An hydraulic press has an input cylinder of 2cm diameter and an output cylinder of 6cm diameter. Find the force exerted by the output piston when a force of 20N is applied to the input piston.
To find the force exerted by the output piston in an hydraulic press system, we can use the principle of Pascal's law. According to Pascal's law, the pressure exerted in a fluid is transmitted uniformly in all directions.
To solve this problem, we need to determine the pressure applied to the fluid by the input piston and then use this pressure to calculate the force exerted by the output piston.
Step 1: Calculate the pressure exerted by the input piston:
The formula to calculate pressure is:
Pressure = Force / Area
The area of a cylinder is given by the formula:
Area = π * (radius^2)
Given that the diameter of the input piston is 2cm, the radius can be calculated as:
radius = diameter / 2 = 2cm / 2 = 1cm = 0.01m (convert cm to m)
Therefore, the area of the input piston is:
Area = π * (0.01m)^2
Step 2: Calculate the pressure exerted by the input piston:
We are given that the force applied to the input piston is 20N. Therefore, the pressure exerted by the input piston is:
Pressure = Force / Area
Step 3: Calculate the force exerted by the output piston:
To find the force exerted by the output piston, we need to use the principle of Pascal's law, which states that the pressure is transmitted uniformly throughout the fluid in all directions. Therefore, the pressure exerted by the input piston is equal to the pressure exerted by the output piston.
The pressure exerted by the output piston can be calculated using the formula:
Pressure = Force / Area
Given that the diameter of the output piston is 6cm, we can calculate the area of the output piston using the formula:
Area = π * (radius^2)
The radius of the output piston can be calculated as:
radius = diameter / 2 = 6cm / 2 = 3cm = 0.03m (convert cm to m)
Therefore, the area of the output piston is:
Area = π * (0.03m)^2
The pressure exerted by the output piston is equal to the pressure exerted by the input piston. So, we can set up the following equation:
Pressure by input piston = Pressure by output piston
Force on input piston / Area of input piston = Force on output piston / Area of output piston
Plugging in the known values:
20N / Area of input piston = Force on output piston / Area of output piston
Step 4: Calculate the force exerted by the output piston:
Rearrange the equation to solve for the force exerted by the output piston:
Force on output piston = (Force on input piston / Area of input piston) * Area of output piston
Plug in the values:
Force on output piston = (20N / Area of input piston) * Area of output piston
Evaluate the expression to find the force exerted by the output piston.
As I recall, the force grows as the ratio of the areas of the pistons. That means, as the square of the diameter.
So, since 6 = 3*2, the force would be 3^2 * 20
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