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.(d) the strain

Answer 1

The strain in the rod is $2.37\times 10^{-3}$

Given:

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

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

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

The speed of the wave in the rod is,

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

Hence the time taken by the wave to travel the end of the rod is,

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

The velocity of the rod is, $v_r = 12.0\ \mathrm{m/s}$

The other end will keep moving after the front end hits the wall until the wave reaches the other end, given the period determined by the above problem.

As a result, before the wave reaches the end of the rod, it has traveled a distance of

$\Delta L = v_r t = (12.0\ \mathrm{m/s}) (1.58\times\ \mathrm{s}) = 1.90\times 10^{-3}\ \mathrm{m} = 1.90\ \mathrm{mm}$

The strain in the rod is given by,

$\frac{\Delta L}{L} = \frac{1.90\times 10^{-3}\ \mathrm{m}}{0.800\ \mathrm{m}} = 2.37\times 10^{-3}$

Hence, the strain in the rod is $2.37\times 10^{-3}$.

What is strain?

In terms of physics, strain is defined as the fractional modification of configuration.

A system's reaction to an applied stress is called a strain, according to 2. A force that loads a material results in a stress that leads to deformation. Formula for a strain

Change in configuration equals strain first arrangement

It is a dimensionless quantity that lacks a unit.

Change in object size / original object size is known as strain.

It is a quantity without units or dimensions.

Strain kind.

Object length change divided by starting object length equals longitudinal strain.

L/L stands for longitudinal strain.

Change in object volume divided by starting object volume equals longitudinal strain

To know more about Strain visit:

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