A student wrote: “The only reason an apple falls downward to meet the earth instead of the earth rising upward to meet the apple is that the earth is much more massive and so exerts a much greater pull.” Please comment.

As a car rounds a banked circular curve at constant speed, several forces are acting on it: for example, air resistance toward the rear, friction from the pavement in the forward direction, gravity, and the normal force from the tilted road surface. In what direction does the net force point? Explain.

If two planets have the same mass, will they necessarily produce the same gravitational pull on $1.0 \mathrm{~kg}$ objects that are
(a) at their surfaces;
(b) the same center-to-center distance from both planets (but above their surfaces)? Explain.

As part of their training before going into orbit, astronauts ride in an airliner that is flown along the same parabolic trajectory as a freely falling projectile. Explain why this gives the same experience of apparent weightlessness as being in orbit.

Sketch a continuous function f on some interval that has the properties described. The function f has one inflection point but no local extrema.

While going to work this morning off site from his office, an engineer accidentally ran a stop sign and was in a car accident that resulted in the death of a 5-year-old child. He has a strong belief in the universal moral that it is wrong to do serious harm to another person. Explain the conflict that can arise for him between the universal moral and his personal moral about doing serious harm, given the accident was deemed his fault.

Europa, a satellite of Jupiter, is believed to have an ocean of liquid water (with the possibility of life) beneath its icy surface. Europa is $3130 \mathrm{~km}$ in diameter and has a mass of $4.78 \times 10^{22} \mathrm{~kg}$. In the future, we will surely want to send astronauts to investigate Europa. In planning such a future mission, what is the fastest that such an astronaut could walk on the surface Europa if her legs are $1.0 \mathrm{~m}$ long?

A satellite can orbit at 5 km above the Moon’s surface but not at 5 km above Earth’s surface. Why?

Four identical charges Q are placed at the corners of a square of side L. (a) In a free-body diagram, show all of the forces that act on one of the charges. (b) Find the magnitude and direction of the total force exerted on one charge by the other three charges.

Ignoring air resistance, could a satellite be put into orbit in a circular tunnel beneath Earth's surface?

When a roller coaster takes a sharp turn to the right, it feels as if you are pushed toward the left. Does a force push you to the left? If so, what is it? If not, why does there seem to be such a force?

Europa, a satellite of Jupiter, is believed to have a liquid ocean of water (with a possibility of life) beneath its icy surface. In planning a future mission to Europa, what is the fastest that an astronaut with legs of length 0.70 m could walk on the surface of Europa? Europa is 3100 km in diameter and has a mass of $4.8 \times 10 ^ { 22 } \mathrm { kg }$.

Perform the addition or subtraction and simplify.

$$\frac { 1 } { x + 1 } + \frac { 1 } { x - 1 }$$

True or false: Ctesipho est in casa amici.