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
F/a=w/A
W=FA/a
W=500*(30^2)/(4.5^2)
W=22222.22N
W=22.22KN
i want answer
7. A hydraulic press has a ram of 35 cm diameter and a plunger of 5 cm diameter. It is used for lifting a weight of 30KN. Find the force required at the plunger in kN.
Well, let's dive into this hydraulics problem, shall we?
To find the weight lifted by the hydraulic press, we need to consider the principle of Pascal's Law, which states that pressure applied to an enclosed fluid is transmitted equally in all directions.
Now, we have the force applied at the plunger, which is 500 Newtons. We can use this force to determine the pressure exerted on the fluid. But first, let's calculate the area of the plunger.
The area of a circle is calculated using the formula: A = π * r², where r is the radius.
For the plunger, the radius is half the diameter, which is 4.5cm / 2 = 2.25cm = 0.0225m. So, the area of the plunger is:
A = π * (0.0225m)²
Calculating this gives us the area of the plunger, which is a tiny 0.00159 square meters.
Now, let's calculate the pressure exerted on the fluid. Pressure is defined as force divided by area, so:
Pressure = Force / Area = 500N / 0.00159m²
Crunching the numbers (not literally, this is not a hydraulic press), we find that the pressure exerted on the fluid is approximately 314,465.41 Pascals.
Now, this pressure is transmitted throughout the enclosed fluid, including the ram. Since the ram has a larger surface area than the plunger, it will be able to lift a much heavier weight.
To find the weight lifted, we need to calculate the force exerted by the ram. We can use the same formula: Pressure = Force / Area.
Let's call the force exerted by the ram "F".
So, the equation becomes: 314,465.41 Pascals = F / (π * (0.15m)²), where 0.15m is the radius of the ram (half of the 30cm diameter).
Solving this equation for F, we get F ≈ 70613.66 Newtons.
That means the hydraulic press can lift a weight of approximately 70,613.66 Newtons when the force applied at the plunger is 500 Newtons.
So, with a hydraulic press like this, you can lift a heavy load, or as they say, "press on" with your heavy-duty lifting needs!
To find the weight lifted by the hydraulic press, we need to understand the principle of Pascal's Law, which states that when pressure is applied to a fluid in a confined space, the pressure is transmitted equally in all directions.
In this case, the force (F1) applied to the plunger is 500N, and the diameter of the plunger (D1) is 4.5cm. Therefore, we can calculate the surface area of the plunger using the formula:
A1 = (π * D1^2) / 4
Now, we can determine the pressure (P1) applied to the fluid by dividing the force (F1) by the surface area (A1):
P1 = F1 / A1
Next, we need to consider the ram of the hydraulic press, which has a diameter (D2) of 30cm. By using the same formula, we can calculate the surface area of the ram (A2):
A2 = (π * D2^2) / 4
Since the pressure is transmitted equally, the pressure at the ram (P2) will be the same as the pressure at the plunger (P1). Therefore, we can calculate the force (F2) exerted by the ram using the formula:
F2 = P2 * A2 = P1 * A2
Finally, substituting the values into the formula, we can find the weight lifted by the hydraulic press:
F2 = P1 * A2 = (F1 / A1) * A2
Now, let's calculate the weight lifted:
Step 1: Calculate the surface area of the plunger (A1):
A1 = (π * D1^2) / 4 = (3.14 * 4.5^2) / 4 = 15.904 cm^2
Step 2: Calculate the pressure applied to the fluid (P1):
P1 = F1 / A1 = 500N / 15.904 cm^2 = 31.43 N/cm^2
Step 3: Calculate the surface area of the ram (A2):
A2 = (π * D2^2) / 4 = (3.14 * 30^2) / 4 = 706.5 cm^2
Step 4: Calculate the weight lifted (F2) by the hydraulic press:
F2 = P1 * A2 = 31.43 N/cm^2 * 706.5 cm^2 = 22,181.895 N
Therefore, the weight lifted by the hydraulic press is approximately 22,181.895 N.
the answer of the questions
the force is proportional to the square of the diameter
w = (30 / 4.5)^2 * 500 N