When a person sits erect, increasing the vertical position of their brain by 36.0 cm, the heart must continue to pump blood to the brain at the same rate. (a) What is the gain in gravitational potential energy for 100 mL of blood raised 36.0 cm? (b) What is the drop in pressure, neglecting any losses due to friction? (c) Discuss how the gain in gravitational potential energy and the decrease in pressure are related.

Solution 78PE

Step 1 of 5</p>

If a person sits erect and the brain vertical position raises by , but the heart will pump the blood with same rate. We need to calculate the gain in gravitational potential energy of of blood when raised to a height of . By neglecting the losses by the friction, we need to estimate the drop in pressure. Also, we need to explain how the gain in potential energy and the decrease in pressure are related.

Given data,

Density of blood,

Volume of blood,

Using

Using

Height,

Using

Acceleration due to gravity,

To find,

(a)Gain in potential energy,

(b)Drop in pressure,

Step 2 of 5</p>

(a)

The change in potential energy of the blood is proportional to change in height and is given by,

Where m is mass , g is acceleration due to gravity and h is height.

Using mass density relation,

Substituting ,, ,

Therefore, the gain in potential energy of the blood is 0.370 J.

Step 3 of 5</p>

(b)

By neglecting the losses due to friction between blood and vessels. We can calculate the change in pressure , which will be equal to the drop in pressure and is given by,

Substituting , ,

Using

Therefore, the drop in pressure of the blood is 3700 Pa.