A hydraulic press had a ram of 30cm in diameter and aplunger of 4.5 cm in diameter . Find the weight lifted by the hydraulic press when the force of 500 N is applied at the plunger ?
500 N * (30 / 4.5)^2
To find the weight lifted by the hydraulic press, we need to use Pascal's Law, which states that the pressure exerted by a fluid in a confined space is transmitted equally in all directions.
First, we need to calculate the pressure exerted on the plunger. The formula for pressure is:
Pressure = Force / Area
The force applied is 500 N, and the area can be calculated using the formula:
Area = π * (radius)^2
The radius of the plunger can be found by dividing the diameter by 2:
Radius of plunger = Diameter of plunger / 2 = 4.5 cm / 2 = 2.25 cm
Now we can calculate the area of the plunger:
Area of plunger = π * (2.25 cm)^2 = 3.14 * (2.25 cm)^2 = 15.9 cm^2
Next, we need to find the area of the ram. The formula for area is the same:
Area = π * (radius)^2
The radius of the ram can be found by dividing the diameter by 2:
Radius of ram = Diameter of ram / 2 = 30 cm / 2 = 15 cm
Now we can calculate the area of the ram:
Area of ram = π * (15 cm)^2 = 3.14 * (15 cm)^2 = 706.5 cm^2
According to Pascal's Law, the pressure is transmitted equally to all parts of the system. Therefore, the pressure on the plunger is the same as the pressure on the ram. Mathematically, this can be written as:
Pressure on plunger = Pressure on ram
Now we can set up the equation using the pressure formula:
Force on plunger / Area of plunger = Force on ram / Area of ram
Substituting the given values, we get:
500 N / 15.9 cm^2 = Force on ram / 706.5 cm^2
Now we can solve for the force on the ram:
Force on ram = (500 N / 15.9 cm^2) * 706.5 cm^2 = 22,204 N
Therefore, the weight lifted by the hydraulic press when a force of 500 N is applied at the plunger is 22,204 N.