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1 yd^2 ×(3 ft/1 yd)^2 = 9 ft^2
1 yd^3 ×(3 ft/1 yd)^3 = 27 ft^3
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C 1 /C 2 = (w 1 /w 2 )^4Answers to self-checks for chapter 1
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The stream has to spread out. When the velocity becomes zero, it seems like the cross-sectional
area has to become infinite. In reality, this is the point where the water turns around and comes
back down. The infinity isn’t real; it occurs mathematically because we used a simplified model
of the the stream of water, assuming, for instance, that the water’s velocity is always straight
up.
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A positive ∆x means the object is moving in the same direction as the positivexaxis. A
negative ∆xmeans it’s going the opposite direction.
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(1) The effect only occurs during blastoff, when their velocity is changing. Once the rocket
engines stop firing, their velocity stops changing, and they no longer feel any effect. (2) It is
only an observable effect of your motion relative to the air.
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Galilean relativity says that experiments can’t come out differently just because they’re per-
formed while in motion. The tilting of the surface tells us the train is accelerating, but it doesn’t
tell us anything about the train’s velocity at that instant. The person in the train might say
the bottle’s velocity was zero (but changing), whereas a person working in a reference frame
attached to the dirt outside says it’s moving; they don’t agree on velocities. Theydoagree on
accelerations. The person in the train has to agree that the train is accelerating, since otherwise
there’s no reason for the funny tilting effect.
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Yes. In U.S. currency, for instance, the quantum of money is one cent.
Answers to self-checks for chapter 2
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There are two reasonable possibilities we could imagine — neither of which ends up making
much sense — if we insist on the straight-line trajectory. (1) If the car has constant speed along
the line, then in the frame we see it going straight down at constant speed. It makes sense
that it goes straight down in the frame of reference, since in that frame it was never moving
horizontally, and there’s no reason for it to start. However, it doesn’t make sense that it goes
down with constant speed, since falling objects are supposed to speed up the whole time they
fall. This violates both Galilean relativity and conservation of energy. (2) If it’s speeding up
and moving along a diagonal line in the original frame, then it might be conserving energy in
one frame or the other. But if it’s speeding up along a line, then as seen in the original frame,
both its vertical motion and its horizontal motion must be speeding up. If its horizontal velocity
is increasing in the original frame, then it can’t be zero and remain zero in the frame. This
violates Galilean relativity, since in the frame the car apparently starts moving sideways for
no reason.