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. Cgchange=10daN*(.05m+.125m)/70
=1/7 (.175m)=.025 or 2.5 cm outboard from the original axis.
b. He has to lean back to keep from falling frontwards.
c. getting the cg lined up, moves the upper body backwards, like a guy walking around bending backwards looking up all the time. Your lower back muscles are constantly in tension to pull backwards, as your expanding uterus is getting weaker. It is actually more complicated that this, hormones, joints, are also involved. A pregnant mom isn't going to see a physicist for back pain... http://www.babycenter.com/0_low-back-pain-during-pregnancy_9402.bc
To answer these questions, we need to consider the concept of center of gravity and its relationship with the woman's changing weight distribution during pregnancy.
(a) The horizontal location of the woman's center of gravity changes due to the additional weight of the fetus. We can calculate this by finding the center of gravity of the combined system of the woman and the added weight of the fetus.
To determine the horizontal location of the center of gravity, we need to consider the moments of the forces acting on the system. The moment of a force is the product of the force and its perpendicular distance from a reference point. In this case, the reference point can be chosen as the original front surface of the woman.
Let's label the original center of the cylinder as point A, and the center of the added weight due to the fetus as point B. We can assume the distance between A and B is 5.00 cm (0.05 m).
The woman's weight distribution can be represented by a uniform cylinder, where the center of gravity is at its geometrical center. Since the cylinder has a diameter of 0.30 m, the distance between the original front surface (point A) and the center of gravity of the cylinder is 0.15 m.
The added weight due to the fetus can be represented by a sphere. The center of gravity of a sphere is at its geometric center. Since the sphere has a diameter of 25.0 cm (0.25 m), the distance between the center of the sphere (point B) and the geometric center is 0.125 m.
Using the principle of moments, we can calculate the horizontal location of the center of gravity (CG) of the combined system:
CG = (mA * xA + mB * xB) / (mA + mB)
Here, mA is the mass of the woman (60.0 daN), mB is the mass of the added weight due to the fetus (10.0 daN), xA is the distance between the original front surface (point A) and the cylinder's center of gravity (0.15 m), and xB is the distance between point A and the center of the sphere (point B) at the added weight of the fetus (0.05 m).
Substituting the values, we get:
CG = (60.0 * 0.15 + 10.0 * 0.05) / (60.0 + 10.0) = 0.14 m
Therefore, the pregnancy changes the horizontal location of the woman's center of gravity by 0.14 meters.
(b) The change in the horizontal location of the center of gravity affects how the pregnant woman must stand and walk to maintain balance. To compensate for the shifted center of gravity, she needs to adjust her posture and position her body in a way that ensures stability.
Typically, pregnant women naturally shift their center of gravity forward as the pregnancy progresses. This shift helps to balance the additional weight carried in the abdomen. To maintain balance, pregnant women often widen their stance while standing, keeping their feet more apart than usual. This wider stance helps to provide a wider base of support and improve stability.
When walking, the pregnant woman may also shorten her strides and take smaller steps to maintain better control and balance. Additionally, she might lean slightly backward to counterbalance the forward shift of the center of gravity.
(c) The reason why pregnant women might have backaches is related to the shift in their center of gravity and the ensuing changes in their posture and weight distribution. As the woman's center of gravity moves forward due to the pregnancy, it alters the normal alignment of the spine. This puts extra stress on the lower back muscles, which can lead to discomfort, pain, and backaches.
The increasing weight carried in the abdomen places additional strain on the lower back, causing it to work harder to maintain posture and stability. The muscles and ligaments supporting the spine can become strained, resulting in back pain.
Furthermore, the altered posture that pregnant women adopt to compensate for the shifted center of gravity can lead to additional stress on the back muscles and increased pressure on the spinal discs.
In summary, the combination of the shifted center of gravity, changes in posture, and increased load on the lower back during pregnancy can contribute to backaches experienced by pregnant women.