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Chapter 1: Problem 71

At a resting pulse rate of 75 beats per minute, the human heart typically pumps about \(70 \mathrm{~mL}\) of blood per beat. Blood has a density of \(1060 \mathrm{~kg} / \mathrm{m}^{3}\). Circulating all of the blood in the body through the heart takes about \(1 \mathrm{~min}\) in a person at rest. (a) How much blood (in \(\mathrm{L}\) and \(\mathrm{m}^{3}\) ) is in the body? (b) On average, what mass of blood (in \(\mathrm{g}\) and \(\mathrm{kg}\) ) does the heart pump with each beat? SSM

Short Answer

Expert verified
a) The total volume of blood in the body is 5.25 L or 0.00525 m^3. b) The mass of blood pumped with each beat is 74.2 g or 0.0742 kg.

Step by step solution

01

Calculate the total amount of blood circulating in the body

Given the pulse rate is 75 beats per minute and the volume of blood per beat is 70 mL, we can calculate the total amount of blood circulating in the body in one minute by multiplying these two values: \(75 \mathrm{~beats/min} \times 70 \mathrm{~mL/beat} = 5250 \mathrm{~mL}\). To convert this to L, we divide by 1000, getting 5.25 L. To convert to m^3, we multiply by 1e-3, yielding \(5.25 \mathrm{~L} \times 1 \times 10^{-3} \mathrm{~m^3/L} = 0.00525 \mathrm{~m^3}\).
02

Determine the mass of blood pumped per beat

The mass of the blood pumped with each beat can be calculated by multiplying the volume of blood per beat by the density of blood: \(70 \mathrm{~mL/beat} \times 1060 \mathrm{~kg/m^3}\). Since 1 mL equals 1e-6 m^3, we need to convert mL to m^3 before calculating this: \(70 \mathrm{~mL} \times 1 \times 10^{-6} \mathrm{~m^3/mL} = 0.00007 \mathrm{~m^3}\). Thus, the mass of blood pumped per beat becomes \(0.00007 \mathrm{~m^3} \times 1060 \mathrm{~kg/m^3} = 0.0742 \mathrm{~kg}\). To convert this to g, we multiply by 1000, getting \(0.0742 \mathrm{~kg} \times 1000 \mathrm{~g/kg} = 74.2 \mathrm{~g}\).

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Key Concepts

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

Circulatory System
The human circulatory system is an amazing network of organs and vessels that circulates blood. It plays a crucial role in maintaining homeostasis in our bodies.
The heart, as the central component, pumps blood through a network that includes arteries, veins, and capillaries. By transporting oxygen, nutrients, hormones, and waste products, it ensures that body tissues receive essential sustenance.
  • At rest, the average human heart beats approximately 75 times per minute.
  • With each beat, it pumps about 70 milliliters of blood.
  • The entire volume of blood circulates through the heart once per minute.
Understanding these basic functions helps us realize the heart's critical performance even when we're at rest, ensuring a continuous circulation vital for health.
Volume and Mass Conversion
In physics and chemistry, converting units is an essential skill. In the context of blood circulation, converting volume units helps us better understand how much blood the heart handles.
To convert milliliters (mL) to liters (L), you divide the volume in milliliters by 1000, since there are 1000 milliliters in a liter:
  • Example: 5250 mL is the total blood volume circulated per minute, equivalent to 5.25 L.
When converting to cubic meters (m^3), further division by 1000 is necessary:
  • Example: 5.25 L or 5250 mL equals 0.00525 m^3.
Mass conversions follow similar principles. From kilograms to grams, you multiply by 1000 because 1 kg equals 1000 grams:
  • Example: A mass of 0.0742 kg is equivalent to 74.2 g, representing the mass of blood with every heartbeat.
Grasping these conversion methods makes it easier to interpret and calculate physical properties in different units.
Density Calculations
Density relates an object's mass to its volume, and in the case of blood, it's a crucial factor in determining the mass of circulating blood.
Blood has a density of 1060 kg/m鲁. When calculating the mass of blood pumped per beat, the process involves multiplying the converted volume (in cubic meters) by the density.
  • First, convert the beat volume (70 mL) to cubic meters: 70 mL = 0.00007 m^3.
  • Then, multiply this volume by density to get mass: 0.00007 m^3 脳 1060 kg/m^3 = 0.0742 kg.
This calculation shows how density ties together volume and mass, allowing us to understand the amount of blood moved with each heartbeat in both kilograms and grams. A firm understanding of density is essential for relating different physical properties.

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