Download Test Review Sheet

Test Review Sheet
There will be a TEST on 5/18(Wednesday). The test will be based on ‘Gravitational
Interaction’ and ‘Fluids’
True or False
1. If Earth had its present mass but twice the radius, the acceleration due to gravity would increase
(True False)
2. The Sun pulls harder on Earth’s ocean than the moon (True False)
3. Ocean tides are caused by differences in the gravitational pull between the moon and the opposite sides
of Earth (True False)
4. If the distance between two objects doubles, then the gravitational force acting between them would be
one half the original force (True False)
5. Pressure at the bottom of a lake depends on the density of the lake and on the volume of the lake
(True False)
6. The strength of the buoyant force that will act on an object depends on the mass of the object
(True False)
7. As a solid object sinks deeper into the water, the pressure will increase (True False)
8. As a solid object sinks deeper into the water, the buoyant force will increase (True False)
9. The strength of the buoyant force that will act on an object depends on the volume of the object
(True False)
10. As a solid object sinks deeper into the water, the buoyant force stays the same (True False)
Multiple Choice
1. Two objects move toward each other because of gravitational interaction. As the objects gets closer and
closer, the force between them
a) increase
b) decrease
c) remain constant
d) increase and then decrease
2. Suppose the gravitational force between two massive spheres is 10N. If the distance between them the
spheres is cut in half, what is the force between the masses?
a) 40N
b) 20N
c) 10N
d) 5N
e) 2.5N
3. Why did Newton think there was a force acting on the moon?
a) Because the moon always keeps one side toward Earth b) Because the moon moves in a curved path
c) Because there is no air on the moon
d) Because the moon is moving
4. The factor most directly responsible for making a black hole invisible is its
a) size
b) mass
c) color
d) escape velocity
5. Two friends say they cannot feel the gravitational attraction between them. The reason for that is because
a) gravitational force does not exist between living things
b) the friend’s masses are too small for the gravitational force between them to be significant
c) gravity only acts at large distance; they are too close together
d) there is too much friction between their chairs and the floor
6. The mass of an object at the surface of the Earth compared to the mass of the same object at a distance of
two Earth radii from the surface of the Earth is:
a) the same
b) one half
c) one quarter
d) one nint
7. Which of the following graphs best represents the gravitational force between two masses as the distance
between the masses change is:
a)
Fg
b)
Fg
r
c)
Fg
d)
Fg
r
r
r
8. A 90kg astronaut weighs 1/6 as much on the moon as on Earth because:
a) the moon is made of denser rock than the Earth
b) the astronaut is closer to the center of the mass when standing on the moon’s surface
c) the mass of the Earth also pulls on the astronaut
d) the mass of the moon is substantially less than the mass of the Earth
9. If the distance between two objects were doubled, the force of gravitational attraction between the object
would be:
a) the same b) double the original force c) one half the original force d) one quarter the original force
10. The force of gravitational attraction between two objects is 20N. If the mass of one of the object were
doubled, the gravitational force between the objects would be:
a) 5.0N
b) 10N
c) 40N
d) 80N
11. Two stars are bound together by gravity. The larger star has four times the mass of the smaller star.
Which diagram best illustrates the orbital motion of the two stars?
a)
b)
c)
d)
12. The reason a life jacket help people float is that
a) jacket and the person together will have less weight than the person alone
b) the jacket has the same density as an average person
c) the jacket repels the water and exerts a buoyant force on the person
13. When first put in water, a plastic toy boat will sink until
a) it displaces a volume of water equal to its own volume
b) it displaces a weight of water equal to its own weight
c) the water density equals the density of the boat
d) the buoyant force equals the volume of the boat
14. In a vacuum on earth, an object has no
a) buoyant force
b) mass
c) heat
d) weight
15. As a whale swims deeper into the ocean, increasing water pressure squeezes its volume, making the
whale smaller. As the whale swims deeper and deeper, the buoyant force on it
a) decreases
b) increases
c) remains the same
d) doubles
Gravitational Interactions
Fg = 𝐺𝐺
𝑚𝑚1 𝑚𝑚2
𝑟𝑟 2
G=6.67×10-11N·m2/kg2
𝑣𝑣 =
2𝜋𝜋𝜋𝜋
𝑇𝑇
𝐺𝐺𝐺𝐺
𝑣𝑣 = �
𝑟𝑟
𝑇𝑇 =
2𝜋𝜋𝑟𝑟 3/2
√𝐺𝐺𝐺𝐺
𝑣𝑣𝑒𝑒 = �
2𝐺𝐺𝐺𝐺
𝑅𝑅
1. The center-to-center distance between the Earth and the Moon 384400km. The moon completes an orbit
2𝜋𝜋𝜋𝜋
.
in 27.3 days. Determine the Moon's orbital speed. Use 𝑣𝑣 =
𝑇𝑇
(remember to convert days into seconds and 1km=1000m)
ans) 1.02×103m/s
2. A m1=200kg mass and a m2=500kg mass are separated by r =0.4m.
m1
(i) Find the net-gravitational force(=∑F) exerted by these
m2
masses on a 50kg mass placed midway between them and
the direction. F1 is the force acting on the 50kg mass due to
m1, . F2 is the force acting on the 50kg mass due to m2.
r
F1
F2
50kg!
ans) 2.5×10-5N toward 500kg
(ii) Find the time it takes for the 50kg mass before it collides with that mass (use ∑F=ma & d=vit + ½at2)
ans) 894s
(iii) At what position (other than infinitely remote ones) can
the 50kg mass be placed so as to experience a net force of
zero?
m1
r
m2
50kg!
ans) 0.155m
3. A satellite with a mass of 200kg is placed in Earth's orbit at a height of 200km above the surface.
i) Assuming circular orbit, how long, in hours, does the satellite take to complete one orbit? (Mass and
radius of Earth Me=6×1024kg, Re= 6.38×106m, 1km=1000m)
ans) 1.47hrs
ii) What is the satellite's speed?
ans) 7.8×103m/s
4. Two objects attract each other with a gravitational force of 1×10-8N when separated by 0.2m. If the total
mass of the two objects is 5kg, what is the mass of each?
ans) 2kg & 3kg
Fg = 𝐺𝐺
𝑚𝑚1 𝑚𝑚2
𝑟𝑟 2
G=6.67×10-11N·m2/kg2
𝑣𝑣 =
2𝜋𝜋𝜋𝜋
𝑇𝑇
𝐺𝐺𝐺𝐺
𝑣𝑣 = �
𝑟𝑟
𝑇𝑇 =
2𝜋𝜋𝑟𝑟 3/2
√𝐺𝐺𝐺𝐺
5. Three uniform spheres of masses m1=6kg, m2=4kg and m3=2kg are
placed at corners of a right triangle. Calculate the resultant
gravitational force on m2. (hint : use Pythagorean theorem r2=x2 + y2)
𝑣𝑣𝑒𝑒 = �
2𝐺𝐺𝐺𝐺
𝑅𝑅
(0, 3)m
m3
F32
ans) 1.16×10-10N
m1
m2
F12
(0,0)
(–4, 0)m
6. If the earth had twice its present mass, the earth's orbital period around the sun(at our present distance
from the sun) would be
ans) 1 year
7. If the sun had twice its present mass, the earth’s orbital period around the sun(at our present distance
from the sun) would be
ans)
1
√2
year
8. When two point masses are a distance D apart, each exerts a gravitational attraction F on the other mass.
𝟏𝟏
To reduce this force to F, you would have to separate the masses to a distance of
𝟑𝟑
ans) D√3
9. If a planet is ever discovered orbiting midway between the earth and the sun, its orbital period will be
closest to
*~ use 𝑇𝑇 =
2𝜋𝜋𝑟𝑟 3/2
√𝐺𝐺𝐺𝐺
ans) 0.35 years
QuizX
If the distance between two objects were doubled, the force of gravitational attraction between the object
would be:
ans) one quarter of the original force
1. The force of gravitational attraction between two objects is 20N. If the mass of both objects were
doubled, the gravitational force between the objects would be:
ans) 80N
Fg = 𝐺𝐺
𝑚𝑚1 𝑚𝑚2
𝑟𝑟 2
G=6.67×10-11N·m2/kg2
𝑣𝑣 =
2𝜋𝜋𝜋𝜋
𝑇𝑇
𝐺𝐺𝐺𝐺
𝑣𝑣 = �
𝑟𝑟
𝑇𝑇 =
2𝜋𝜋𝑟𝑟 3/2
√𝐺𝐺𝐺𝐺
𝑣𝑣𝑒𝑒 = �
2𝐺𝐺𝐺𝐺
𝑅𝑅
2. Suppose the gravitational force between two massive spheres is 10N. If the distance between the spheres
is cut in half, what is the force between the masses?
ans) 40N
4. If two small identical spheres attract each other with a force of 3×10-9N when they are 0.25m apart, what
is the mass of each sphere?
Ans) 1.68kg
5. Deimos, a moon of Mars, has a diameter about 12km(1km=1000m), with a mass of 2×1015kg. Suppose
you are alone on Deimos and want to play a one-person game of baseball. You would be the pitcher, and
you would be the batter! With what speed would you have to throw a baseball so that it would go into orbit
and return to you so you could hit it?
Ans) 4.71m/s
6. An Earth satellite moves in a circular orbit with an orbital speed of 6200m/s. Find the time it takes to
complete one orbit around the Earth. Mass of Earth Me=6×1024kg. hint: you need to use two formulas
Ans) 1.05×104s
7. On October 15, 2001, a planet was discovered orbiting around a star called HD68988. The planets orbital
distance was measured to be 1.05×1010m from the center of the star, and its orbital period was estimated at
6.3 days. What is the mass of HD68988?
Ans) 2.3×1030kg
8. Solve the following two questions. All the masses are 2kg.
i) Find the strength and direction(left or right) of the net
gravitational force on mass A due to mass B and C.
C
0.1m
ans) 2.5×10-8N left
ii) Find the strength and direction(left or right) of the
net gravitational force on mass A due to mass B and C
but this time A on left of C.
A
A
0.4m
C
0.1m
ans) 2.8×10-8N right
B
B
0.4m
Pendulum
𝐿𝐿
The period of a pendulum is 𝑇𝑇 = 2𝜋𝜋 � where L is the length of the string and g=9.8m/s2
𝑔𝑔
1. What is the period of pendulum consisting of a 6kg object oscillating on a 4m string?
ans) 4.0s
2. A man enters a tall tower, needing to know its height. He notes that a long pendulum extends from the
ceiling almost to the floor and that its period is 12s.
(a) How tall is the tower?
Ans) 35.8m
(b) If this pendulum is taken to the moon, where the g=1.67m/s2, what is its period there?
Ans) 29s
3. A pendulum is made from a 0.65m long string and a small ball attached to its free end. The ball is pulled
to one side through a small angle then released from rest. After the ball is released, how much time elapsed
before it attains its greatest speed?
ans) 0.4s
4. A science museum has asked you to design a pendulum that will make 25 complete swings in 85s. What
length should you specify for this pendulum?
ans) 2.87m
5. A pendulum in a science museum entry hall is 3.5m long, has a 1.25kg bob at its lower end, and swings
with an amplitude of 11°. How much time does the pendulum take to swing from its extreme right side to
its extreme left side?
ans) 1.88s
Fluids
1. An object’s mass is 2kg. If the buoyant force acting on the object is 20N, would the object float, sink or
stay still? Justify your answer~
Ans) float
2. An object’s mass is 4kg. If the buoyant force acting on the object is 20N, would the object float, sink or
stay still? Justify your answer
Ans) sink
The information below will be needed to solve questions 3 ~ 4
A 1-liter container filled with water has a mass of 1kg and weighs 9.8N. A 1-liter container filled with
mercury. A 1-liter container filled with mercury has a mass of 13.6kg and weighs 133N. Weight Wg=mg
,where g=9.8m/s2.
3. i) If you fill up 1liter container with sand, and immerse into a pool of liquid mercury, how much buoyant
force will act on the object?
Ans) 133N
ii) You weigh the sand-filled container and discover it weighs 17.64N. Will the container sink or float?
Justify your answer~
ans) float
iii) If you take that same sand-filled container and immerse into water, what is the buoyant force and
explain whether the container will sink or float.
Ans) 9.8N, sink
4. i) What is the buoyant force acting on an empty 1-liter container when completely submerged into
water? Will it float, sink or stay still in the water? Justify your answer~!
Ans) 9.8N, float
ii) What is the buoyant force acting on an empty 1-liter container when submerged halfway into water?
That is, half a liter is submerged into water. Justify your answer~!
Ans) 4.9N
5. A boat is floating in water. The maximum volume of water the boat
can displace before it sinks is 520 liters. If each cargo weighs 30N,
how many cargos can be loaded onto the boat before the boat sinks?
1liter of water weighs 9.8N
cargos!
boat!
Ans) 169 cargos
6. A piece of wooden block has a dimension as shown.
*i) If the block sinks 1.7m before floating, then what is the weight of
the block in Newton? 1m3 of water weighs 1000kg! Hint: for any
floating object, the weight of the displaced water will be equal to its
weight!!
2m
4m
8m
Ans) 266560N
**ii) If a cargo is placed on the wood making the wood sink 0.2m
more, than what is the weight of the cargo?
1.7m
cargo!
1.9m
Ans) 31360N
*~The weight of an object under water is called apparent weight(Wa)
Wa=Fg – Fb
5. If an object is submerged into a container filled
with water, and the water rose half a liter(=0.5 liter),
then volume of the object is 0.5 liter.
i) How much buoyant force is acting on the object?
amount of water risen
0.5 liter
Ans) 4.9N
ii) If the mass of the object is 6kg, then what is the apparent weight(Wa) of the object under water?
Ans) 53.9N
6. What is the apparent weight of an object if the buoyant force is equal or greater than the actual weight?
Ans) 0N
7. An object has mass of 14.1kg. Answer the questions below
i) Use Fg=mg to find the actual weight in air, where g=9.8m/s2.
Ans) 138.18N
ii) When the object is immersed into water, a buoyant force of 110N of force is acting on the object. How
much force is needed to lift the object?
Ans) 28.18N
An object with a volume of 1 liter in air will displace 1 liter of air. Since the weight of 1 liter of air is equal
to 0.0126N, the buoyant force acting on the 1 liter object in air will always be 0.0126N.
*~ the weight of 1 liter of air = 0.0126N
8. i) If a container has a volume of 1.2 liter and it is empty, how much buoyant force is acting on it in air?
Ans) 0.01512N
ii) If the container above is now filled up with water, how much buoyant force is acting on it in air?
Ans) 0.01512N
9. The picture below is top view of a soccer ball. If the ball is kick as shown below, which direction will the
ball curve? Left, right or just straight? Explain using Bernoulli’s principle.
left!
Kicked this side!!
straight!
right!