My question is about number 4 on the physical sciences section. I guess I just don't understand the concept behind setting the torque equal to the gravitational potential energy in that I can't visualize/understand why they would be equal.
Also, for number 49 on the biological science section of Kaplan Full Length 8, wouldn't the flow be reversed and be from the pulmonary artery to the aorta?
Thanks!
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For the first question, let's start by considering the forces acting on each of the small balls (m). They each have a force of gravity created by Earth acting downwards (F = mg), and a force of gravity created by the large balls (F = GMm/r2). Let’s then translate these forces into torques. We have forces in two directions, so let’s consider rotation caused by torques in those two directions. The two forces of gravity from Earth are acting in opposite directions by rotation, so the two torques cancel out. That is to say that we have rotational equilibrium, looking only at the forces of gravity from Earth.
For the other direction, we have a torque on each ball pulling counterclockwise. Since they’re pulling the same rotational direction, we can just add them up. Torque = (lever arm)(force), so torque from each is (L/2)(GMm/r2). Adding the torques together, we have 2(L/2)(GMm/r2) = GMm/r2. That’s answer (D).
Overall, we’re not setting equal to gravitational potential energy; we’re calculating the torque by multiplying the lever arm (L/2) by the force between the two masses – a gravitational force equal to GMm/r2.
For the other question, remember that this question says after birth. The ductus arteriosus connects the pulmonary artery and the aorta. After birth, when an individual has the adult-style circulation, the pressure in the aorta is MUCH higher than the pulmonary artery. Thus, we would expect blood to travel through the shunt – if it’s still open – from the area of higher pressure to lower pressure. Therefore, there will be flow from the aorta to the pulmonary artery.
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