When you suddenly stand up after lying down for a while, your body may not compensate quickly enough for the pressure changes and you might feel dizzy for a moment.

(a) If the gauge pressure of the blood at your heart is 14.3 kPa and your body doesn't compensate, what would the pressure be at your head, 41.2 cm above your heart?
1 kPa

(b) If the gauge pressure of the blood at your heart is 14.3 kPa and your body doesn't compensate, what would it be at your feet, 1.30 multiplied by 102 cm below your heart? Hint: The density of blood is 1060 kg/m3.
2 kPa

To answer these questions, we can use the principle of hydrostatic pressure in a fluid.

(a) To find the pressure at your head, we can use the equation for hydrostatic pressure:

P = P₀ + ρgh

where P is the pressure, P₀ is the initial pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height difference.

Given:
P₀ = 14.3 kPa = 14.3 × 10³ Pa
h = 41.2 cm = 0.412 m

We are asked to find the pressure at the head, which is above the heart. Therefore, the height difference (h) is positive.

Now, we can substitute the given values into the equation:

P = P₀ + ρgh
P = 14.3 × 10³ Pa + (1060 kg/m³)(9.8 m/s²)(0.412 m)

Calculating this expression will give us the pressure at the head.

(b) To find the pressure at your feet, we can use the same equation as before:

P = P₀ + ρgh

Given:
P₀ = 14.3 kPa = 14.3 × 10³ Pa
h = 1.30 × 10² cm = -1.30 m (since it is below the heart)

Notice that the height difference (h) is now negative because we are moving downward from the heart to the feet.

Now, we can substitute the values into the equation:

P = P₀ + ρgh
P = 14.3 × 10³ Pa + (1060 kg/m³)(9.8 m/s²)(-1.30 m)

Calculating this expression will give us the pressure at the feet.

To answer these questions, we need to consider the relationship between pressure, height, and density.

(a) To find the pressure at your head, 41.2 cm above your heart, we can use the equation for gauge pressure in a fluid:

P = P₀ + ρgh,

where P is the pressure at the desired location, P₀ is the pressure at the reference location (your heart), ρ is the density of the fluid (in this case, blood), g is the acceleration due to gravity, and h is the vertical height difference between the two locations.

We are given that the gauge pressure at the heart (P₀) is 14.3 kPa and the height difference (h) is 41.2 cm. The density of blood (ρ) is not needed for this part.

First, let's convert the height difference to meters:

h = 41.2 cm = 0.412 m.

Now we can plug the values into the equation:

P = 14.3 kPa + (density of blood) × (acceleration due to gravity) × (41.2 cm).

Note that acceleration due to gravity (g) is approximately 9.8 m/s².

P = 14.3 kPa + (1060 kg/m³) × (9.8 m/s²) × (0.412 m).

Now, calculate the value of P.

(b) To find the pressure at your feet, 1.30 × 10² cm below your heart, we can use the same equation:

P = P₀ + ρgh.

We are given that the gauge pressure at the heart (P₀) is 14.3 kPa and the height difference (h) is 1.30 × 10² cm. The density of blood (ρ) is given as 1060 kg/m³.

First, let's convert the height difference to meters:

h = 1.30 × 10² cm = 1.30 m.

Now we can plug the values into the equation:

P = 14.3 kPa + (density of blood) × (acceleration due to gravity) × (1.30 m).

Calculate the value of P using the provided values.

Keep in mind that always double-check your calculations and units to ensure accuracy.