Read Chapter 4
2.) Provide an example of "free fall"
Answer: If you dive off of a diving board, you are in free fall from
the time that you leave the board to the time that you touch the
water. If you drop your pencil onto your desk,
it is in free fall from the time
that you drop it to the time that it hits your desk.
If you ride on the space shuttle as it is orbiting the Earth (without
firing its engines in order to change its direction or velocity),
you are in free fall.
3.) According to Newton's 3rd Law,
a.) The Earth's gravitational pull on the Sun is greater than the Sun's
gravitational pull on the Earth
b.) The Sun's gravitational pull on the Earth is greater than the Earth's
gravitational pull on the Sun
c.) The Earth's gravitational pull on the Sun is equal in magnitude
to the Sun's gravitational pull on the Earth
Answer: c, they are equal.
4.) Asteroid "Zot", a fictional asteroid in our
solar system, is traveling on an extremely eccentric orbit.
During Asteroid Zot's trip around the Sun,
a.) Asteroid Zot's speed is constant
b.) Asteroid Zot's velocity is constant
c.) Asteroid Zot's momentum is constant
d.) Asteroid Zot's angular momentum is constant
e.) the Sun's gravitational force on Asteroid Zot is constant
Answer: d, Asteroid Zot's angular momentum is constant.
Option "a" doesn't work because Zot speeds up as
it approaches the Sun and slows down as it
moves away from the Sun.
Option "b" doesn't work because Zot's speed and direction change during
its orbit.
Option "c" doesn't work because Zot's velocity changes (see "b" above)
and Zot's mass cannot vary to compensate for the velocity variation.
Option "e" doesn't work because the the strength
of the Sun's force on Zot depends on the distance and between
the Sun and Zot and this distance changes during the orbit.
5.) In Asteroid Zot's orbit (from the previous question):
a.) The distance between Asteroid Zot and the Sun is constant
b.) Asteroid Zot's potential energy is constant
c.) Asteroid Zot's speed is constant
d.) Asteroid Zot's kinetic energy is constant
e.) Asteroid Zot's kinetic energy plus potential energy is constant
Answer: "e" Energy is conserved and so
Asteroid Zot's kinetic energy plus potential energy remains the
same during Zot's orbit around the Sun.
Option "a" doesn't work because the distance between Zot and the
Sun varies -- remember that the orbital path is an extremely
eccentric ellipse.
Option "b" doesn't work because the potential energy depends on the
distance between Zot and the Sun and that distance changes during
Zot's travel around the Sun.
Option "c" doesn't work because Zot speeds up as it approaches
the Sun and slows down as it moves away from the Sun.
Option "d" doesn't work for the same reason that option "c" doesn't
work.
6.) Asteroid "Zerf" is on a perfectly circular orbit around the
Sun. Why doesn't the Sun's gravitational pull cause a 'twisting
force' (or torque) that would speed up Asteroid Zerf?
Answer: In order to speed up,
Zerf would need to be pushed forward in its orbit.
However, the Sun's gravitational pull is along the direction
from Zerf to the Sun. Therefore, the Sun's force isn't in the right
direction to be able to speed up Asteroid Zerf.
7.) Which has more thermal energy per gallon:
a.) a pot of boiling water (temperature = 212 degrees Fahrenheit)
b.) the air inside a warm oven (temperature = 212 degrees Fahrenheit)
c.) both have the same amount of thermal energy per gallon
Answer: "a". The pot of water has much, much more thermal energy
than the air inside a warm oven.
Thermal energy is the sum of kinetic energies of all of the
particles. Since "a" and "b" have the same temperature,
we know that the average kinetic energy of a particle is the
same in both cases. But, the pot of water has many more
particles in it that the air in the warm oven (the
water molecules are packed much closer together in the pot
of water than the air molecules are in the warm oven.) So, the
sum of the kinetic energies of all the water molecules (i.e.
its thermal energy) in the pot of water
is greater than the sum of all the kinetic energies of the air
in the warm oven.
(Note, I've ignored the fact that option "a" refers to water
while option "b" refers to air, but that difference
does not change the fact that the boiling water has more
thermal energy than the air in the warm oven.)
8.) Fill in each blank with a type of energy.
a.) The rocket's fuel was burned in order to speed up the rocket.
This is an example of converting ________ energy to _______ energy.
Answer: chemical potential energy or mass energy (depending on the
type of engine) was converted to kinetic energy
b.) After the fuel was exhausted and while the rocket was still
moving away from the Earth, it slowed as it moved further from the
Earth. This is an example of _________ energy being converted into
__________ energy.
Answer: converting kinetic energy into potential energy
c.) The rocket was powered by a nuclear engine, which consumed atoms
and heated the bath around the hydrogen chamber. This is an example
of _________ energy being converted into __________ energy.
Answer: converting mass energy into thermal energy
d.) The rocket also had a solar panel, which collected sun light in order
to charge a battery. This is an example of converting _________ energy
into __________ energy.
Answer: converting radiant energy into chemical potential energy
9.) Consider a binary star system in which each star has the same
mass and radius as the other.
a.) Where is the center of mass of the binary star system?
Answer: Halfway between the two stars.
c.) If each star's mass is equal to 1030 kilograms, and each
of the stars is located 1012meters from the point about which
it orbits. How long does it take for each star to make a complete
orbit? Hint: use the general form of Kepler's Third Law, which
is p2 =
(4 pi2 a3) / (G (M1 + M2) ),
where G = 6.67 x 10-11 m3/kg/sec2,
second hint: the "exp" key on your calculator is equivalent
to "10 to the". So, to key in 1030, you key in
"exp" "30".
If you were to key in "10" "x" "exp" "30", you would
have 1031, which wouldn't be what you intended.
Answer: Start with
p2 =
(4 pi2 a3) / G (M1 + M2)
and set a = 1012meters,
M1 + M2 = 2 x 1030 kilograms,
G = 6.67 x 10-11 m3/kg/sec2, and
pi = 3.14.
p2 =
(4 x 3.142 x (1012m)3) /
(6.67 x 10-11 m3/kg/sec2 x
(2 x 1030 kg)
p2 = 3.944 x 1037 meters3 /
(1.334 x 1020 m3/sec2)
p2 = 2.96 x 1017 sec2,
then take the square root to get
p = 5.4 x 108 sec (this is about 17 years)
Note: We did not cover the material after this point.
Thus, you do not need to solve the following problems or
study them for the first midterm.
10.) Regarding bound and unbound orbits:
a.) What is the difference between a bound orbit and an unbound
orbit?
Answer: For ease, let us imagine cases in which one object is
much lighter than the other.
A bound orbit is one in which the light object makes many
loops around the heavier object.
For example, the planets are in bound orbits around the Sun.
An unbound orbit is one in which the light object is gravitationally
attracted toward the heavier object, but the attraction is not strong
enough to cause the light object's path to bend enough for it to
make full loops around the heavier object.
b.) If there is an object on a bound orbit around the Sun and you want
to change its orbit to make it an unbound orbit, do you need to
give it energy or take away some of its energy?
Answer: You need to give it energy.
11.) Tides on Earth are caused by:
a.) winds pushing water
b.) the Moon's gravitational attraction
c.) the Earth rotating slower than the synchronous rotation rate
d.) all of the above
e.) none of the above
Answer: "b" the Moon's gravitational attraction
12.) Why does the same side of the Moon face the Earth, 24 hours
a day, 365 days a year?
Answer: Tidal friction has slowed the Moon's rotation rate so that
currently, the moon takes the same amount of time to rotate once
as it does to orbit the Earth once. Since the rotation period
and orbital period match, the same side of the Moon faces the
Earth throughout the month, month after month.