Final answer:
The force exerted on a piston is calculated using Pascal's principle, which is demonstrated in the context of an automobile hydraulic system. By knowing the pressure and the area of the piston, one can find the force using the formula: force = pressure × area. The given example in hydraulics considers a slave cylinder with a known force exertion, illustrating Pascal's principle in action.
Step-by-step explanation:
The calculation of the force exerted on a piston relies on Pascal's principle, which states that pressure applied to a confined fluid is transmitted undiminished throughout the fluid. This is a fundamental concept within hydraulics and fluid mechanics. In the automobile hydraulic system example, the pressure created in a master cylinder is transferred to the slave cylinders, leading us to calculate the force exerted on these slave components based on their surface areas.
Given a slave piston with a surface area of 40 cm² (which is 0.004 m² in SI units), we use the formula force (F) = pressure (P) × area (A) to find the force exerted on this piston. Prior information states that each slave cylinder will exert a force of 1.25×10´ N, which demonstrates Pascal's principle where the force applied to the master cylinder is amplified in the slave cylinders due to their larger surface areas.
To apply this in practice, let us consider a hypothetical scenario where a master cylinder has a force of 500 N exerted on it. If the pressure transmitted to the slave piston with a 40 cm² surface area is the same as in the master cylinder, the calculation would be straightforward: simply multiply the pressure in the master cylinder by the area of the slave piston. However, to perform this calculation, one would require the pressure exerted on the master cylinder, which can be derived from the force and the cross-sectional area of the master cylinder.