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Chapter 2: Problem 90

If the contraction of the left ventricle lasts 250 ms and the speed of blood flow in the aorta (the large artery leaving the heart) is 0.80 m/s at the end of the contraction, what is the average acceleration of a red blood cell as it leaves the heart? (a) 310 ms\(^2\); (b) 31 m/s\(^2\); (c) 3.2 m/s\(^2\); (d) 0.32 m/s\(^2\).

Short Answer

Expert verified
The average acceleration is 3.2 m/s虏 (option c).

Step by step solution

01

Understand the Given Parameters

We have been given the duration of the left ventricle's contraction as 250 ms (milliseconds) and the final speed of blood in the aorta as 0.80 m/s. The average acceleration is required.
02

Convert Time to Seconds

Convert the given time from milliseconds to seconds. Since 1 second is 1000 milliseconds, \[250\text{ ms} = \frac{250}{1000}\text{ seconds} = 0.25\text{ seconds}.\]
03

Use the Formula for Average Acceleration

The formula for average acceleration is given by \[a = \frac{v - u}{t},\]where \(v\) is the final velocity, \(u\) is the initial velocity, and \(t\) is the time. Substitute the values given:- \(v = 0.80\text{ m/s}\)- \(u = 0\text{ m/s}\) (since the blood starts from rest)- \(t = 0.25\text{ seconds}\)
04

Calculate the Average Acceleration

Substitute the known values into the formula:\[a = \frac{0.80 - 0}{0.25} = \frac{0.80}{0.25} = 3.2\text{ m/s}^2.\]
05

Choose the Correct Answer

The calculated average acceleration of the red blood cell as it leaves the heart is 3.2 m/s虏. Hence, the correct answer is option (c) 3.2 m/s虏.

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Key Concepts

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

Kinematics
Kinematics is a branch of physics that deals with motion. It does so without considering the forces that cause it. In kinematics, we describe the motion of objects, such as their positions, velocities, and accelerations. This particular problem is about blood flow, which we can understand using kinematics principles.
By analyzing how blood moves through the aorta, we can determine properties like velocity and acceleration. This gives us insights into the cardiovascular function and efficiency.
Using the kinematic formulas, we can calculate the average acceleration by understanding the initial and final velocities as well as the elapsed time.
Velocity
Velocity is a key concept in understanding motion. It describes how fast an object is moving and in which direction.
In the exercise, the final velocity of the blood as it exits the heart through the aorta is given as 0.80 m/s. This is a vector quantity, meaning it has both magnitude and direction.
Initial velocity is zero because the blood starts from rest. As such, to determine acceleration, we use these velocities to find out how rapidly the speed changes over time.
Time Conversion
Time conversion is crucial in problems that involve calculations using time. Different units of time measurement are often interchanged during such calculations.
In the provided exercise, we need to convert the contraction duration from milliseconds to seconds because standard time units in physics are seconds.
  • 1 second is equal to 1000 milliseconds.
  • Hence, 250 milliseconds is converted to 0.25 seconds.
This allows for consistent and accurate computations throughout the calculation process.
Unit Conversion
Unit conversion involves changing one unit of measure to another to ensure consistency across calculations, especially in physics problems.
In our exercise, the initial velocity is considered in meters per second (m/s), which aligns with standard metric units of speed and velocity in physics.
Ensuring that all quantities are in compatible units, such as time in seconds and speed in meters per second, prevents errors in calculations, specifically when applying formulas like those for average acceleration.

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Most popular questions from this chapter

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