, $x$ is the displacement. In order to evaluate the total energy of the spring, We use the following relation:

$\begin{align*} E &= \dfrac{1}{2} m v_{x}^{2} + \dfrac{1}{2} k x^{2} \end{align*}$

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Physics

3rd Edition•ISBN: 9780073512150Alan Giambattista, Betty Richardson, Robert Richardson#### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th Edition•ISBN: 9780133942651 (8 more)Randall D. Knight#### Mathematical Methods in the Physical Sciences

3rd Edition•ISBN: 9780471198260 (1 more)Mary L. Boas#### Fundamentals of Physics

10th Edition•ISBN: 9781118230718 (3 more)David Halliday, Jearl Walker, Robert Resnick## More related questions

1/4

1/7