The human ciculatory system can be thought of as a closed system of interconnecting pipes through which fluid is continuously circulated by two pumps the two pumps the right and left verticles of the heart, work as simple two-stroke force pumps. The muscles of the heart regulate the force by contracting and relaxing. the contraction (systole) lasts about 0.2s and a complete systole/diastole (contraction/relaxation) cycle lasts about 0.8s. For flood pressures and speeds in the normal range. the volume flow rate of blood through a blood vessel is directly proportional tot he pressure difference over a length of the vessel and to the fourth power of the radius of the vessel. The total mechanical energy per unit volume of blood just as it leaves the heart is `E//V=rhogh+P+rhov^(2)`
Q. The blood pressure in a capillary bed is essentially zero, allowing blood to flow extremely slowly through the tissues in order to maximize exhange of gases nutrients and waste products what is the work on `200cm^(3)` of blood against gravity to bring it to the capillaries to the brain 50 cm above the heart?

Options

A. 5145 J
B. 105 J
C. 10 J
D. 1 J

Answer

To solve the problem of calculating the work done on 200 cm³ of blood against gravity to bring it to the capillaries in the brain, which are 50 cm above the heart, we can follow these steps:

### Step-by-Step Solution

1. **Convert Volume to Cubic Meters**:
The volume of blood given is 200 cm³. We need to convert this to cubic meters for consistency with SI units.
\[ \text{Volume} = 200 \, \text{cm}^3 = 200 \times 10^{-6} \, \text{m}^3 = 2 \times 10^{-4} \, \text{m}^3 \]

2. **Calculate the Mass of Blood**:
The density of blood is approximately \( \rho = 1050 \, \text{kg/m}^3 \). We can calculate the mass using the formula:
\[ \text{Mass} (m) = \text{Density} (\rho) \times \text{Volume} (V) \]
\[ m = 1050 \, \text{kg/m}^3 \times 2 \times 10^{-4} \, \text{m}^3 = 0.21 \, \text{kg} \]

3. **Identify the Height**:
The height \( h \) to which the blood needs to be raised is given as 50 cm. We convert this to meters:
\[ h = 50 \, \text{cm} = 0.5 \, \text{m} \]

4. **Calculate the Work Done Against Gravity**:
The work done against gravity can be calculated using the formula:
\[ W = mgh \]
where \( g \) (acceleration due to gravity) is approximately \( 9.8 \, \text{m/s}^2 \).
\[ W = 0.21 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 0.5 \, \text{m} \]
\[ W = 0.21 \times 9.8 \times 0.5 = 1.029 \, \text{J} \]

5. **Round the Result**:
Rounding to two significant figures, we get:
\[ W \approx 1 \, \text{J} \]

### Final Answer
The work done on 200 cm³ of blood against gravity to bring it to the capillaries in the brain is approximately **1 Joule**.

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