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 $\square$
failed

Solution

failed
failed

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.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Simplify the integrand completely. L = ∫ from 0 to 1 sqrt(1 + ( (1-2x) / (2 sqrt(x-x^2)) + 1/(2 sqrt(x) sqrt(1-x)) )^2 ) dx = ∫ from 0 to 1 square dx
failedAnswered
An atomic cation with a charge of +2 has the following electron configuration: [Kr] 5s^2 4d^10 5p^1 What is the chemical symbol for the ion? How many electrons does the ion have? How many 5p electrons are in the ion?
failedAnswered
Check all the possible rational roots for the function f(x)=3x^3+2x^2+3x+6 Select one or more: a. -1 / 2 b. -4 c. -1 / 3 d. -3 / 2 e. 6 f. 0 g. -2 / 3 h. 3
failedAnswered
Assume an economy where there are two producers: a computer components producer and a computer producer. Assume the computer components producer makes 3,000,000 worth of computer components in the current year, while incurring costs of 1,500,000 in labor and 500,000 in taxes. Suppose the computer components company sells all its product to the computer producer who builds five supercomputers. The costs of the computer producer include 3,000,000 in computer components, 800,000 in labor, and 200,000 in taxes. Suppose that the computer producer sells two of the supercomputers for 1,000,000 each to the domestic government, 1 supercomputer for 1,000,000 to a foreign government, and at the end of the year it had not sold the fourth and fifth computer. The unsold computers are carried on the computer manufacturer's books as an 2,000,000 increase in inventory. Using the income approach, what is the total cost for the computer producer? 5,000,000 4,000,000 3,000,000 2,000,000 1,000,000
failedAnswered
Solve using a proportion. Tim takes his pulse for 10 sec and counts 30 beats. How many beats per minute is this? Tim's pulse is beats per minute.