Women often suffer from back pains during pregnancy. Let us investigate the caus

Question

Women often suffer from back pains during pregnancy. Let us investigate the cause of these pains, assuming that the woman's mass is 63.0 { m kg} before pregnancy. Typically, women gain about 10.0 { m kg} during pregnancy, due to the weight of the fetus, placenta, amniotic fluid, etc. To make the calculations easy, but still realistic, we shall model the unpregnant woman as a uniform cylinder of diameter 30.0 { m cm}. We can model the added mass due to the fetus as a 10.0 { m kg} sphere 25.0 { m cm} in diameter and centered about 5.00 { m cm} outside the woman's original front surface.

Explanation / Answer

M1=63 kg.

D1=x (unknown distance from mother to center of mass of system)

M2=10 kg

D2=.20-x (unknown distance from baby to center of mass of system)

The .20 value is the distance in meters between the mother's center of mass and that of the baby. Drawing out the cylinder and the sphere and putting in the known values, you will be able to see this value. The center of mass location (x) is chosen as an arbitrary point between the two known centers of mass of the mother and baby.

Balancing the moments about the unknown center of mass location you get:

M1D1-M2D2=0

M1D1=M2D2

63x=10(.2-x)

x=.02740 m = 2.740 centimeters forward from the mother's center of mass

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