Problem 35 - College Physics

Question

Fig. 1.18 is a picture of red blood cells seen under a scanning electron microscope. Normally, women possess about 4.5 million of these cells in each cubic millimeter of blood. If the blood flow to the heart is \(250 \mathrm{~mL} / \mathrm{min}\), how many red blood cells does a woman's heart receive each second?

Step-by-Step Solution

Answer

18,750,015,000 red blood cells per second.

Step 1: Convert Blood Flow to Cubic Millimeters

We start by converting the blood flow rate from milliliters per minute to cubic millimeters per second, since we need the final number of red blood cells per second. We know that 1 milliliter is equal to 1000 cubic millimeters, and there are 60 seconds in a minute. So the blood flow rate of 250 mL/min is equivalent to \(250 \times 1000 = 250,000\) cubic millimeters per minute. Dividing by the 60 seconds in a minute, the flow in cubic millimeters per second is \(\frac{250,000}{60} \approx 4166.67\).

Step 2: Calculate Red Blood Cells per Second

With the number of cubic millimeters of blood per second known, multiply by the number of red blood cells per cubic millimeter. Women have about 4.5 million red blood cells per cubic millimeter. So, the number of red blood cells flowing to the heart per second is \(4166.67 \times 4,500,000 = 18,750,015,000\).

Key Concepts

Scanning Electron Microscope

When we need to take a closer look at tiny objects, like red blood cells, we use a device called a scanning electron microscope (SEM). A SEM is an incredibly powerful tool that allows us to observe very small specimens by using a focused beam of electrons. Unlike a regular light microscope, which uses visible light, a SEM can produce images with much higher resolution. This means we can see fine details. These details include the shape and surface features of the cells.

A SEM works by scanning an electron beam across the surface of a specimen. The electrons interact with the atoms in the specimen, producing different signals that a detector translates into a detailed image. These images are typically viewed in black and white, but they can be colored later for specific purposes or aesthetic enhancement.

Scientists often use SEM to study biological samples, including cells and tissues. They provide valuable insights into the structure and function of different cellular components.

Blood Flow

Blood flow refers to the movement of blood through the circulatory system. Blood flows through our veins and arteries, constantly supplying organs and tissues with oxygen and nutrients.

The heart is responsible for pumping blood throughout the body. It maintains an average blood flow rate, which can vary depending on a person's activity level and health conditions.

Understanding blood flow is crucial, especially when analyzing how many red blood cells pass through a particular organ over time. In the heart, blood flow is typically measured in milliliters per minute, which can then be converted into other units depending on the data required.

Unit Conversion

Unit conversion is a handy tool when we want to switch between different measurement units. In the context of blood flow, we often need to convert volumetric units, like milliliters, into cubic millimeters, which are smaller and more precise.

To convert milliliters to cubic millimeters, we remember that 1 milliliter equals 1,000 cubic millimeters. Therefore, for a measurement given in milliliters per minute, we multiply by 1,000 to find the equivalent value in cubic millimeters per minute.

Since time is often involved in these calculations, converting minutes to seconds is also necessary. As 1 minute has 60 seconds, dividing by 60 converts a per-minute rate to a per-second rate. These conversions allow us to determine how many red blood cells flow to the heart per second in a blood flow scenario.

Anatomy

Anatomy is the study of the structure of living organisms. When we talk about red blood cells and blood flow, we're delving into human anatomy.

Red blood cells are a type of cell in our blood. They are disc-shaped and play a vital role by carrying oxygen from the lungs to the rest of the body and bringing carbon dioxide back for elimination.

The circulatory system, composed of the heart, blood, and blood vessels, is an intricate network that enables body function. In this network, the heart is central, pumping blood and ensuring a continuous flow through the body, which is essential for life.

Understanding anatomy helps us appreciate how systems like the circulatory system operate cohesively, maintaining health and supporting body functions.