Download Chap 9: Gravity flexbook

Unless otherwise noted, the following is a direct borrowing
or simplification of: The Free High School Science Texts:
Textbooks for High School Students
Studying the Sciences Chemistry Grades 10 – 12 Version 0
November 9, 2008
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10-Gravity
Weight
Weight is the gravitational force that the Earth exerts on any object. The
weight of an objects gives you an indication of how strongly the Earth
attracts that body towards its centre. Weight is calculated as follows: Weight
= mg where m = mass of the object (in kg) and g = the acceleration due to
gravity (9.8 m/s2)
Important: Weight is sometimes abbreviated as Fg which refers to the force of
gravity. Do not use the abbreviation “W” for weight since it refers to Work.
Now, we have said that the value of g is approximately 9.8 m/s2 on the surface
of the Earth. The actual value varies slightly over the surface of the Earth.
Each planet in our Solar System has its own value for g. These values are
listed as multiples of g on Earth.
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Differences between Mass and Weight
Mass is measured in grams (g) and is the amount of matter in an object. An
object’s mass does not change unless matter is added or removed from the
object. The differences between mass and weight can be summarized in the
following table:
Questions
1. A bag of sugar has a mass of 1 kg. How much does it weigh:
(a) on Earth?
(b) on Jupiter?
(c) on Pluto?
2. Neil Armstrong was the first man to walk on the surface of the Moon. The
gravitational acceleration on the Moon is 1/6 of the gravitational acceleration
on Earth, and there is no gravitational acceleration in outer space. If Neil’s
mass was 90 kg, what was his weight:
(a) on Earth?
(b) on the Moon?
(c) in outer space?
3. A monkey has a mass of 15 kg on Earth. The monkey travels to Mars.
What is his mass and weight on Mars?
4. Determine your mass by using a bathroom scale and calculate your weight
for each planet in the Solar System, using the values given in the table above
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Weight & Mass Lab
Procedure:
1. Hang a spring scale from a ringstand using the setup illustrated here.
clamp arm
ring clamp
spring scale
weights
ringstand
2. At 3 different times, hang 3 different weights from the scale. Record both the
weight in Newtons and the mass in grams.
Don’t forget
to make the
Trial
Newtons
Kilograms
conversion.
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2
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3. Graph your results, with Newtons as the Y-axis and Kilograms as the X-axis.
4. What units do Newtons break apart into?
5. What is the relationship between weight and mass? (Give me a number by
finding the slope of the line on your graph.)
6. What are its units? Explain how you got them using your graph.
7. The number you provided in 5 and 6 above corresponds to a very important
number on Earth. What is the importance of the number you found?
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Acceleration due to Gravity
Gravitational Fields
A field is a region of space in which a mass experiences a force. Therefore, a
gravitational field is a region of space in which a mass experiences a
gravitational force.
Free fall
Free fall is the term used to describe a special kind of motion in a
gravitational field— motion when no forces other than gravity act on the
object. It is found naturally in space which is a near vacuum, but on a planet
there is always some air friction which slows down the fall.
The acceleration of an
object due to gravity is
independent of the
mass of the object. It
does not matter what
the mass of the object
is. The shape of the
object, however, is
important. A sheet of
paper would take much
longer to reach the
ground than would a
tennis ball. This is
because air friction on
the paper is much
greater than air friction
on the tennis ball.
If we lived in a world
where there was no air
resistance, the sheet of
paper and the tennis
ball would reach the
ground at the same
time. This would
happen in outer space
or in a vacuum.
If a metal ball and
tennis ball were
Case Study : Galileo Galilei
In the late sixteenth century, it was generally believed
that heavier objects would fall faster than lighter objects.
The Italian scientist Galileo Galilei thought differently.
Galileo hypothesized that two objects would fall at the
same rate regardless of their mass. Legend has it that in
1590, Galileo planned out an experiment. He climbed to
the top of the Leaning Tower of Pisa and dropped several
large objects to test his theory. He wanted to show that
two different objects fall at the same rate (as long as we
ignore air resistance). Galileo’s experiment proved his
hypothesis correct; the acceleration of a falling object is
independent of the object’s mass.
A few decades after Galileo, Sir Isaac Newton would show
that acceleration depends upon both force and mass. While
there is greater force acting on a larger object, this force is
canceled out by the object’s greater mass. Thus two objects
will fall (actually they are pulled) to the earth at exactly
the same rate.
Questions:
Read the case study above and answer the following
questions.
1. Divide into pairs and explain Galileo’s experiment to
your friend.
2. Write down an aim and a hypothesis for Galileo’s
experiment.
3. Write down the result and conclusion for Galileo’s
experiment.
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dropped from the same height down a tube from which all air had been
removed, both would reach the ground at the same time. It would not matter
that one ball was heavier than the other.
Objects in orbit, like satellites or the space station, are in free fall. They
would be weightless if there were no gravity effecting them. Astronauts on
the space station feel like they are weightless, but actually they are not, they
are falling toward Earth. Orbit occurs when the object is moving sideways so
fast that it is continually missing the ground but not so fast that it can escape
the gravity of Earth. In this scenario, since the velocity sideways and the
acceleration downward are constant and in exactly the right amount, the
path taken by the object is a circular orbit. Suppose a person tied a ball onto
a string and then swung the string+ball around their head. If they swing it
the right speed, the ball orbits their head. If the ball moves too slowly, it
crashes into the person. If it moves too fast, it might break the string and fly
away. This example is similar to that of a satellite orbiting a planet. Gravity
for the satellite does the job done by the string onto the ball. (BVHS).
Notice in the above example if the string were to break, the ball would fly
away in a straight line. This shows that the motion of the ball is in a straight
line. The string forces the motion to curve, but without the string the motion
returns to being a straight line. The same is true for a satellite orbiting a
planet. Its motion is in a straight line, but the motion is artificially curved by
the presence of gravity. If the gravity were to suddenly shut off, the satellite
would zoom away on a straight line path. (BVHS).
To train for free fall, astronauts ride the vomit comet, a cargo airplane with a
graining room where the cargo should be. The airplane rises as high as it can
and then cuts its engines and dives, falling unpowered toward the ground.
The astronauts in the training room feel weightless because the floor beneath
them is falling at the same rate they are. We normally feel our weight
because the floor beneath us isn’t falling. The floor and our bones and
skeleton form a counter force to gravity. On the other hand, if the floor was
falling at the same rate we were, we would have no ability to stand up
against gravity. We would be in free fall. The physical feeling of free fall is
that of falling. Astronauts in free fall experience a sense of falling
continually, as long as they are in free fall (BVHS).
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The acceleration due to gravity is constant. This means we can use the
equations of motion under constant acceleration to describe the motion of an
object in free fall. The equations are repeated here for ease of use.
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By now you should have seen that free fall motion is just a special case of
motion with constant acceleration, and we use the same equations as before.
The only difference is that the value for the acceleration, a, is always equal to
the value of gravitational acceleration, g. In the equations of motion we can
replace a with g.
Review Concepts
Review Questions
1. A brick falls from the top of a 5 m high building. Calculate the velocity
with which the brick reaches the ground. How long does it take the brick to
reach the ground?
2. A stone is dropped from a window. It takes the stone 1,5 seconds to reach
the ground. How high above the ground is the window?
3. An apple falls from a tree from a height of 1,8 m. What is the velocity of the
apple when it reaches the ground?
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Vocabulary
gravity—the mass-based attraction between two objects
mass—an object’s resistance to being accelerated
weight—the effect of gravity upon mass
g—9.8 m/s2
gravitational field—a region where any objects fall in the same direction. For
example, Earth’s gravitational field extends until Mars’ gravitational
field is reached. Just a little toward Earth from the separating line
between the two gravity fields, an object falls toward Earth. Just a
little toward Mars, an object falls toward Mars.
free fall—a situation simulating weightlessness where an object falls with no
resistance toward the center of the gravity field.
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Gravity Lab
Set up your track (2 meter sticks) on a lab table.
Using a protractor, measure the angle of the track to the table top.
track
measure this angle
Time how long it takes the marble to roll
down the length of the track.
table top
Do this for 3 different angles.
Record your values in the table below.
angle (degrees)
time (s)
length (m)
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1
2
1
3
1
velocity (m/s)
Graph velocity on the vertical axis and angle on the horizontal axis. Extrapolate the line
to the ends of the graph. Answer questions 1-4 based on your graph.
1) What would the velocity be if the angle were 90 degrees?
2) The velocity found this way is an average velocity because the marble starts at 0m/s
and gradually picks up speed. All the velocities it has while accelerating down the ramp
are part of the time you recorded. To get the final velocity (the fastest velocity it
reached), double the answer to 1). What was the final velocity on a 90 degree ramp?
3) Time how long it takes a marble to drop 1m straight down. Record this time ________
4) Divide your answer to 2) by your answer to 3). This is the acceleration of the marble
when it is falling. Since gravity is the only force accelerating it, this is the acceleration
due to gravity. What is your value for the acceleration due to gravity?
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Gravity of a Black Hole
The mass of a dead star is 2 x 1031 kg. The mass of your spaceship is 5 x 104 kg. Complete the following
table by dividing the previous distance in half for each new row.
G= (6.7 x 10-11 m3) / (kg s2) and F=(Gmm)/r2.
distance between
1.5 x 108 km
force of gravity between
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