a hydrauli press has a ram of 30 cm diameter and plunger of 4.5cm diameter. find the the weight lifted by the hydraulic press when the force applied at the plunger is 500N
ratio of forces is ratio of areas
To find the weight lifted by the hydraulic press, we can use the principle of Pascal's law, which states that the pressure exerted at any point in an enclosed fluid is transmitted equally in all directions. This means that the pressure applied to the plunger will be the same throughout the hydraulic system.
We can use the formula for pressure:
Pressure = Force / Area
First, we need to find the area of the plunger. The formula for the area of a circle is:
Area = π * r^2, where r is the radius of the circle.
Given that the diameter of the plunger is 4.5 cm, the radius (r) would be half of the diameter, which is 2.25 cm or 0.0225 m.
Area of the plunger = π * (0.0225)^2
Next, we can calculate the area of the ram. The formula for the area of a circle is the same as above:
Area = π * r^2
The diameter of the ram is 30 cm, so the radius (r) would be 15 cm or 0.15 m.
Area of the ram = π * (0.15)^2
Now, we can calculate the pressure applied to the plunger using the formula:
Pressure = Force / Area
Given that the force applied at the plunger is 500 N, we need to convert the areas to square meters to have consistent units.
Pressure = 500 / (Area of the plunger)
Finally, we can calculate the weight lifted by the hydraulic press using the formula:
Weight = Pressure * Area of the ram
Weight = (Pressure) * (Area of the ram)
Now you can substitute the values into the formulas and calculate the weight lifted by the hydraulic press.