The large piston in hydraulic mechanism moves a distance of 20mm with a force of 30n the small piston moves a distance of 50mm.what force is required to move the small piston?
To determine the force required to move the small piston in a hydraulic mechanism, we can use Pascal's Law, which states that the pressure exerted in a fluid is transmitted uniformly in all directions. In a hydraulic system, the pressure is the same for both pistons.
Here's how to get the answer:
1. Determine the area of the large piston (A1) by using the formula: Area = π * (radius)^2.
2. Determine the area of the small piston (A2) using the same formula.
3. Utilize the equation: Pressure1 = Pressure2 to calculate the force required to move the small piston (F2). Rearranging the equation gives us: F2 = (Pressure1 * A1) / A2.
4. Calculate the pressure (Pressure1) by dividing the force applied to the large piston (30 N) by its area (A1).
5. Plug in the values and solve for F2.
Let's calculate step by step:
1. Suppose the radius of the large piston is r1. Calculate the area of the large piston (A1): A1 = π * (r1)^2.
2. Suppose the radius of the small piston is r2. Calculate the area of the small piston (A2): A2 = π * (r2)^2.
3. Calculate Pressure1: Pressure1 = Force1 / A1 = 30 N / A1.
4. Calculate F2: F2 = (Pressure1 * A1) / A2 = (Pressure1 * π * (r1)^2) / (π * (r2)^2).
5. Finally, substitute the given values for Pressure1, A1, and A2 into the equation to find the force (F2) required to move the small piston.
By following these steps, you can compute the force required to move the small piston in the hydraulic mechanism.