The amount of work done by the heart\'s main pumping chamber, the left ventricle

Question

The amount of work done by the heart's main pumping chamber, the left ventricle, is given by the equation font size decreased by 1 Upper W equals PV plus StartFraction Upper V delta upsilon squared Over 2 g EndFractionW=PV+ V2 2g, where W is the work per unit time, P is the average blood pressure, V is the volume of blood pumped out during the unit of time, delta ('delta') is the weight density of the blood, nu is the average velocity of the exiting blood, and g is the acceleration of gravity. When P, V, delta, and nu remain constant, W becomes a function of g, and the equation takes the simplified form font size decreased by 1 Upper W equals a plus StartFraction b Over g EndFractionW=a+ b g where a and b are constants. The sensitivity of W to apparent changes in g caused by flight maneuvers depends on the initial value of g. Compare the effect on W of a given change dg on the moon of Planet A, where gequals=5.45.4 ft/sec2 with the effect the same change dg would have on Planet A, where gequals=4444 ft/sec2. Use the simplified equation above to find the ratio of dWmoon to dWplanet.

Explanation / Answer

Given that W= a + (b/g) where a, b are constants.

gmoon = 545.4 ft/sec2

gplanet = 4444 ft/sec2

dWmoon = -(bg2)dg

dWmoon/dg= -b/gmoon2

similarly for planet A

dWplanet/dg = -b/gplanet2

Ratio of dWmoon to dWplanet= gplanet2/gmoon2

= (4444)2/(545.4)2

= 66.39

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