Problem 17 - University Physics with Modern Physics

Question

A rather ordinary middle-aged man is in the hospital for a routine checkup. The nurse writes "200" on the patient's medical chart but forgets to include the units. Which of these quantities could the 200 plausibly represent? The patient's (a) mass in kilograms; (b) height in meters; (c) height in centimeters; (d) height in millimeters; (e) age in months.

Step-by-Step Solution

Answer

The quantity 200 could plausibly represent the patient's height in centimeters.

Step 1: Assess Patient's Mass in Kilograms

First, we consider if the number 200 could represent the patient's mass in kilograms. Typically, an average adult has a mass ranging from around 50 to 150 kg, depending on height and body composition. A mass of 200 kg would be considered quite high for an ordinary middle-aged man unless he has a condition such as obesity. While it's possible, it's not very likely for an 'ordinary' man in this scenario.

Step 2: Evaluate Patient's Height in Meters

Next, consider if 200 might represent height in meters. Since 1 meter equals 100 centimeters, a height of 200 meters would be excessively large and not physically possible for any human being. Therefore, 200 cannot represent the patient's height in meters.

Step 3: Consider Patient's Height in Centimeters

Now consider if 200 could mean the patient's height in centimeters. Average human height typically ranges from about 150 cm to 200 cm. A height of 200 cm is plausible, especially for a tall person. This unit effectively matches a reasonable human height range, making it a likely candidate.

Step 4: Consider Patient's Height in Millimeters

Then analyze whether 200 could be the patient's height in millimeters. Since there are 1000 millimeters in a meter, 200 millimeters would correspond to 20 centimeters, which is too short for a human adult. This unit does not fit a plausible human height, eliminating it as an option.

Step 5: Examine Patient's Age in Months

Finally, consider 200 as representing age in months. To convert months to years, divide by 12. Thus, 200 months is approximately 16.67 years, which doesn't match the description of a 'middle-aged' man, typically someone between 40 and 60 years old. Therefore, this unit doesn't fit.

Key Concepts

Dimensional Analysis

Dimensional analysis is an essential tool in physics and engineering. It helps us understand relationships between different physical quantities by analyzing their dimensions. Dimensions refer to the nature of a quantity, such as length, mass, time, etc. When assessing problems, dimensional analysis can guide us toward the correct interpretation of numerical values by checking if units are consistent across equations or expressions.
For example, in the exercise with a value of 200 written without a unit, it's crucial to analyze plausible dimensions of the quantity that 200 might represent. By comparing it with known magnitudes for various conceivable dimensions, such as mass in kilograms or height in centimeters, we can eliminate possibilities that don't fit known physical norms.
Remember:

• Dimensions help verify the correctness of an equation.
• Assist in converting units to ensure consistency.
• Provide constraints that refine possible solutions.

Thus, dimensional analysis acts as a powerful check on the plausibility of numerical quantities associated with various units.

Units and Measurement

Units are fundamental in expressing any physical quantity. They give meaning to numbers in scientific observations, making it possible to communicate and verify results accurately. Units of measurement are standardized, allowing us to ensure consistency and comparability across different studies and applications.
Consider the example where the nurse forgot to include units with the number 200. Without the unit, the number is ambiguous and hard to interpret accurately. By reassigning correct units, like centimeters for height, we bring clarity and accuracy back into the equation. Every measurement needs a unit to relay correct and meaningful information.
Key points about units and measurement include:

• Units provide context and clarity to raw numbers.
• They ensure universal understanding and reduce misinterpretation.
• Consistently used units allow seamless data comparison and integration across studies.

In summary, always remember that while measurements can vary, their significance and understanding are deeply tied to the units they are expressed in.

Physical Quantities

Physical quantities are properties or characteristics of phenomena that can be quantified by measurement. Some common examples include length, mass, time, and temperature.
Each physical quantity is expressed as the product of a numerical value and a unit. For instance, in the exercise, possible interpretations of the number 200 could relate to different physical quantities like height or mass, depending on the unit used (e.g., centimeters, kilograms). This demonstrates the necessity for associating quantities with their relevant units.
Important aspects of physical quantities involve:

• They represent measurable properties of matter or phenomena.
• Each has specific units that must be used for measurement.
• Quantities and units must be appropriate to the context for an accurate representation.

Recognizing and connecting physical quantities with their respective units helps ensure clear and precise communication in science and everyday applications.