The diameter of ram and plunger of a hydraulic press are 200 mm and 30 mm respectively.find the weight lifted by the hydraulic press when the force applied at the plungeris 400 N
The diameter of ram and plunger of an hydraulic press are 200mm and 30mm respectively. Find the weight lifted by the hydraulic press, if 400N force is applied at the plunger.
pressure the same in both cylinders
so gain (mechanical advantage) = ratio of piston areas
ratio of areas is 200^2/30^2 = 44.4
400 * 44.4 = ?
i need answers
Answer please
The diameter of ram and plunger of a hydraulic press are 200 mm and 30 mm respectively.find the weight lifted by the hydraulic press when the force applied at the plungeris 400 N
Well, let's see. Since we know the diameter of the ram and the plunger, we can find their respective areas. The area of the ram is pi times the radius squared, which is approximately 31416 square millimeters. The area of the plunger is pi times the radius squared, which is approximately 706.86 square millimeters.
Now, to find the weight lifted by the hydraulic press, we can use the formula:
weight = force / (Area of ram / Area of plunger)
So, let's plug in the values:
weight = 400 N / (31416 mm^2 / 706.86 mm^2)
And... drumroll please... the weight lifted by the hydraulic press is approximately 10.47 N.
Now, that might not sound like a lot, but hey, it's still impressive for a little hydraulic press. It's like lifting a bag of oranges or a small sack of potatoes. So, get yourself a hydraulic press and start lifting those spuds!
To find the weight lifted by the hydraulic press, we need to understand how hydraulic systems work.
In a hydraulic system, pressure is transmitted equally throughout an incompressible fluid. This means that the pressure at any point in the system will be the same. With this information, we can use the principle of Pascal's law, which states that the pressure applied to a fluid in a confined space is transmitted undiminished to every portion of the fluid and the walls of the container.
Now, let's calculate the surface area of the ram and plunger:
Surface area of the ram = π * (diameter of ram)^2 / 4
= π * (200 mm)^2 / 4
= 31416 mm^2
Surface area of the plunger = π * (diameter of plunger)^2 / 4
= π * (30 mm)^2 / 4
= 706.86 mm^2
According to Pascal's law, the pressure applied at the plunger will be transmitted equally to the ram. So, the pressure exerted at the plunger is given by:
Pressure = Force / Surface area of the plunger
= 400 N / 706.86 mm^2
≈ 0.566 N/mm^2
Now we can calculate the force exerted by the ram using the pressure and its surface area:
Force = Pressure * Surface area of the ram
= 0.566 N/mm^2 * 31416 mm^2
≈ 17800.38 N
Therefore, the weight lifted by the hydraulic press when the force applied at the plunger is 400 N is approximately 17800.38 N.