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Question
A 50 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter 1.0 cm. What is the pressure exerted by the heel on the horizontal floor?
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Solution 1
Mass of girl, m = 50 kg
∴Force on the heel, F = mg = 50 x 9.8 = 490 N
Diameter, D = 1.0 cm = `1 xx 10^(-2)m`
`:. "Area A" =(piD^2)/4 = (3.14xx(1xx10^(-2))^2)/4 = 7.85 xx 10^(-5) m^2`
`:. "Pressure", P = F/A = 490/(7.85xx10^(-5)) = 6.24xx10^6 "Pa"`
Solution 2
Mass of the girl, m = 50 kg
Diameter of the heel, d = 1 cm = 0.01 m
Radius of the heel = `r = d/2 = 0.005 m`
Area of the heel = `pir^2`
= π (0.005)2
= 7.85 × 10–5 m2
Force exerted by the heel on the floor:
F = mg
= 50 × 9.8
= 490 N
Pressure exerted by the heel on the floor:
`P = "Force"/"Area"`
`= 490/(7.85xx10^(-5))`
= 6.24 × 106 N m–2
Therefore, the pressure exerted by the heel on the horizontal floor is 6.24 × 106 Nm–2.
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