1.Putting magnets on your body will improve your energy fields.
This is NOT falsifiable and hence not a scientific hypothesis. 'Energy
fields' are one of those scientific sounding but actually meaningless phrases
that bogus medicine delights in. Since the term is meaningless, it
cannot be measured and therefore the hypothesis does not make a testable prediction.
2.Putting magnets on your body will reduce muscle aches and pains.
This is a scientific hypothesis because it makes a measurable prediction and
therefore you can test it. Pain is definable and measurable (if only
by people reprting how they feel). Find some people with muscles aches
and pains. Put magnets on half of them and see how they feel in a week.
Compare that to how the other half feel in a week. (In practice
you want to be sneakier than that. Put real magnets on half of them
and put fake magnets on the other half. That way all of the subjects
feel like they're being given the 'special' treatment.)
3.The moon causes ocean tides.
This is a scientific hypothesis because it makes a measurable prediction and
therefore you can test it. There are several ways to test this:
a) Timing: if the moon causes tides, then the high tide should always occur
when the moon is at the same location in the sky (eg: directly overhead, two
hours after the moon is directly overhead, etc). In effect, as the
Earth spins on its axis, the high tide should stay approximately underneath
the moon. b) observational: if we find other planets with oceans,
only the ones with moons should have tides. c) experimental: in the
far future we could have enough technology to be able to move the moon and
see how it affects the tides.
2) Unit conversions: a) How many inches are there in a kilometer? b) How many seconds are there in a month?
a) 1 km = 1 km * (0.62 mi/km) * (5280 ft/mi) * (12 in/ft) = 3.9 * 10^4 in
b) Let's use a 30 day month because it's September (28, 29, 30 and 31 are
all OK):
then 1 month = 1 month *
(30 days/month) * (24 hours/day) * 60 min/hr * 60 s/min= 2.6 * 10^6
s
Note that in both cases I only wrote down two digits of my answer (3.9 and 2.6 respectively). This is because I do not know the answer more precisely than that. (I don't care how many digits your calculator gives you.) In the first problem, I only had two digits for the number of miles per kilometer. In the second problem, the number of days in the month is not precise. Writing the second number as 2.592 * 10^6 s would be wrong because it implies that I know the answer MUCH more precisely than I do.
Chapter 2:
Exercise 8: If inertia kept the Earth moving, then the Earth would continue to move in a straight line. It does not. It orbits the Sun travelling around a huge circle. Therefore there must be a force on it to make it go in a circle. This force is the gravitational attraction of the Sun. We will learn about it next month.
14: When the bus suddenly slows, I keep moving at the same (previous) speed until a force acts on me. This means that I am moving faster than the bus and I lurch forward relative to the bus. When the bus suddenly accelerates, I keep moving at the same (previous) speed until a force acts on me. This means that I am moving slower than the bus and I lurch backward. (Then the back of the seat hits my back and applies a force to me to make me go faster.)
16: Newton's Law of Inertia says that the cart will keep moving at the same speed in a straight line unless another force acts on it. Friction between the cart and road and friction in the bearings of the cart wheels will apply a force on the cart that will make it slow down. Thus this does NOT violate Newton's law of inertia. (Note that if there was no very little friction, the cart would keep going for a long time before stopping. If there was no friction at all then the cart would not stop [until it hit something].)
18: Consider a situation where you and your friend are both pushing on a box. The maximum force is when you and your friend are both pushing in the same direction. Then the forces add to give 20 N + 12 N = 32 N. The minimum force is when you are pushing in opposite directions. Then the forces subtract to give 20 N - 12 N = 8 N.
23: The total upward force (400 N + X) must equal the total downward force (250 N + 300 N + 300 N = 850 N). Thus, 400 N + X = 850 N or X = 450 N.
24: You should take a look at the answer to exercise 25 in the back of the book for more information. Each of her arms supports half of her weight. Therefore, each end of the rope supports half of her weight. Therefore, the reading on the scale is half of her weight.
30: Why does the upward force of the table on the book exactly balance the balance the downward force of gravity on the book? How can the table be that smart? How does the table 'know' to push harder on heavier books? The answer is that when you put something on the table, it compresses the table a little bit (you can see the compression more clearly if you use a piece of foam instead of a table). The book compresses the table until the force opposing the compression exactly equals the weight of the book. You can see that with a spring where you have to exert more and more force to compress the spring more and more. The more force you exert, the more the spring compresses until the force of the spring exactly opposes the force you exert. The same thing happens when you put a book on a table. A light book compresses the table less than a heavy book so the force of the table on alight book is less than the force of thetable on a heavy book.
38: a) If you toss a coin straight up when the train is in uniform
straight line motion, then the coin will land on your lap (just like the ball
and the cart).
b) If the train slows suddenly while the ball is in midair, then the ball
keeps moving at constant horizontal speed (there is no horizontal force on
the ball to change its motion) and lands ahead of your lap.
c) If the train turns suddenly, then the ball will keep moving in a straight
line at constant horizontal speed and will land to the side of your lap.
Estimation:
One deck of 52 cards is about a cm thick. (No, I don't care if
it is 0.8 cm or 1.5 cm. It's somewhere between 0.5 and 2.5 cm and that's
close enough for this.) That means that 100 cards are about 2 cm thick.
That means that 100 million cards are about 2 cm * 10^6 thick. Now
we need to convert this to meters: 2 * 10^6 cm = 2 * 10^6 cm * (1 m/100 cm)
= 2 * 10^4 m. This is twice the height of Mt Everest or about 20 km.
That's a pretty tall stack of cards (reaching up twice as high as jet planes
fly).