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Chapter 15: Problem 85

BIO Measuring Pain Threshold A useful instrument for evaluating fibromyalgia and trigger-point tenderness is the doloriometer or algorimeter. This device consists of a force meter attached to a circular probe that is pressed against the skin until pain is experienced. If the reading of the force meter is \(3.25 \mathrm{lb}\), and the diameter of the circular probe is \(1.39 \mathrm{cm},\) what is the pressure applied to the skin? Give your answer in pascals.

Short Answer

Expert verified
The pressure applied to the skin is approximately 95181 Pa.

Step by step solution

01

Convert the Force to Newtons

Given the force reading in pounds (lb), we need to convert it to newtons (N). The conversion factor is 1 lb = 4.44822 N. Thus, the force is \( F = 3.25 \, \text{lb} \times 4.44822 \, \text{N/lb} = 14.456715 \, \text{N} \).
02

Calculate the Area of the Probe

The area of the circular probe is needed to determine the pressure. The formula for the area \( A \) of a circle is \( A = \pi r^2 \), where \( r \) is the radius. The diameter given is 1.39 cm, so the radius \( r \) is \( \frac{1.39}{2} = 0.695 \text{ cm} = 0.00695 \text{ m} \) (converted to meters). Thus,\[ A = \pi (0.00695 \, \text{m})^2 = 1.51873 \times 10^{-4} \, \text{m}^2 \].
03

Compute the Pressure Applied

Pressure \( P \) is calculated using the formula \( P = \frac{F}{A} \). Using the force in newtons and the area in square meters,\[ P = \frac{14.456715 \, \text{N}}{1.51873 \times 10^{-4} \, \text{m}^2} = 95181.35 \, \text{Pa} \].
04

Verify and Present the Answer in SI Units

Ensure the dimensions are correct, and the pressure value is expressed in pascals (Pa), which are appropriate SI units for pressure. The calculated pressure on the skin is \( 95181.35 \, \text{Pa} \), or approximately 95181 Pa to 5 significant figures.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Force Conversion
When dealing with forces in physics, it is important to be able to convert between different units of measurement. In this exercise, the force was initially given in pounds (lb), which is a unit used in the imperial system. For consistency and to align with the metric system, it was necessary to convert this force into newtons (N).
  • 1 pound (lb) is equal to approximately 4.44822 newtons (N).
  • The conversion from pounds to newtons allows us to proceed with calculations that require metric measurements.
  • For example, the force in this problem is converted from 3.25 lb to 14.456715 N using the equation: \[ F = 3.25 imes 4.44822 = 14.456715 \, \text{N} \]
Understanding force conversion is especially useful in contexts where standardized measurements are needed for scientific evaluations. This ensures accuracy and clarity in results, particularly when performing calculations like pressure, which depends on force.
Area of Circle
Determining the area of a circle is crucial for computing pressure when a circular probe is used. The area represents the contact surface, which affects the distribution of force applied.
  • The formula for the area \( A \) of a circle is \( A = \pi r^2 \), where \( r \) is the radius.
The diameter provided was 1.39 cm.
  • The radius \( r \) is half of the diameter: \( r = \frac{1.39 \text{ cm}}{2} = 0.695 \text{ cm} \).
  • We converted the radius to meters, obtaining \( 0.00695 \text{ m} \).
  • Then, the area is calculated as: \[ A = \pi (0.00695 \text{ m})^2 = 1.51873 \times 10^{-4} \text{ m}^2 \]
Using accurate measurements is essential in identifying the correct area, which directly affects the computed pressure value.
SI Units
SI Units, or the International System of Units, is the globally accepted method for measuring science-related quantities. It provides uniformity and accuracy in calculations across different scientific fields. Using SI units promotes easy comparison and understanding of results worldwide.
  • In the context of this exercise, newtons (N) were used for force and pascals (Pa) for pressure, both of which are SI units.
  • When expressing the force as 14.456715 N and the final pressure as 95181.35 Pa, using SI units facilitates clear and precise communication of the findings.
By ensuring all calculations conform to SI standards, we avoid discrepancies that could arise from using multiple measurement systems.
Pain Threshold Measurement
Measuring the pain threshold using instruments like a doloriometer involves assessing the minimum force that causes discomfort. This is particularly useful in medical evaluations, such as determining sensitivity levels in individuals with conditions like fibromyalgia.
  • The purpose of using a circular probe during measurement is to focus the force application, isolating specific areas for more precise evaluations.
  • The force reading helps understand how much pressure, in terms of newtons and pascals, is needed to cross the pain threshold.
Understanding pain threshold measurements is critical in diagnosing and managing pain-related conditions and ensuring proper patient care.
Fibromyalgia Evaluation
Fibromyalgia is a chronic condition characterized by widespread musculoskeletal pain, among other symptoms. Evaluating fibromyalgia often involves measuring tenderness or pain thresholds at various trigger points using specialized tools.
  • The doloriometer is one such tool used to apply a controlled force to specific body areas to determine sensitivity.
  • This evaluation helps diagnose fibromyalgia by measuring how much pressure triggers pain, providing essential data for treatment planning.
Objective measurements, like force and pressure, provide insight into fibromyalgia's impact on patients, aiding clinicians in tailoring management approaches accordingly.

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Most popular questions from this chapter

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