An elephant weighing $40,000\ N$ stands on one foot of area $1000\ cm^2$ whereas a girl weighing $400\ N$ is standing on one ‘stiletto’ heel of area $1\ cm^2$.
(a) Which of the two, elephant or girl, exerts a larger force on the ground and by how much?
(b) What pressure is exerted on the ground by the elephant standing on one foot?
(c) What pressure is exerted on the ground by the girl standing on one heel?
(d) Which of the two exerts larger pressure on the ground: elephant or girl?
(e) What is the ratio of pressure exerted by the girl to the pressure exerted by the elephant?


Weight of elephant $W_{elephant}=40000\ N$

Area of one foot $A_{elephant}=1000\ cm^2=1000\times10^{-4}\ m^2$

Weight of girl $W_{girl}=400\ N$

Area of heel of girl $A_{girl}=1\ cm^2=1\times10^{-4}\ m^2$

(a). After observing we find that the elephant has a larger weight of $40000\ N$, therefore, the elephant exerts a larger force on the ground.

Elephant exerts a larger force on the ground by $40000\ N-400\ N=39600\ N$.


(b). The pressure exerted on the ground by the elephant standing on one foot:

$P_{elephant}=\frac{W_{elephant}}{A_{elephant}}$

Or $P_{elephant}=\frac{40000\ N}{1000\times10^{-4}\ m^2}$

Or $P_{elephant}=4.0\times10^5\ N/m^2$

(c). The pressure exerted on the ground by the girl standing on one heel 

$P_{girl}=\frac{W_{girl}}{A_{girl}}$

Or $P_{girl}=\frac{400\ N}{1\times10^{-4}\ m^2}$

Or $P_{girl}=4.0\times10^6\ N/m^2$

(d). Pressure exerted by the girl on the ground is greater than the pressure exerted by the elephant.

(e). Ratio of pressure exerted by the girl to the pressure exerted by the elephant: $=\frac{P_{girl}}{P_{elephant}}$

$=\frac{4.0\times10^6\ N/m^2}{4.0\times10^5\ N/m^2}$

$=\frac{10}{1}$

Therefore, the ratio of pressure exerted by the girl to the pressure exerted by the elephant is $10:1$

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Updated on: 10-Oct-2022

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