Women often experience back pain when they are pregnant. suppose a woman's mass before pregnancy is 66 kg and her center of mass when standing is located directly above the hips. by the thirty-fourth week of pregnancy, she has gained 8.2 kg (the combined mass of the fetus, the placenta, and the amniotic fluid). the center of mass of this 8.2 kg is 16 cm in front of the hips. if she hasn't changed her posture, how far in front of the hips is her center of mass? women have three wedge-shaped lumbar vertebrae, whereas men have only two. this evolutionary adaptation permits a greater curvature of the lumbar spine to keep a pregnant woman's cm above the hips.

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)