Q90PP - University Physics with Modern Physics

Question

The human circulatory system is closed—that is, the blood pumped out of the left ventricle of the heart into the arteries is constrained to a series of continuous, branching vessels as it passes through the capillaries and then into the veins as it returns to the heart. The blood in each of the heart’s four chambers comes briefly to rest before it is ejected by contraction of the heart muscle.

If the contraction of the left ventricle lasts 250ms 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 m/s²; (b) 31 m/s²; (c) 3.2 m/s²; (d) 0.32 m/s².

Step-by-Step Solution

Answer

The average acceleration of the left ventricle is${\mathrm{a}}_{\mathrm{av}}=3.2\mathrm{m}/{\mathrm{s}}^2$.

Step 1: Identification of given data

• The final velocity of the contraction is,$v=0.80\mathrm{m}/\mathrm{s}$.
• The initial velocity of the contraction is,$v_0=0$.
• The time of contraction of left ventricle is,$t=250\mathrm{ms}\left(\frac{\mathrm{s}}{1000\mathrm{ms}}\right)=250\times {10}^{-3}\mathrm{S}$.

Step 2: Concept of average acceleration

Velocity fluctuates at a constant rate, and this is known as the average acceleration. Average acceleration of everything is determined by dividing actual change in speed by amount of time from the beginning.

As a result, we may say the average acceleration is indeed the ratio of velocity change to time change during a certain period of time.

The average acceleration is given by,

$a_{av}=\left(\frac{v-v_0}{t}\right)$… (i)

Step 3: Evaluate the average acceleration of ventricle

The average acceleration of ventricle is evaluated using equation (i),

$$\begin{gathered} a_{av}=\left(\frac{0.80\mathrm{m}/\mathrm{s}-0}{\left(250\times {10}^{-3} \mathrm{s}\right)}\right) \\ {a}_{av}=3.2\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$