Download Gravity

Physics 102-002, Mar 7
Announcements
• Exam 2 graded
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Average = 71.4
Standard Deviation = 15.8
High score = 96
Median score = 72
• Exam 2 corrections due Wednesday, March 21
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Typed
Include copy of original answer sheet
Give and explain correct answer
Give reference (a page number in the text or the
date of the lecture notes) for the correct answer
– Turn in hard copy or by email.
If these things
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you don’t get
credit
• WebAssign –
– Chapter 8 and 9 due Wednesday, March 21
Picture: International Space Station in orbit around Earth
Chapter 9
Gravity
• The Universal Law of Gravity
• The Universal Gravitational Constant, G
• Gravity and Distance: The Inverse-Square
Law
• Weight and Weightlessness
Skip pgs 168-178
The Universal Law of Gravity
Massive objects exert a force on each other that pulls them toward each
other.
We call this “force of attraction” GRAVITY, or the “gravitational force”.
The gravitational force is the same on both objects.
m1
-F
F
m2
d
There can be more than 2 objects involved. For example the solar system
has 9 planets (give or take), and the gravitational attraction is the same on all
of them, directed toward the center of mass of the solar system.
Actually, every body in the universe attracts every other body.
Center of Mass Applet 1
Center of Mass Applet 2
The
Universal
Law
of
Gravity
Since Isaac Newton, we’ve known that the gravitational force is directly
proportional to the mass of both objects, and inversely proportional to the
square of the distance between them:
m1
-F
F
m2
d
Force ~
mass1 x mass2
distance2
Or
F~
m1 x m2
d2
Of course, the gravitational attraction between the
moon and Earth make them revolve around each
other, but because we’re on the earth, we say that
the moon orbits the earth.
Actually, the moon “falls” toward the earth. It has
just enough tangential speed to travel in a
trajectory parallel to the earth’s surface.
Moon orbit applet
The Universal Gravitational Constant, G
Remember the equation:
F~
m1 x m2
d2
Mathematically, when you have a “proportionality” equation like this,
you can do experiments to find a “proportionality constant” that you can
use to make the equation an exact equality. For gravity, experiments
have shown that the exact equation is:
F G
m1 x m2
d2
Where G is called the Universal Gravitational Constant, and has the value:
G = 6.67 x 10-11 Nm2/kg2
Physics Place Videos
You can calculate your weight from this equation if you know
Your mass
The earth’s mass
Your distance from the earth’s center of mass
You should get the same answer as you do when you use “Weight = mg”
The Inverse Square Law
F G
m1 x m2
d
2
A law that has an equation with a “squared”
term on the bottom is called an “inverse
square law”. We’ll see other examples of
this later in the course.
Physics Place Videos
The equation says that the force gets smaller very fast as you get farther
away from the other object. This is because the force of attraction is spread
out over a much bigger area as you get farther away.
Physics Place
Interactive Figure
Question 1
Question 2
Weight and Weightlessness
What if the chair is falling?
Do you “feel” your weight?
This is like you feel when
you ride an elevator
downward.
The space shuttle is in orbit around the earth, so obviously it (and the astronauts
on board) have “weight”. Yet, we always see and hear that they are experiencing
“weightlessness”! The space shuttle is literally “falling around” the earth, so the
astronauts don’t feel like they weigh anything.
Weightlessness is only a sensation; it is not a reality corresponding to an
individual who has lost weight. As you are free-falling on a roller coaster ride (or
other amusement park ride), you have not momentarily lost your weight.
Weightlessness has very little to do with weight and mostly to do with the
presence or absence of contact forces.
Physics Place Videos