Question

Review. For a certain type of steel, stress is always proportional to strain with Young's modulus 20 × 10¹⁰ N/m² . The steel has density 7.86× 10³kg / m³. It will fail by bending permanently if subjected to compressive stress greater than its yield strength бy = 400MPa. A .rod 80.0cm long, made
of this steel, is fired at 12.0 m/s straight at a very hard wall.(b) After the front end of the rod hits the wall and stops, the back end of the rod keeps moving as described by Newton's first law until it is stopped by excess pressure in a sound wave moving back through the rod. What time interval elapses before the back end of the rod receives the message that it should stop?

Answer 1

$1.58\times 10^{-4}\ \mathrm{s}$ is the time interval elapses before the back end of the rod receives the message that it should stop.

Given:

Length of the rod, L = 80 cm = 0.800 m

Young's modulus, Y = $20 \times 10^{10}\;N/m^{2}$

steel density, $\rho = 7.86 \times 10^{3}\;kg/m^{3}$

The speed of the wave in the rod is,

$v = \sqrt{\frac{Y}{\rho}} = \sqrt{\frac{20\times 10^{10}\ \mathrm{N/m^2}}{7.86\times 10^3\ \mathrm{kg/m^3}}} = 5044\ \mathrm{m/s}$

Consequently, the length of the rod's end is traveled by the wave in at

$t=\frac{L}{v} = \frac{0.800\ \mathrm{m}}{5044\ \mathrm{m/s}} = 1.58\times 10^{-4}\ \mathrm{s}$

Hence, $1.58\times 10^{-4}\ \mathrm{s}$ is the time interval elapses before the back end of the rod receives the message that it should stop.

What are Newtons Laws?

The three fundamental laws of classical mechanics known as Newton's laws of motion describe how an object's motion and the forces acting on it interact. The following paraphrase of these statutes is available

Unless a force acts upon a body, it remains at rest or in continual straight-line motion.

When a force acts on a body, the force is equal to the time rate at which the body's momentum changes.

When two bodies exert force on one another, the direction and amount of the force are opposed.

Isaac Newton first identified the three laws of motion in his 1687 book Philosophize Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy).

They served as the cornerstone for classical mechanics as Newton used them to examine and explain the motion of numerous physical objects and systems. The conceptual foundations of classical physics have been reconstructed in several ways since Newton, utilizing various mathematical techniques that have revealed insights that were hidden in the original, Newtonian formulation.

To know more about Newtons Laws, visit:

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