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
D- 4.0N
To calculate the output force of the hydraulic press, we can use the principle of Pascal's law, which states that the pressure exerted in a confined fluid is transmitted equally in all directions.
Since the hydraulic press has a larger input piston and a smaller output piston, the force will be magnified. The relationship between the force and the area of the pistons is given by the formula:
Force = Pressure × Area
The pressure is the same throughout the system, so we can calculate the force ratio based on the ratio of the areas of the pistons:
Force ratio = Area output / Area input
Given that the diameter of the input piston is 20mm, we can calculate the area input:
Area input = π × (diameter input / 2)^2
= π × (20mm / 2)^2
= 314.16 mm^2
Similarly, for the output piston with a diameter of 10mm, we can calculate the area output:
Area output = π × (diameter output / 2)^2
= π × (10mm / 2)^2
= 78.54 mm^2
Now we can calculate the force ratio:
Force ratio = Area output / Area input
= 78.54 mm^2 / 314.16 mm^2
= 0.25
Therefore, the output force will be 0.25 times the input force.
Given that the input force is 1.0N, the output force will be:
Output force = Force ratio × Input force
= 0.25 × 1.0N
= 0.25N
Therefore, the correct answer is a) 0.25N.
To determine the output force of a hydraulic press, we can use the principle of Pascal's law, which states that the pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.
The formula to calculate force in a hydraulic system is:
Force = Pressure x Area
Given that the input piston has a diameter of 20mm and the output piston has a diameter of 10mm, we can find the respective areas by using the formula:
Area = π * (radius)^2
For the input piston:
Radius = (20mm / 2) = 10mm = 0.01m
Area = π * (0.01m)^2 = 0.000314 m^2
For the output piston:
Radius = (10mm / 2) = 5mm = 0.005m
Area = π * (0.005m)^2 = 0.0000785 m^2
Now, we know that the input force is 1.0N. To find the output force, we can rearrange the formula:
Force (output) = Pressure (output) x Area (output)
Since the pressure is the same in a hydraulic system, we don't need to calculate it. Therefore:
Force (output) = Force (input) x (Area (output) / Area (input))
= 1.0N x (0.0000785 m^2 / 0.000314 m^2)
= 1.0N x 0.25
Hence, the output force will be:
1.0N x 0.25 = 0.25N
Therefore, the correct answer is a) 0.25N.