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pascal (unit of pressure or stress)

The pascal (pronounced pass-KAL and abbreviated Pa) is the unit of pressure or stress in the International System of Units (SI). It is named after the scientist Blaise Pascal. One pascal is equivalent to one newton (1 N) of force applied over an area of one meter squared (1 m2). That is, 1 Pa = 1 N · m-2. Reduced to base units in SI, one pascal is one kilogram per meter per second squared; that is, 1 Pa = 1 kg · m-1 · s-2.

If a pressure p in pascals exists on an object or region whose surface area is A meters squared, then the force F, in newtons, required to produce p is given by the following formula:

F = pA

Suppose a small rocket engine produces 100,000 (105) Pa of pressure, and the nozzle has a cross-sectional area of 1/10,000 of a square meter (10-4 m2). Then the force F, in newtons, produced by the engine is:

F = pA = 105 x 10-4 = 10

Imagine that this engine is used in a propellant pack for a space walker whose mass is 50 kg. How fast will the person accelerate relative to nearby objects in the weightless environment of earth orbit? The answer is found by the familiar formula stating that force is equal to mass times acceleration (F = ma). This can be manipulated to obtain:

a = F / m

where a is the acceleration in meters per second squared, F is the force in newtons, and m is the mass in kilograms. Plugging in the known numbers:

a = 10 / 50 = 0.20

The acceleration is 0.20 m/s2. If the rocket engine is fired continuously by a space walker who is stationary relative to another object nearby, then after one second she will be moving at a speed of 0.20 m/s with respect to that object; after two seconds she will be traveling at 0.40 m/s; after three seconds she will be moving at 0.60 m/s; and so on.

Also see kilogram, meter, meter per second, meter per second squared, newton, second, SI, and Table of Physical Units.

This was last updated in September 2005

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