The general definition of the average pressure P exerted by a normal (perpendicular) force F on an area A is P = F/A. The SI unit for pressure is N/m2 = Pa (Pascal). If the same force is distributed over a larger area, then the pressure is reduced. Many injuries to the human body are caused by a small area of the body being exposed to a large force and therefore high pressure.
Example:
 | Grab a pencil with one hand and press the flat end
against your other hand. Press hard. Does it hurt? Now turn the pencil around and press the tip of the pencil against your other hand with the same force. Does it hurt now? |
| A 50 kg woman balances on one heel of a high-heel shoe. If the heel is circular with radius 0.5cm, the pressure she exert on the floor is P = F/A = (50 kg 9.8 m/s2)/(p(0.005 m)2) = 6.2´106 N/m2 = 6.2 MPa. (1 MPa = 1000000 Pa) If the woman wears a flat-heel shoe with a radius of 3 cm then the pressure she exerts on the floor is P = F/A = (50 kg 9.8 m/s2)/(p(0.03 m)2) = 1.7´105 N/m2 = 0.17 MPa. The pressure she exerts is reduced by a factor of 36. Be careful around women with high-heel shoes! |
Experiment:
A hard surface can distribute the force over a larger area and therefore reduce the pressure.
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We measure change in pressure in a
precision-ground Pyrex cylinder. A
graphite piston fits snugly into the
cylinder. If a weight is put on the platform, the
pressure in the cylinder increases.
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We have two
cylinders. A pressure sensor is connected to the pressure port
of cylinder one and the output of the sensor is displayed by a
computer. The cross sectional area of the cylinder is 8.3 cm2 = 0.00083 m2. A mass m of 0.5 kg on the platform of cylinder
1 produces a force F of (1 kPa = 1000 Pa) |
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A wooden block (a hard surface) on the platform of cylinder 1 produces a pressure of 4.2 kPa in cylinder 1. |
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The block and the.5
kg mass on the platform of cylinder 1 should produce a pressure of
5.9 + 4.2 = 10.1 kPa in cylinder 1. The experimentally measured value is close to the expected value. |
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We now use the block
(the hard surface) to distribute the force over two platforms.
The block rests on the platforms of cylinder 1 and cylinder 2. The pressure in cylinder 1 drops to 5.1 kPa, approximately half the pressure measured with the force acting only on the platform connected to cylinder 1. The wooden block (hard surface) distributes the force over twice the area, and therefore the pressure decreases by a factor of 2. |
Movie:
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A balloon is
pressed against a bed of nails. When the balloon is
in contact with many nails, the pressure exerted by each
individual nail is too small to burst the balloon. When the balloon is in contact with only one nail, the force is no longer distributed over a large area and the pressure exerted by the one nail is large enough to burst the balloon. |
The bed of nails:
