A force of 120.0 N is applied to 2.00 cm diameter piston in a closed container of water with a density of 1,000 kg/m2. What is the force on another piston with diameter of 25.0 cm connected to the container?
To find the force on the second piston connected to the container, we can use the principle of Pascal's law. Pascal's law states that pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.
To calculate the force on the second piston, we need to determine the pressure exerted on the first piston by the force applied to it.
Step 1: Calculate the area of the first piston.
Given the diameter of the first piston (2.00 cm), we can calculate its radius (r) by dividing the diameter by 2:
r = diameter / 2 = 2.00 cm / 2 = 1.00 cm.
The area of the first piston (A1) can be calculated using the formula:
A1 = π * r^2,
where π (pi) is a constant approximately equal to 3.14.
Substituting the value of the radius, we get:
A1 = 3.14 * (1.00 cm)^2
Step 2: Calculate the pressure exerted on the first piston.
Pressure (P) is defined as the force (F) exerted per unit area (A):
P = F / A1.
Rearranging the formula, we can solve for F:
F = P * A1.
We are given the force applied to the first piston, which is 120.0 N.
Substituting the values into the formula, we can solve for the pressure (P):
P = 120.0 N / A1.
Step 3: Calculate the area of the second piston.
Given the diameter of the second piston (25.0 cm), we can calculate its radius (R) using the same formula:
R = diameter / 2 = 25.0 cm / 2 = 12.50 cm.
The area of the second piston (A2) can be calculated using the same formula as before:
A2 = π * R^2.
Step 4: Calculate the force on the second piston.
Using Pascal's law, we know that the pressure exerted on the first piston is transmitted undiminished to all portions of the fluid. Therefore, the pressure acting on the second piston is the same as that on the first piston: P.
The force (F2) on the second piston can be calculated using the formula:
F2 = P * A2.
Substituting the value of pressure (P) and area (A2) into the formula, we can calculate the force on the second piston.