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Question

A 60 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a radius 1 cm. What will be the pressure exerted by the heel on the horizontal floor?

A
1.87×103 pascal
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B
1.78×103 pascal
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C
1.87×106 pascal
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D
1.78×106 pascal
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Solution

Step 1: Given that:

The mass(m ) of the girl= 60kg

The radius(r ) of the circular heel of the girl= 1cm=1100cm=0.01m


Step 2: Calculation of pressure exerted by the heel on the horizontal floor:

Pressure= Force(F)Area(A)

Force applied by girl on the floor= Weight of the girl

Thus,

F=mg =60kg×9.8ms2=588N

Where g is the acceleration due to gravity.

Now,

Area of the heel of the girl= π×(0.01m)2=0.0001πm2

A=0.0001×227m2

A=0.00227m2

A=22×1047m2

Hence,

The pressure applied by the heel of the girl will be;

P=588N22×1047m2

P=588×722×104

P=411622×104

P=187.1×104

P=1.87×106Pa

Thus,

The pressure applied by the heel of the girl on the floor will be 1.87×106Pa


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