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# 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 â€˜stilettoâ€™ 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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