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.
(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 = 40000N
Area of one foot = 1000 cm2
= 1000 x 10-4 m2
Weight of girl = 400N
Area of heel of girl = 1 cm2
= 1 x 10-4 m2
(a) Elephant has a larger weight of 40000N, therefore, elephant exerts a larger force on the ground.
Elephant exerts a larger force on the ground by 40000N – 400 N = 39600N.
(b)Weight of elephant = 40000N
Area of one foot = 1000 cm2 = 1000 x 10-4 m2
Pressure = \(\frac{Force}{Area}\)
Pressure = \(\frac{40000}{1000 \times 10^{-4}}\)
= 400000 N/m2
(c) Weight of the girl = 400 N
Area of heel of girl = 1 cm2 = 1 x 10-4 m2
Pressure = \(\frac{Force}{Area}\)
Pressure = \(\frac{400}{1 \times 10^{-4}}\)
= 4000000 N/m2
(d) Girl exerts a larger pressure on the ground.
(e) Ratio = \(\frac{Pressure\;exerted\;by\;the\;girl}{Pressure\;exerted\;by\;the\;elephant}\)
= \(\frac{4000000}{400000}\) = \(\frac{10}{1}\)
The pressure exerted by girl is 10 times greater than that exerted by the elephant.