Question

An african elephant has a mass of 600kg. The diameter of each foot is approximately 0.4m. Calculate the stress on the surface of each foot

Answer 1

Given :

• Mass of Elephant (m) = 600 kg
• Diameter of each foot (d) = 0.4 m

To Find :

• Stress on the surface of each foot

Solution :

Diameter of each foot of elephant is 0.4 m. So, we gave to find radius of foot.

$\longrightarrow \sf{Diameter \: = \: 2(Radius)} \\ \\ \longrightarrow \sf{Radius\ =\ \dfrac{Diameter}{2}} \\ \\ \longrightarrow \sf{Radius\ =\ \dfrac{0.4}{2}} \\ \\ \longrightarrow \sf{Radius\ =\ 0.2} \\ \\ \dashrightarrow \underline {\boxed{\sf{Radius\ =\ 0.2\ m}}}$

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$\longrightarrow \sf{Area\ =\ \pi r^2} \\ \\ \longrightarrow \sf{Area\ = \ (3.14)\ \times\ (0.2)^2} \\ \\ \longrightarrow \sf{Area\ = \ (3.14)\ \times\ 0.04} \\ \\ \longrightarrow \sf{Area\ =\ 0.1256} \\ \\ \dashrightarrow \underline {\boxed{\sf{Area \: = \: 0.1256 \: m^2}}}$

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$\longrightarrow \sf{Stress\ =\ \dfrac{Force}{Area}} \\ \\ \longrightarrow \sf{Stress\ =\ \dfrac{Mass\ \times\ Acceleration}{Area}} \\ \\ \longrightarrow \sf{Stress \: = \: \dfrac{600\ \times\ 10}{0.1256}} \\ \\ \longrightarrow \sf{Stress\ =\ \dfrac{6000}{0.1256}} \\ \\ \longrightarrow \sf{Stress \: \approx \: 47770.70}$

This is stress of all the four legs.So,stress of one leg will be :

$\longrightarrow \sf{Stress \: = \: \dfrac{47770.70}{4}} \\ \\ \longrightarrow \sf{Stress \: \approx \: 11942.67} \\ \\ \dashrightarrow \underline{\boxed{\sf{Stress\ =\ 11942.67\ Nm^{-2}\ (approx) }}}$