A force of 120.0 N is applied to 2.000 cm diameter piston, which is in contact with a closed container of water (density of water = 1,000 kg/m3). A second piston, with a diameter of 25.00 cm and at the same height as the first piston, is also in contact with the water. What force does the water pressure exert on the second piston?
Question
A force of 120.0 N is applied to 2.000 cm diameter piston, which is in contact with a closed container of water (density of water = 1,000 kg/m3). A second piston, with a diameter of 25.00 cm and at the same height as the first piston, is also in contact with the water. What force does the water pressure exert on the second piston?
Solution
To solve this problem, we need to use the principle of Pascal's law, which states that a change in pressure at any point in an enclosed fluid is transmitted undiminished to all points in the fluid.
Step 1: Calculate the area of the first piston (A1) using the formula for the area of a circle, A = πr². The radius is half the diameter, so r1 = 1.000 cm = 0.01 m. Therefore, A1 = π(0.01 m)² = 0.000314 m².
Step 2: Calculate the pressure exerted by the force on the first piston using the formula P = F/A. So, P = 120.0 N / 0.000314 m² = 382165.605 N/m² = 382165.605 Pa.
Step 3: Calculate the area of the second piston (A2) in the same way as step 1. The radius is half the diameter, so r2 = 12.50 cm = 0.125 m. Therefore, A2 = π(0.125 m)² = 0.049087 m².
Step 4: Calculate the force exerted by the water pressure on the second piston using the formula F = P*A. So, F = 382165.605 Pa * 0.049087 m² = 18769.5 N.
So, the force that the water pressure exerts on the second piston is approximately 18769.5 N.
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