Problem 6 - Fundamentals of Physics

Question

You inflate the front tires on your car to 28 psi. Later, you measure your blood pressure, obtaining a reading of \(120 / 80\), the readings being in \(\mathrm{mm} \mathrm{Hg}\). In metric countries (which is to say, most of the world), these pressures are customarily reported in kilopascals (kPa). In kilopascals, what are (a) your tire pressure and (b) your blood pressure?

Step-by-Step Solution

Answer

The tire pressure is 193.05 kPa and blood pressure is 16.00/10.67 kPa.

Step 1: Understand the Conversion Factors

To convert pressure from psi (pounds per square inch) to kPa (kilopascals), use the conversion factor: \(1 \text{ psi} = 6.89476 \text{ kPa}\). For converting mmHg to kPa, use the conversion: \(1 \text{ mmHg} = 0.133322 \text{ kPa}\).

Step 2: Convert Tire Pressure to kPa

The tire pressure is initially 28 psi. To convert this to kPa, use the conversion factor: \(28 \text{ psi} \times 6.89476 \text{ kPa/psi} = 193.05328 \text{ kPa}\). Thus, the tire pressure is approximately \(193.05 \text{ kPa}\).

Step 3: Convert Systolic Blood Pressure to kPa

The systolic blood pressure reading is 120 mmHg. To convert this to kPa, use the conversion: \(120 \text{ mmHg} \times 0.133322 \text{ kPa/mmHg} = 15.99864 \text{ kPa}\). Thus, the systolic blood pressure is approximately \(16.00 \text{ kPa}\).

Step 4: Convert Diastolic Blood Pressure to kPa

The diastolic blood pressure reading is 80 mmHg. To convert this to kPa, use the conversion: \(80 \text{ mmHg} \times 0.133322 \text{ kPa/mmHg} = 10.66656 \text{ kPa}\). Thus, the diastolic blood pressure is approximately \(10.67 \text{ kPa}\).

Key Concepts

Tire Pressure

Tire pressure is the measure of the amount of air inside your tire, which supports the weight of the vehicle and its passengers. Proper tire pressure is crucial for maintaining optimal vehicle performance, safety, and fuel efficiency. For car tires, this pressure is commonly measured in psi, which stands for pounds per square inch.
When tires are correctly inflated, they wear evenly, provide more traction, and improve fuel economy. Incorrectly inflated tires, either over or under, can lead to several issues, such as uneven tire wear, poor handling, and decreased fuel efficiency.
Most car manuals specify the ideal tire pressure, often found on a sticker inside the driver's door or the glove box. Always measure tire pressure when the tires are cold for the most accurate reading.

Blood Pressure

Blood pressure refers to the force of blood against the walls of your arteries as the heart pumps it through the body. It is represented by two numbers in a measurement, such as 120/80 mmHg. The top number, called systolic pressure, measures the force during heartbeats, while the bottom number, called diastolic pressure, measures the force between beats.
Maintaining healthy blood pressure is vital for preventing heart disease and stroke. Doctors commonly use a sphygmomanometer to measure blood pressure in millimeters of mercury (mmHg).
Understanding your blood pressure readings and consulting with healthcare professionals can help manage and prevent long-term health problems.

Kilopascals

Kilopascals (kPa) are a metric unit of pressure, which is broadly used around the world for reporting both tire and blood pressure. One kilopascal is equivalent to 1,000 pascals (Pa), with a pascal defined as one newton per square meter.
In many countries, including those using the metric system, pressure is primarily recorded in kPa due to its simplicity and ease of understanding. Many people prefer kPa in scientific contexts because it's part of the SI (International System of Units), which helps standardize measurements globally.
For automotive and health applications, converting psi and mmHg to kPa ensures consistency, particularly in international settings.

Psi to kPa Conversion

When converting tire pressure from psi to kilopascals, you use a specific conversion factor. For this conversion, 1 psi is equal to 6.89476 kPa.
To convert, you multiply the psi value by 6.89476 to find your pressure in kilopascals. For example, if you have a tire pressure of 28 psi, you calculate it as:

• \(28 \text{ psi} \times 6.89476 \text{ kPa/psi} = 193.05328 \text{ kPa}\)

Thus, the converted tire pressure is approximately 193.05 kPa. This step is crucial for those living or working in areas where the metric system is prevalent.

mmHg to kPa Conversion

To convert blood pressure readings from mmHg to kilopascals, a different conversion factor is used. Here, 1 mmHg is equal to 0.133322 kPa.
To perform the conversion, multiply your blood pressure readings by 0.133322. For example:

• Systolic Pressure: \(120 \text{ mmHg} \times 0.133322 \text{ kPa/mmHg} = 15.99864 \text{ kPa}\)
• Diastolic Pressure: \(80 \text{ mmHg} \times 0.133322 \text{ kPa/mmHg} = 10.66656 \text{ kPa}\)

These results indicate that the systolic pressure is approximately 16.00 kPa, and the diastolic pressure is about 10.67 kPa. Converting these values is particularly important in international environments where kPa is the standard unit.