When a person sits erect, increasing the vertical position of their brain by 38.6 cm, the heart must continue to pump blood to the brain at the same rate. (a) What is the gain in gravitational potential energy (in J) for 110 mL of blood raised 38.6 cm

the gain in gravitational potential energy is 0.4369 J

Explanation:

Given the data in the question;

from the definition of density, we know that;

ρ = m / V

where ρ is density, m is the mass and V is the volume.

Now, lets make mass the subject of the formula

m = ρV   let this be equation 1

Now, we know that potential energy PE = mgh let this be equation 2

where m is mass, g is acceleration due gravity, and h is the height.

substitute equation 1 into 2

PE = ρVgh

given that; V =  110 mL = 110 × 10⁻⁶ m³, h = 38.6 cm = 38.6 × 10⁻² m, g = 9.8 m/s², ρ = 1.05 × 10³ kg/m³

we substitute

PE = (1.05 × 10³ kg/m³) × (110 × 10⁻⁶ m³) × 9.8 m/s² × 38.6 × 10⁻² m

PE =  0.4369 J

Therefore,  the gain in gravitational potential energy is 0.4369 J

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explanation:

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s