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?
Given:
Mass of the girl (m) = 50kg
Diameter of the heel (d) = 1.0cm
Radius of the heel (r) = d/2 = 0.5cm
Area of the heel(A) = π × r2
= π × (0.5 × 10-2 m)2
= 7.8539 × 10-5 m2
We know that Pressure (P) = F/A
F = Force exerted by heel on the floor
A = Area of the heel
F = m × g where m = mass of the girl
= 50 kg × 9.8 m/s2 g = acceleration due to gravity
= 490 N
P = F/A
= 490 N/(7.8539 × 10-5) m2
= 6.24 × 106 N/m2
Pressure exerted by heel on the horizontal floor is 6.24 × 106N/m2