Final answer:
To find the diameter of the largest piston in the hydraulic press, we can use Pascal's Law and the formula for pressure. Once we calculate the force exerted by the smaller piston, we can use the equation for pressure to find the diameter of the larger piston. Finally, we can substitute the values and solve for the diameter of the largest piston.
Step-by-step explanation:
To calculate the diameter of the largest piston in the hydraulic press, we can use the principle of Pascal's Law. According to Pascal's Law, the pressure applied to a fluid is transmitted uniformly in all directions. In this case, the smaller piston has a radius of 0.200 m and a force of 25.0 N is exerted on it. The larger piston, which is used to lift the vehicle, supports the weight of the vehicle. We can calculate the force exerted by the larger piston using the formula:
Force1/Force2 = Area1/Area2
First, let's calculate the area of the smaller piston:
Area1 = π * radius1^2
Substituting the values, we have:
Area1 = π * (0.200 m)^2
Next, we can calculate the force exerted by the larger piston:
Force2 = Force1 * (Area2/Area1)
Substituting the values, we have:
Force2 = 25.0 N * (Area2 / (π * (0.200 m)^2)
We can rearrange the equation to solve for the diameter of the larger piston:
Diameter2 = 2 * sqrt((Force2 * 4) / (π * Pressure))
Substituting the known values, we can calculate the diameter of the largest piston:
Diameter2 = 2 * sqrt((Force2 * 4) / (π * Pressure))
Learn more about Pascal's Law