In a humanpyramid in a circus, the entire weightof the balancedgroup 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, planks 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 humanpyramid in a circus, the entire weightof the balancedgroup i

1.	In a humanpyramid in a circus, the entire weightof the balancedgroup 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, planks 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» Solution :Total mass of all the PERFORMERS, tables plaques etc. = 280 kg Mass of the PERFORMER= 60 kg Mass supported by the legs of the performer at the bottom of the pyramid`=280-60=220kg` Weightof this supported mass `=220 kg WT. = 220xx9.8=2156 N`. Weight supported by each thighbone of the performer `=1//2(2156)=1078N`. The young.s modulus `Y=9.4xx10^(9)Nm^(-2)` (COMPRESSIVE) Length of each thighbone `L=0.5m` the radius of thighbone= 2.0 cm Thus the cross-sectional area of thighbone `A=pi xx (2xx10^(-2))^(2)m^(2)` `=1.26xx10^(-3)m^(2)`. The compression in each thighbone `DeltaL=[(FxxL)//(YxxA)]` `=[(1078xx0.5)//(9.4xx10^(9)xx1.26xx10^(-3))]` `=4.55xx10^(-5)m`.