Small piston in hydraulic system experience a force of 12n and moves a distance of 50mm the large piston experience a force of 24n.calculate the distance that the large piston will move
To calculate the distance that the large piston will move, we can use the principle of Pascal's Law, which states that the pressure applied to a fluid in a closed system is transmitted equally in all directions.
In a hydraulic system, the pressure exerted by the small piston will be equal to the pressure exerted by the large piston. We can determine this by comparing the forces applied to each piston, using the equation:
Force = Pressure × Area
Since the force on the small piston is 12 N and the force on the large piston is 24 N, we can write two equations:
12 N = P × A1 (for the small piston)
24 N = P × A2 (for the large piston)
Here, P represents the pressure, A1 represents the area of the small piston, and A2 represents the area of the large piston.
To find the distance the large piston will move, we need to determine the ratio of the areas between the small and large pistons. This is because the force applied by the smaller piston will be transmitted to the larger piston, causing it to move a greater distance.
The ratio of the areas can be expressed as:
A2/A1 = F2/F1
where A2 and A1 are the areas of the large and small pistons, respectively, and F2 and F1 are the forces applied to the large and small pistons, respectively.
In this given situation, we have:
A2/A1 = 24 N / 12 N
Simplifying, we find:
A2/A1 = 2/1
This means that the area of the large piston is twice the area of the small piston.
Now, let's calculate the distance that the large piston will move, denoted by d2:
d2 = (A1/A2) × d1
where d1 is the distance moved by the small piston.
Since the area ratio is 1/2 and the small piston moves a distance of 50 mm, we can substitute these values into the equation:
d2 = (1/2) × 50 mm = 25 mm
Therefore, the large piston will move a distance of 25 mm.