Final answer:
The question is about applying Pascal's law in a hydraulic system to calculate the force required on the pedal cylinder to lift a 2000-kg car. Using the provided diameters, the areas of both cylinders can be calculated and then used to find the required force, demonstrating the force amplification in hydraulic systems.
Step-by-step explanation:
The physics question is asking for the force needed to be exerted on the pedal cylinder of a hydraulic system to support the weight of a 2000-kg car. In such a scenario, the hydraulic press is the essential element that uses the principles of pressure transmission through a fluid to exert a greater force on the larger cylinder (wheel cylinder) when a smaller force is applied to the smaller cylinder (pedal cylinder). This occurs due to the fact that the pressure exerted must be equal on both sides of the system (Pascal's law), and since pressure is defined as the force divided by the area, the larger area on the wheel cylinder results in a larger force to support the weight of the car.
By using the diameters provided, one can find the areas of the pedal and wheel cylinders and thus calculate the force required using the formula for hydraulic lift mechanics:
- Area of pedal cylinder = π * (diameter/2)^2
- Area of wheel cylinder = π * (diameter/2)^2
- Force exerted by the car = Weight of the car = mass * acceleration due to gravity
- Force required on the pedal cylinder = (Area of pedal cylinder / Area of wheel cylinder) * Force exerted by the car
As shown, it can be seen that hydraulic systems can, indeed, increase force, allowing smaller input forces to lift heavy loads, which has practical applications in various forms of machinery and in nature, as with the jumping spider mentioned. This system leverages the conservation of work where a smaller input force travels over a larger distance to apply a larger output force, which moves over a smaller distance.