Explain with illustration cranes regarding the applications of elastic behaviour of materials.
Explain with illustration cranes regarding the applications of elastic behaviour of materials.
For in all engineering designs, elastic behaviour of materials play important role. Let us consider the illustration of cranes for this.
Cranes used for lifting and moving heavy loads from one place to another have a thick metal rope to which the load is attached and so rope (Cable) is under stress.
Suppose we want to make a crane, which has a lifting capacity of $10$ tonnes or metric tons ( $1$ metric ton $=1000 \mathrm{~kg}$ ). How thick should the steel rope be ?
For that load does not deform the rope permanently. Therefore, the extension should not exceed the elastic limit.
Means the value of yield strength $\mathrm{S}_{y}$ produced in rope is less than the value of elastic limit. Suppose the least cross sectional area of rope of mild steel is A and yield strength of mild steel $\left(\mathrm{S}_{y}\right)$ is $300 \times 10^{6} \mathrm{~N} \mathrm{~m}^{-2}$
$\therefore \mathrm{A} \geq \frac{\mathrm{W}}{\mathrm{S}_{y}}$
$=\frac{\mathrm{Mg}}{\mathrm{S}_{y}}$
$\quad=\frac{10^{4} \mathrm{~kg} \times 10 \mathrm{~ms}^{-2}}{300 \times 10^{6} \mathrm{Nm}^{-2}}$
$\quad=3.3 \times 10^{-4} \mathrm{~m}^{2}$
$\therefore \mathrm{A} \geq 3.3 \times 10^{-4} \mathrm{~m}^{2}$
If $g=3.1 \pi \mathrm{ms}^{-2}$ and $\mathrm{A}=\pi r^{2}$ then
From $\mathrm{A}=\frac{\mathrm{Mg}}{\mathrm{S}_{y}} \quad\left[\because g=9.8=3.1 \times \pi \mathrm{ms}^{-2}\right]$
Similar Questions
Column$-II$ is related to Column$-I$. Join them appropriately :
Column $-I$
Column $-II$
$(a)$ When temperature raised Young’s modulus of body
$(i)$ Zero
$(b)$ Young’s modulus for air
$(ii)$ Infinite
$(iii)$ Decreases
$(iv)$Increases
Column$-II$ is related to Column$-I$. Join them appropriately :
| Column $-I$ | Column $-II$ |
| $(a)$ When temperature raised Young’s modulus of body | $(i)$ Zero |
| $(b)$ Young’s modulus for air | $(ii)$ Infinite |
| $(iii)$ Decreases | |
| $(iv)$Increases |
A uniformly tapering conical wire is made from a material of Young's modulus $Y$ and has a normal, unextended length $L.$ The radii, at the upper and lower ends of this conical wire, have values $R$ and $3R,$ respectively. The upper end of the wire is fixed to a rigid support and a mass $M$ is suspended from its lower end. The equilibrium extended length, of this wire, would equal
A uniformly tapering conical wire is made from a material of Young's modulus $Y$ and has a normal, unextended length $L.$ The radii, at the upper and lower ends of this conical wire, have values $R$ and $3R,$ respectively. The upper end of the wire is fixed to a rigid support and a mass $M$ is suspended from its lower end. The equilibrium extended length, of this wire, would equal
- [JEE MAIN 2016]
A copper wire of length $2.2 \;m$ and a steel wire of length $1.6\; m ,$ both of diameter $3.0 \;mm ,$ are connected end to end. When stretched by a load, the net elongation is found to be $0.70 \;mm$. Obtain the load applied in $N$.
A copper wire of length $2.2 \;m$ and a steel wire of length $1.6\; m ,$ both of diameter $3.0 \;mm ,$ are connected end to end. When stretched by a load, the net elongation is found to be $0.70 \;mm$. Obtain the load applied in $N$.
Stress required in a wire to produce $0.1\%$ strain is $4 \times10^8\, N/m^2$. Its yound modulus is $Y_1$. If stress required in other wire to produce $0.3\%$ strain is $6 \times 10^8\, N/m^2$. Its young modulus is $Y_2$. Which relation is correct
Stress required in a wire to produce $0.1\%$ strain is $4 \times10^8\, N/m^2$. Its yound modulus is $Y_1$. If stress required in other wire to produce $0.3\%$ strain is $6 \times 10^8\, N/m^2$. Its young modulus is $Y_2$. Which relation is correct
The pressure that has to be applied to the ends of a steel wire of length $10\ cm$ to keep its length constant when its temperature is raised by $100^o C$ is: (For steel Young's modulus is $2 \times 10^{11}$ $Nm^{-1}$ and coefficient of thermal expansion is $1.1 \times 10^{-5}$ $K^{-1}$ )
The pressure that has to be applied to the ends of a steel wire of length $10\ cm$ to keep its length constant when its temperature is raised by $100^o C$ is: (For steel Young's modulus is $2 \times 10^{11}$ $Nm^{-1}$ and coefficient of thermal expansion is $1.1 \times 10^{-5}$ $K^{-1}$ )
- [JEE MAIN 2014]