Question

An elephant weighing $40000N$ stands on one foot of area $1000c{m^2}$ whereas a girl weighing $400N$ is standing on one 'stiletto' heel of area $1c{m^2}$.
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?

Answer 1

Hint: Pressure is the force applied per unit area. Unit of it is Pascal (Pa). Here the weight of the girl and the elephant becomes the force applied. Divide them by their respective contact areas to get the pressures exerted by them and then compare.

Complete step by step solution:
From question, weight of an elephant is $40000N$
Area occupied by one foot is $1000c{m^2} = 1000 \times {10^{ - 4}}{m^2}$
Weight of a girl is $400N$
Area occupied by her heel is $1c{m^2} = 1 \times {10^{ - 4}}{m^2}$

A) Now as we can see the weight of the elephant is greater compared to that of the girl. Therefore, elephants exert more force as compared to girls because the force exerted in this case is equal to the weight of them. Elephant exert more force that is
$ \Rightarrow 40000 - 400 = 39600 N$

B) Now pressure is equal to $P = \dfrac{F}{A}$
Therefore pressure exerted by elephant by inserting values in pressure formula we get
${P_{elephant}} = \dfrac{{40000}}{{1000 \times {{10}^{ - 4}}}}$
So pressure by elephant is
$ \Rightarrow {P_{elephant}} = 400000N{m^{ - 2}} = 4 \times {10^5}N{m^{ - 2}}$

C) Pressure exerted by a girl standing on heel by putting values we get
${P_{girl}} = \dfrac{{400}}{{1 \times {{10}^{ - 4}}}}$
So pressure exerted by girl is
$ \Rightarrow {P_{girl}} = 4000000N{m^{ - 2}} = 4 \times {10^6}N{m^{ - 2}}$

D) As we see from above parts pressure by elephant is $ \Rightarrow 400000N{m^{ - 2}} = 4 \times {10^5}N{m^{ - 2}}$ and by girl is $ \Rightarrow 4000000N{m^{ - 2}} = 4 \times {10^6}N{m^{ - 2}}$.

Therefore, girls wearing heels exerts more pressure on the ground.

E) Now, ratio of pressure exerted by girl to pressure exerted by elephant
$ \Rightarrow \dfrac{{4000000}}{{400000}} = 10$
Thus the pressure exerted by a girl is ten times that of an elephant.

Note: As we know pressure is force per unit area. So during solving problems always remember about the units of quantities. All the quantities should be in the same system whether it is in the SI system or in the CGS system.