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Mechanical Systems Topic 4: Force, Pressure, and Area When force acts over a certain area it is called pressure. If the force is constant (the same) but if the area changes, so does the pressure. i.e. snow shoes do not push down with any less force, but by increasing the area you decrease the pressure. An equation for this can be written as: Pressure = _Force_ = _F_ Area A Units: Force is measured in Newtons, N. Area is measure in meters squared, m2. Therefore pressure is measure in Newtons per meter squared, N/m2. 1 N/m2 = 1 Pascal (Pa), usually measured by the thousand, kPa. Pascal’s Law Pascal’s law states that if pressure is exerted on a contained fluid than it will be transmitted in all directions throughout the fluid and perpendicular to walls of the container. A hydraulic lift uses these principles to lift heavy objects. Fluid pressure is used in a closed system (or self contained collection of parts) Your circulatory system is a closed hydraulic system. A hydraulic system consists of a small cylinder, and a large cylinder, a connecting pipe, and fluid (usually oil). Each cylinder will also have a type of platform closing it off. In this hydraulic lift, pressure applied to a small piston is transmitted to a large piston by means of a hydraulic fluid. By manipulating the pressure equation to be: p x A= F You can understand the mechanical advantage of hydraulics. If you applied 500N of force to a 5cm2 piston it would produce 100Pa of pressure in the fluid. p=F/A 500N/5cm2= 100Pa If the piston on the other side was 50cm2 then the 100Pa of pressure acting on it would produce a force of 5000N. Because the piston is 10 times larger in area it will produce 10 times as much force. What is Work? Work occurs when you are exerting a force on an object that causes it to move. The equation for work is: Work= Force x distance Or W= F x d The units for work are joules (or J) A joule is the amount of work it takes to move a 1N weight 1m. Pascal’s Law and Mechanical Advantage The area of the small piston is 1 unit. If you push down on the piston with a force of 10 N, you will generate a pressure in the fluid of 10 N per unit of area. The large piston has an area of 9 units. According to Pascal’s law the pressure on every unit of area of the large piston with be 10 N. __10 N__ unit area = 90N x 9 unit areas By exerting 10 N of effort force you could cause the large piston to exert 90 N of force on the load. Therefore, the hydraulic lift provides a mechanical advantage. The mechanical advantage of hydraulics can be written as: MA = Load Force = 90 N = 9 Effort Force 10 N If the MA is 9. Then the force on the larger piston will be 9 times greater than the force on the smaller piston. However you will have to move the small piston 9 times further than the large one. This is because the total work done must be equal in both pistons. Work (effort) = Work (load) This can be shown in the equation: Work = Force x Distance or W=Fxd