Question

What is the pressure in pascals if a force of \(4.88 \mathrm{kN}\) is pressed against an area of \(235 \mathrm{~cm}^{2} ?\)

Short answer

The pressure is approximately 207,659.57 pascals.

Step-by-step solution

Convert Units for Force

Convert the force from kilonewtons (kN) to newtons (N). We know that 1 kN = 1000 N. So, 4.88 kN is equivalent to \( 4.88 \times 1000 = 4880 \) N.

Convert Units for Area

Convert the area from square centimeters (\( \mathrm{cm}^{2} \)) to square meters (\( \mathrm{m}^{2} \)). We know that \( 1 \mathrm{m}^{2} = 10,000 \mathrm{cm}^{2} \). So, \( 235 \mathrm{~cm}^{2} \) is calculated as \( 235 \div 10,000 = 0.0235 \mathrm{~m}^{2} \).

Use the Pressure Formula

Pressure is defined by the formula \( P = \frac{F}{A} \), where \( P \) is pressure, \( F \) is force, and \( A \) is area. Plug in the converted values to get \( P = \frac{4880 \text{ N}}{0.0235 \text{ m}^{2}} \).

Calculate Pressure

Perform the calculation: \( P = \frac{4880}{0.0235} \approx 207,659.57 \text{ Pa} \). Therefore, the pressure is approximately 207,659.57 pascals.

Key concepts

Force Unit Conversion

Understanding unit conversion is crucial when dealing with different units of measurement in physics. In the given problem, we are asked to convert a force from kilonewtons (kN) to newtons (N). This is because the standard unit of force in the International System of Units (SI) is the newton.

• 1 kilonewton (kN) equals 1000 newtons (N). This means that each kilonewton contains one thousand newtons.
• To convert kilonewtons to newtons, simply multiply the number of kilonewtons by 1000. So in our problem, we take 4.88 kN and multiply it by 1000, resulting in 4880 N.
• This conversion is vital for calculating pressure correctly, as the pressure formula requires force to be in newtons.

Remember, correct unit conversion is the first step towards solving physics problems accurately. Missteps in this initial stage can lead to incorrect results later on.

Area Unit Conversion

Converting area units is another important aspect of this problem. We need to change the area from square centimeters (\( \text{cm}^{2} \)) to square meters (\( \text{m}^{2} \)), which is the standard SI unit for area.

• There are 10,000 square centimeters in one square meter. This emphasizes how much smaller a square centimeter is compared to a square meter.
• To perform the conversion, divide the number of square centimeters by 10,000. For instance, converting 235 \( \text{cm}^{2} \) to square meters involves calculating \( 235 \div 10,000 = 0.0235 \text{ m}^{2} \).
• Using square meters in the formula is essential for acquiring the correct measurement of pressure in pascals.

Accurate area unit conversion ensures that our calculation of pressure, which involves dividing force by this area, is consistent and correct.

Pressure Formula

The pressure formula is a fundamental concept in physics for calculating the force applied over an area. Pressure (\( P \)) is defined using the formula:\[ P = \frac{F}{A} \]where:

• \( P \) stands for pressure, measured in pascals (Pa).
• \( F \) represents the force applied, measured in newtons (N).
• \( A \) is the area over which the force is distributed, measured in square meters (\( \text{m}^{2} \)).

In the given problem, we have already converted the force to 4880 N and the area to 0.0235 \( \text{m}^{2} \). Plugging these values into the formula gives:\[ P = \frac{4880}{0.0235} \approx 207,659.57 \text{ Pa} \]This calculation shows how the force is spread over the specific area, producing a pressure of approximately 207,659.57 pascals. Using the correct units and formula ensures a precise and reliable calculation.