In a human pyramid in a circus, the entire weight of the balanced group is supported by the legs of a performer who is lying on his back. The combined mass of all the persons performing the act, and the tables, plaques etc. Involved is $280\; kg$. The mass of the performer lying on his back at the bottom of the pyramid is $60\; kg$. Each thighbone (femur) of this performer has a length of $50\; cm$ and an effective radius of $2.0\; cm$. Determine the amount by which each thighbone gets compressed under the extra load.
In a human pyramid in a circus, the entire weight of the balanced group is supported by the legs of a performer who is lying on his back. The combined mass of all the persons performing the act, and the tables, plaques etc. Involved is $280\; kg$. The mass of the performer lying on his back at the bottom of the pyramid is $60\; kg$. Each thighbone (femur) of this performer has a length of $50\; cm$ and an effective radius of $2.0\; cm$. Determine the amount by which each thighbone gets compressed under the extra load.
Answer Total mass of all the performers, tables,
$\text { plaques etc. } \quad=280 kg$
Mass of the performer $=60 kg$ Mass supported by the legs of the performer at the bottom of the pyramid
$=280-60=220 kg$
Weight of this supported mass
$=220 kg wt .=220 \times 9.8 N =2156 N$
Weight supported by each thighbone of the performer $=1 / 2(2156) N =1078 N$
the Young's modulus for bone is given by
$Y=9.4 \times 10^{9} N m ^{-2}$
Length of each thighbone $L=0.5 m$ the radius of thighbone $=2.0 cm$ Thus the cross-sectional area of the thighbone
$A=\pi \times\left(2 \times 10^{-2}\right)^{2} m ^{2}=1.26 \times 10^{-3} m ^{2}$
the compression in each thighbone $(\Delta L)$ can be computed as
$\Delta L =[(F \times L) /(Y \times A)]$
$=\left[(1078 \times 0.5) /\left(9.4 \times 10^{9} \times 1.26 \times 10^{-3}\right)\right]$
$=4.55 \times 10^{5} m \text { or } 4.55 \times 10^{-3} cm .$
This is a very small change! The fractional decrease in the thighbone is
$\Delta L / L=0.000091$ or $0.0091 \%$
Similar Questions
A brass rod of length $2\,m$ and cross-sectional area $2.0\,cm^2$ is attached end to end to a steel rod of length $L$ and cross-sectional area $1.0\,cm^2$ . The compound rod is subjected to equal and opposite pulls of magnitude $5 \times 10^4\,N$ at its ends. If the elongations of the two rods are equal, then length of the steel rod $(L)$ is ........... $m$ $(Y_{Brass}=1.0\times 10^{11}\,N/m^2$ and $Y_{Steel} = 2.0 \times 10^{11}\,N/m^2)$
A brass rod of length $2\,m$ and cross-sectional area $2.0\,cm^2$ is attached end to end to a steel rod of length $L$ and cross-sectional area $1.0\,cm^2$ . The compound rod is subjected to equal and opposite pulls of magnitude $5 \times 10^4\,N$ at its ends. If the elongations of the two rods are equal, then length of the steel rod $(L)$ is ........... $m$ $(Y_{Brass}=1.0\times 10^{11}\,N/m^2$ and $Y_{Steel} = 2.0 \times 10^{11}\,N/m^2)$
The length of an iron wire is $L$ and area of cross-section is $A$. The increase in length is $l$ on applying the force $F$ on its two ends. Which of the statement is correct
The length of an iron wire is $L$ and area of cross-section is $A$. The increase in length is $l$ on applying the force $F$ on its two ends. Which of the statement is correct
Four uniform wires of the same material are stretched by the same force. The dimensions of wire are as given below. The one which has the minimum elongation has
Four uniform wires of the same material are stretched by the same force. The dimensions of wire are as given below. The one which has the minimum elongation has
The temperature of a wire of length $1$ metre and area of cross-section $1\,c{m^2}$ is increased from $0°C$ to $100°C$. If the rod is not allowed to increase in length, the force required will be $(\alpha = {10^{ - 5}}/^\circ C$ and $Y = {10^{11}}\,N/{m^2})$
The temperature of a wire of length $1$ metre and area of cross-section $1\,c{m^2}$ is increased from $0°C$ to $100°C$. If the rod is not allowed to increase in length, the force required will be $(\alpha = {10^{ - 5}}/^\circ C$ and $Y = {10^{11}}\,N/{m^2})$
The force required to stretch a wire of crosssection $1 cm ^{2}$ to double its length will be ........ $ \times 10^{7}\,N$
(Given Yong's modulus of the wire $=2 \times 10^{11}\,N / m ^{2}$ )
The force required to stretch a wire of crosssection $1 cm ^{2}$ to double its length will be ........ $ \times 10^{7}\,N$
(Given Yong's modulus of the wire $=2 \times 10^{11}\,N / m ^{2}$ )
- [JEE MAIN 2022]