A piston has a diemaeter of .64 cm. A second piston has a diameter of 3.8 cm. determine the Force necessary on Piston A to support the 500.0 Newton weight on piston B (in the absence of friction.)
To determine the force necessary on Piston A to support the weight on Piston B, we can use the principle of Pascal's law, which states that pressure is transmitted equally in all directions within an enclosed fluid.
Step 1: Calculate the area of Piston A.
To calculate the area of a piston, we can use the formula:
Area = π * (radius)^2
Since the diameter of Piston A is given as 0.64 cm, we first need to calculate the radius:
Radius = diameter / 2
Radius = 0.64 cm / 2 = 0.32 cm = 0.0032 m (converting to meters)
Now we can calculate the area using the formula:
Area = π * (0.0032)^2
Step 2: Calculate the area of Piston B.
Using the same formula, we can calculate the area of Piston B.
Since the diameter of Piston B is given as 3.8 cm, we first need to calculate the radius:
Radius = 3.8 cm / 2 = 1.9 cm = 0.019 m (converting to meters)
Now we can calculate the area:
Area = π * (0.019)^2
Step 3: Calculate the force on Piston A.
According to Pascal's law, the pressure exerted on Piston A must be equal to the pressure exerted on Piston B. The pressure in a fluid can be calculated using the formula:
Pressure = Force / Area
Let's denote the force on Piston A as F_A, and the weight on Piston B as W_B.
Since the weight is given as 500.0 N, we can substitute the values into the formula:
Pressure on Piston B = W_B / Area of Piston B
Using Pascal's law, we can equate the pressure on Piston B to the pressure on Piston A:
Pressure on Piston A = Pressure on Piston B
Therefore,
Pressure on Piston A = W_B / Area of Piston B
Now, we know that Pressure on Piston A = F_A / Area of Piston A.
Equating the two expressions, we can calculate the force on Piston A:
F_A / Area of Piston A = W_B / Area of Piston B
Rearranging the equation, we have:
F_A = (W_B * Area of Piston A) / Area of Piston B
Substituting the calculated values for the areas of Piston A and Piston B, as well as the weight on Piston B, we can calculate the force on Piston A.
To determine the force necessary on Piston A, we can use the principle of Pascal's law, which states that when a pressure is applied to a fluid in a closed system, it is transmitted equally in all directions.
First, we need to find the areas of the two pistons using their diameters:
Area of Piston A = π * (radius of Piston A)^2
Area of Piston B = π * (radius of Piston B)^2
Given the diameter of Piston A is 0.64 cm, we can calculate the radius by dividing it by 2:
radius of Piston A = 0.64 cm / 2 = 0.32 cm
Given the diameter of Piston B is 3.8 cm, we can calculate the radius of Piston B in the same way:
radius of Piston B = 3.8 cm / 2 = 1.9 cm
Now, we can plug these values into the area formulas:
Area of Piston A = π * (0.32 cm)^2
Area of Piston B = π * (1.9 cm)^2
Area of Piston A = 0.1024π cm^2
Area of Piston B = 11.3781π cm^2
Next, we need to determine the pressure exerted on Piston A, which can be found by dividing the force on Piston B by the area of Piston B:
Pressure on Piston B = Force on Piston B / Area of Piston B
Given that the weight on Piston B is 500.0 Newton, we can substitute this value into the equation:
Pressure on Piston B = 500.0 N / 11.3781π cm^2
Finally, to find the force necessary on Piston A, we can multiply the pressure on Piston B by the area of Piston A:
Force on Piston A = Pressure on Piston B × Area of Piston A
Now, you can substitute the calculated values to get the final result.
Fa/Aa=Fb/Ab
this is the same as saying the pressure on each side is the same (Pa=Pb)