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 ?
Solution and Explanation
Mass of the girl, m = 50 kg
Diameter of the heel, d = 1 cm = 0.01 m
Radius of the heel,\( r = \frac{d }{ 2}\) = 0.005 m
Area of the heel = πr2
= 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 :
\(P = \frac{Force }{ Area }\)
\(= \frac{490 }{7.85 × 10 ^{- 5}} \)
= 6.24 × 10 6 N m - 2
Therefore, the pressure exerted by the heel on the horizontal floor is 6.24 × 10 6 N m-2.
Top Questions on Pressure
- The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of \( 7 \times 10^6 \) Pa, would be _____ mm\(^3\). (Given bulk modulus of copper = \( 1.4 \times 10^{11} \) N m\(^{-2}\))
- The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of \( 7 \times 10^6 \) Pa, would be ________________________ mm\(^3\). (Given bulk modulus of copper = \( 1.4 \times 10^{11} \) N m\(^{-2}\))
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- Pressure inside a soap bubble is greater than the pressure outside by an amount;(given : R = Radius of bubble, S = Surface tension of bubble)
- Mercury is filled in a tube of radius \(2 \, \text{cm}\) up to a height of \(30 \, \text{cm}\). The force exerted by mercury on the bottom of the tube is ___N.
(Given, atmospheric pressure = \(10^5 \, \text{N/m}^2\), density of mercury = \(1.36 \times 10^4 \, \text{kg/m}^3\), \(g = 10 \, \text{m/s}^2\), \(\pi = \frac{22}{7}\))
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Concepts Used:
Pressure
Pressure is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Everyday examples of pressure are:
- The working of the vacuum cleaner is an example of pressure. The fan inside the vacuum creates a low-pressure region which makes it easy to suck the dust particles inside the vacuum.
- Using a knife for cutting is another example of pressure. The area exposed from the knife is small but the pressure is high enough to cut the vegetables and fruits.
Formula:
When a force of ‘F’ Newton is applied perpendicularly to a surface area ‘A’, then the pressure exerted on the surface by the force is equal to the ratio of F to A. The formula for pressure (P) is:
P = F / A
Units of Pressure:
The SI unit of pressure is the pascal (Pa)
A pascal can be defined as a force of one newton applied over a surface area of a one-meter square.