The input piston of a hydraulic press is 20mm in diameter, and the output piston is 10mm in diameter. an input force of 1.0N will produce an output force of:
a- 0.25N
b- 0.50N
c- 2.0N
D- 4.0N
To calculate the output force of a hydraulic press, you can use the formula:
Output Force = (Input Force * Output Area) / (Input Area)
Given:
- Diameter of input piston (D1) = 20mm
- Diameter of output piston (D2) = 10mm
- Input Force (F1) = 1.0N
First, let's calculate the areas of the pistons:
- Input Area (A1) = π * (D1/2)^2 = π * (20/2)^2 = 314.16 mm^2
- Output Area (A2) = π * (D2/2)^2 = π * (10/2)^2 = 78.54 mm^2
Now, we can substitute these values into the formula:
Output Force = (Input Force * Output Area) / (Input Area)
Output Force = (1.0N * 78.54 mm^2) / 314.16 mm^2
Output Force = 0.25N
Therefore, the correct answer is a- 0.25N.
To determine the output force of a hydraulic press, you can use Pascal's Law, which states that pressure is transmitted equally in all directions in an enclosed fluid.
The formula to find the relationship between force, pressure, and area is: Force = Pressure × Area.
In this case, the input piston has a diameter of 20mm, which means its radius is 10mm (half of its diameter). The output piston has a diameter of 10mm, so its radius is 5mm.
To find the ratio of the input and output areas, you need to square the ratio of their radii.
The ratio of the input piston radius to the output piston radius is 10mm/5mm = 2, which means the input piston radius is twice that of the output piston radius.
Now, square the ratio: 2^2 = 4.
This means that the input piston area is 4 times greater than the output piston area.
Given an input force of 1.0N, the output force can be found by multiplying the input force by the ratio of the output to input area.
Output force = (Output piston area / Input piston area) × Input force
Output force = (1/4) × 1.0N = 0.25N
Therefore, the correct answer is a) 0.25N.