Questions: A cylinder measuring 6.5 cm wide and 7.8 cm high is filled with gas and the piston pushed down with a steady force. Calculate the force on the piston if the pressure in the gas is measured to be 585 kPa. Write your answer in units of kilonewtons. Be sure your answer has the correct number of significant digits.

A cylinder measuring 6.5 cm wide and 7.8 cm high is filled with gas and the piston pushed down with a steady force.

Calculate the force on the piston if the pressure in the gas is measured to be 585 kPa. Write your answer in units of kilonewtons. Be sure your answer has the correct number of significant digits.

Transcript text: A cylinder measuring 6.5 cm wide and 7.8 cm high is filled with gas and the piston pushed down with a steady force. Calculate the force on the piston if the pressure in the gas is measured to be $585 . \mathrm{kPa}$. Write your answer in units of kilonewtons. Be sure your answer has the correct number of significant digits. $\square$ kN $\square$

Solution

Solution Steps

Step 1: Identify the given values

Diameter of the cylinder (d) = 6.5 cm
Pressure in the gas (P) = 585 kPa

Step 2: Convert the diameter to radius

Radius (r) = Diameter / 2 = 6.5 cm / 2 = 3.25 cm

Step 3: Convert the radius to meters

Radius in meters (r) = 3.25 cm * 0.01 m/cm = 0.0325 m

Step 4: Calculate the area of the piston

Area (A) = π * r² = π * (0.0325 m)² ≈ 3.14159 * 0.00105625 m² ≈ 0.00332 m²

Step 5: Convert pressure to Pascals

Pressure (P) = 585 kPa = 585,000 Pa

Step 6: Calculate the force on the piston

Force (F) = Pressure (P) * Area (A) = 585,000 Pa * 0.00332 m² ≈ 1940.2 N

Step 7: Convert the force to kilonewtons

Force in kilonewtons (F) = 1940.2 N * 0.001 kN/N ≈ 1.94 kN

Final Answer

The force on the piston is approximately 1.94 kN.

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