How to Calculate the Weight Lifted by a Hydraulic Press

How can you calculate the weight lifted by a hydraulic press?

Given a hydraulic press with a RAM of 2.5 m diameter and a plunger of 0.8 m diameter, and a force of 7000 N applied at the plunger, how can you determine the weight lifted by the hydraulic press?

Calculation of the Weight Lifted

The weight lifted by the hydraulic press when the force applied at the plunger is 7000 N is 68,373 N.

To find the weight lifted by the hydraulic press, we can use Pascal's Law, which states that the pressure applied to a fluid in a confined space is transmitted equally in all directions. First, we can calculate the pressure exerted by the force applied at the plunger. The formula for pressure is P = F/A, where P is the pressure, F is the force, and A is the area.

The area of the plunger can be calculated using the formula for the area of a circle, A = πr^2, where r is the radius. The radius of the plunger is half of its diameter, so it is 0.8 m / 2 = 0.4 m. Therefore, the area of the plunger is A = π(0.4 m)^2 = 0.502 m^2.

Now we can substitute the values into the pressure formula: P = 7000 N / 0.502 m^2 = 13,944 Pa.

Next, we can calculate the force exerted by the RAM of the hydraulic press using the same formula. The diameter of the RAM is 2.5 m, so the radius is 2.5 m / 2 = 1.25 m. The area of the RAM is A = π(1.25 m)^2 = 4.909 m^2.

Finally, we can find the weight lifted by the hydraulic press by multiplying the pressure by the area of the RAM: Weight = P * A = 13,944 Pa * 4.909 m^2 = 68,373 N.

Therefore, the weight lifted by the hydraulic press when the force applied at the plunger is 7000 N is 68,373 N.