Question

An elephant weighing 40,000 N stands on one foot of area 1000 cm² whereas a girl weighing 400 N is standing on one 'stiletto' heel of area 1 cm².

Figure

(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

a) Elephant has larger weight of 40,000 N, so elephant exerts larger force on the ground. Elephant exerts a large force on the ground by 40,000 N − 400 N= 39,600 N.
b) Area of elephant’s one foot = 1,000 cm² (1,000/10,000= 0.1m²)
Pressure = ?
Weight of the elephant = 40,000 N
$$\begin{gathered} \mathrm{Pressure}=\frac{\mathrm{Weight}}{\mathrm{Area}} \\ =\frac{40,000}{0.1} \\ =4\times {10}^5\mathrm{Pa} \end{gathered}$$

Answer: Pressure exerted by one foot of elephant on the ground = 4 × 10⁵ Pa.
c) Area of one stiletto foot = 1 cm² = 0.0001 m²
Pressure = ?
Weight of the girl = 400 N
$$\begin{gathered} \mathrm{Pressure}=\frac{\mathrm{Weight}}{\mathrm{Area}} \\ =\frac{400}{0.0001} \\ =4\times {10}^6\mathrm{Pa} \end{gathered}$$
Answer: Pressure exerted by one foot of stiletto heel on the ground = 4 × 10⁶ Pa.

d) The girl standing on stiletto heel would exert larger pressure on the ground because the surface area covered by the heel is small as pressure is inversely proportional to the surface area of the heel.
e) 40,00,000 : 4,00,000 = 10:1
The pressure exerted by the girl is 10 times greater than the elephant.