Women and overweight people often experience backpain. Let us explore the reason for this. Assume
the women has a weight of 60.0 daN before pregnancy. Suppose she gains 10.0 daN during pregnancy,
due to weight of the fetus, placenta, amniotic fluid, etc. To make the calculation easy, but still realistic,
we shall model the unpregnant women as a uniform cylinder of diameter 0.30 m. We can model the
added weight due to the fetus as a 10.0 daN sphere with a 25.0 cm diameter and centered about 5.00
cm outside the woman’s original front surface.
(a) By how much does her pregnancy change the horizontal location of the woman’s center of gravity?
(b) How does the change in part (a) affect the way the pregnant woman must stand and walk? i.e.,
what must she do to her posture to make up for her shifted center of gravity?
(c) Can you now explain why she might have backaches?
(a) To calculate the change in the horizontal location of the woman's center of gravity, we need to find the distance between the original center of gravity and the new center of gravity due to the added weight of the fetus.
1. Calculate the original center of gravity:
For a uniform cylinder, the center of gravity is at its geometric center. Given the diameter of the cylinder is 0.30 m, the radius (r) is half the diameter, so r = 0.30 m / 2 = 0.15 m.
2. Calculate the new center of gravity:
The added weight due to the fetus can be modeled as a sphere of diameter 25.0 cm (0.25 m). It is centered about 5.00 cm (0.05 m) outside the woman's original front surface.
The distance between the original center of gravity and the new center of gravity can be found using the Pythagorean theorem. Let's call this distance "d".
d^2 = r^2 + (r + 0.05 m)^2
d^2 = 0.15^2 + (0.15 + 0.05)^2
d^2 = 0.0225 + 0.02
d^2 = 0.0425
d ≈ 0.206 m
Therefore, the pregnancy changes the horizontal location of the woman's center of gravity by approximately 0.206 m.
(b) The change in the horizontal location of the center of gravity affects the way the pregnant woman must stand and walk. To maintain balance and prevent falling forward, she must adjust her posture by:
1. Leaning slightly backward:
By shifting her upper body slightly backward, the woman aligns her body's center of gravity with the new center of gravity, helping to maintain balance.
2. Widening her stance:
By placing her feet slightly wider apart, the woman increases her base of support, providing more stability.
3. Adjusting her stride:
During walking, she might need to adapt her stride to ensure her body remains balanced. This may include taking smaller steps or slowing down her walking pace.
The exact adjustments in posture may vary depending on the individual and their specific condition.
(c) The change in the location of the center of gravity and the adjustments in posture can lead to backaches for pregnant women due to the following reasons:
1. Increased strain on the back muscles:
The altered posture, including leaning backward and widening the stance, puts additional strain on the lower back muscles as they have to work harder to maintain balance and support the shifted center of gravity.
2. Changes in spinal curvature:
The adjustments in posture can cause changes in the natural curvature of the spine, leading to increased pressure on certain spinal discs and muscles. This can result in discomfort and backaches.
3. Ligament and joint laxity:
During pregnancy, hormonal changes can lead to increased ligament and joint laxity, making pregnant women more susceptible to backaches. The altered posture and weight distribution further increase the stress on these already weakened structures.
It is important for pregnant women to practice proper posture, engage in regular exercise, and seek medical advice to manage and alleviate backaches during pregnancy.