Each cyclist must convert the energy stored in his or her muscles into torque to move the pedals. To go uphill, the necessary rate of work (power) increases as does the required torque. (Corbis Corporation) Pressure
Pressure is force divided by the area over which the force acts:
or
In the metric system, pressure has a unit of newtons per square meter, which is called a pascal (Pa). Although the pascal is the scientific unit and is preferred, pounds per square inch (lbs/in2) is common in the United States. For example, in most of Europe, tire pressure is recorded in pascals (typically 220,000 Pa), whereas tire pressure in American cars is measured in pounds per square inch (typically 32 lbs/in2). As a point of reference, the pressure that the earth's atmosphere exerts on anything at the earth's surface is roughly 100,000 Pa or 15 lbs/in2.
A large pressure does not necessarily mean a large force because a large pressure can be accomplished by making the contact area small. For example, a 160-pound man having fifty square inches in his shoe soles produces a pressure of 3.2 lbs/in2 on the ground when he stands flatfooted. But the same person wearing ice skates having 2.5 square inches in the runners of the blades produces a pressure of 64 lbs/in2 when standing on ice. When a person pushes down on the head of a thumbtack, the pressure at the point is quite large because the contact area of the sharp thumbtack is small.
Blaise Pascal, the French scientist for whom the pascal pressure unit is named, was the first to discover that a pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and the walls of the containing vessel. The earth's atmosphere exerts a pressure on the surface of water in a swimming pool (a container) and this pressure is felt equally throughout the pool including the walls. This principle is employed in a hydraulic press that has many applications. The pressure due to the force f on the piston of area a is P = f/a. The piston of area A feels a force F creating a pressure P = F/A. According to Pascal's principle, the two pressures are equal so that F/A = f/a or F = (A/a)f. If the area A is larger than a, then the force F is larger than f. Therefore, a small force on the left piston causes a larger force on the right piston. Lifting an object requires an upward force larger than the weight of the object. This is why rather massive objects such as automobiles, trucks, and elevators can be lifted with a hydraulic press. For example, a car weighing 10,000 N (about 2,000 pounds) can be raised with a hundred N force if the ratio of the areas of the pistons (A/a) is one hundred.
Work is done by both forces when the pistons move and the larger force cannot do more work (force × displacement) than the smaller force. Accordingly, the larger piston moves a much smaller distance than the smaller piston. Theoretically, if the ratio of the areas is one hundred then the smaller piston must move one hundred times further than the larger piston.
The mechanism for rotating the wheels in a car or truck has its origin in pistons in the engine that are forced to move by expanding gases in the cylinders. The expanding gas is a result of igniting a mixture of gasoline vapor and air. An expanding gas exerts a force on a piston doing work as the piston moves. In principle, it is no different than a person doing work by pushing a box on the floor of a hallway. The energy for the work comes from the energy of the gas produced by the ignition of the gasoline vapor and air mixture. As in the calculation of work done by a constant force the work done by the gas is the product of the force (F) and displacement (d, the distance the piston moves). Because the force on the piston is equal to the pressure (P) times the area (A) of the piston the work (W) can be written W = PAd. The quantity Ad is just the change in volume (ΔV) of the gas so that the work can also be written as W = PΔV. This is the basic idea in determining the performance of engines, which are used to power cars, trucks, and all sorts of other equipment.
The expansion of a balloon when it is inflated is evidence of the pressure exerted on the interior walls by molecules blown into the balloon. If you tie off the open end of the balloon, you can squeeze the balloon with your hands and actually feel the result of the pressure in the balloon. If you were to cool the balloon you find that the pressure goes down. Warming causes the pressure to increase. This happens also with the pressure in an automobile tire after it has warmed by running on a road. When there is no change in the pressure, temperature, and volume, we say the gas is in equilibrium. The pressure, volume, and temperature of a gas in equilibrium and how they are related is an important feature for describing the behavior of a gas when the gas does work. The relationship for all possible variations of P, V, and T is very complicated, but for moderate temperatures (around 300 K or 70°F) the equilibrium state of all gases is given by PV = NkT where N is the number of atoms (or molecules) and k is the Boltzmann constant, 1.38 × 10-23 joules/kelvin. A gas is said to be ideal if it subscribes to the relationship PV = NkT and the equation is called the ideal gas equation.
Bibliography
Hobson, A. (1999). Physics: Concepts and Connections. Englewood Cliffs, NJ: Prentice-Hall.
Priest, J. (2000). Energy: Priciples, Problems, Alternatives, 5th ed. Dubuque, IA: Kendal/Hunt Publishing.
Serway, R. A. (1997). Physics for Scientists and Engineers, 4th ed. Fort Worth, TX: Saunders College Publishing.
Serway, R. A., and Faughn, J. (1999). College Physics, 5th ed. Fort Worth: Saunders College Publishing.
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