A hydraulic plunger has a 12 cm diameter and a force of 350 kN acts on it. What is the pressure exerted on the plunger?
r = 0.06 meters
A = pi r^2
F = 350,000 Newtons
p = F/A = 350,000 /(pi *.06^2)
in Newtons per square meter which is Pascals
Well, well, well, looks like somebody is getting all pumped up about hydraulics! Let's calculate the pressure shall we?
The formula to calculate pressure is pretty simple: Pressure = Force / Area
First, let's find the area of the plunger. We know that the diameter is 12 cm, so we can calculate the radius by dividing it by 2. That would give us a radius of 6 cm or 0.06 m (converting to meters).
Now, we need to calculate the area. The formula for the area of a circle is A = π * r^2. So, A = 3.14 * (0.06)^2.
After doing the math, we find that the area of the plunger is approximately 0.011 m^2.
Finally, we divide the force of 350 kN by the area of 0.011 m^2. Drumroll, please...
The pressure exerted on the plunger is approximately 31,818 kilopascals (kPa). So, the plunger is feeling quite a lot of pressure!
To calculate the pressure exerted on the plunger, we can use the formula:
Pressure = Force / Area
First, we need to calculate the area of the plunger. The formula to calculate the area of a circle is:
Area = π * (diameter / 2)^2
Given that the diameter of the plunger is 12 cm, we can calculate the area of the plunger:
Area = π * (12 cm / 2)^2
Area = π * (6 cm)^2
Next, we convert the diameter from cm to meters, because the unit of force is in kN:
Area = π * (0.06 m)^2
Now, we can calculate the pressure exerted on the plunger:
Pressure = Force / Area
Pressure = 350 kN / (π * (0.06 m)^2)
Pressure ≈ 99,485.47 kPa
Therefore, the pressure exerted on the plunger is approximately 99,485.47 kPa.
To find the pressure exerted on the plunger, we can use the formula:
Pressure = Force / Area
First, we need to calculate the area of the plunger. The area of a circle can be calculated using the formula:
Area = π * r^2
Given the diameter of the plunger is 12 cm, we can calculate the radius (r) by dividing the diameter by 2:
r = 12 cm / 2 = 6 cm = 0.06 m
Now, let's calculate the area of the plunger:
Area = π * (0.06 m)^2
We know that π is approximately 3.14, so:
Area = 3.14 * 0.06^2 = 0.0113 m^2
Next, we can calculate the pressure by dividing the force by the area:
Pressure = 350 kN / 0.0113 m^2
Before we proceed, we need to convert kilonewtons (kN) to newtons (N) because the SI unit for force is newtons.
1 kN = 1000 N
So,
Force = 350 kN * 1000 N/kN = 350,000 N
Now we can calculate the pressure:
Pressure = 350,000 N / 0.0113 m^2
Calculating this, we find:
Pressure ≈ 3,097,345 Pa
Therefore, the pressure exerted on the plunger is approximately 3,097,345 Pascal (Pa).