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gtnhenbr [62]
3 years ago
13

A circular bar is 800mm in length and 32mm in diameter. The bar is made from a material with a modulus of elasticity E = 150 GPa

and Poisson’s ratio of 0.27. When a force is applied to the bar, it extends by 0.7mm. What is the change in diameter and the force applied?
Engineering
1 answer:
Yuki888 [10]3 years ago
5 0

Answer:

For any material if ∈ is the axial strain then the lateral strain is given by -μ∈ is the lateral strain in the object

Where,

μ is the poisson's ratio of the material

The longitudinal strain is calculated as follows

\varepsilon _{axial}=\frac{\Delta length}{Length_{original}}\\\\\therefore \varepsilon _{axial}=\frac{0.7}{800}=8.75\times 10^{-4}

Thus the lateral strain becomes

\varepsilon _{lateral}=-\mu\varepsilon _{axial}\\\\\varepsilon _{lateral}=-0.27\times 8.75\times 10^{-4}=-2.36\times 10^{-4}

now by definition of lateral strain we have

\varepsilon _{lateral}=\frac{\Delta diameter}{diameter_{original}}\\\\\Rightarrow \Delta Diameter=-2.36\times 10^{-4}\times 32=-7.56\times 10^{-3}\\\\D_{f}-D_{i}=-7.56\times 10^{-3}\\\\D_{f}=32-7.56\times 10^{-3}=31.992mm

By hookes law the stress developed due to the given strain is given by

\sigma =\varepsilon _{axial}E

Applying values we get

\sigma =8.75\times 10^{-4}\times 150\times 10^{9}\\\\\sigma =131.25MPa

Thus the force is calculated as

Force=\sigma \times Area\\\\Force=131.25\times 10^{6}\times \frac{\pi (32\times 10^{-3})^{4}}{4}\\\\Force=105.55kN

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A rigid, insulated tank that is initially evacuated is connected through a valve to a supply line that carries helium at 200 kPa
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b 393.15 K

Explanation:

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a since no change in pressure =0 the system does work thus

FOR HELIUM  properties in standard thermodynamic chart

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Answer:

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For the above-cited practical reasons and because it is also an aesthetically pleasing medium, brick has been used as a building material for at least 5,000 years. The first brick was probably made in the Middle East, between the Tigris and Euphrates rivers in what is now Iraq. Lacking the stone their contemporaries in other regions used for permanent structures, early builders here relied on the abundant natural materials to make their sun-baked bricks. These, however, were of limited use because they lacked durability and could not be used outdoors; exposure to the elements caused them to disintegrate. The Babylonians, who later dominated Mesopotamia, were the first to fire bricks, from which many of their tower-temples were constructed.

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