Download Gravitation and Grav fields

Newton’s Universal Law of Gravitation
Newton’s conceptual leap in
understanding
gravity was his realization
that the same force governs
the motion of a falling object
on Earth & the motion of the
Moon in its orbit around
the Earth.
Universal Force
Universal Law of Gravitation
• Every mass attracts every other mass through
gravity.
• The force of attraction between any 2 objects is
directly proportional to the product of their masses.
• Doubling the mass of 1object doubles Fg between the
2 objects.
Gravity and Weight
• Definition: The weight of an object is a measure
of the Fg one object feels in the presence of
another.
• Weight Fg = mg. Where g is known.
Mass can be measured in 2 ways
• Inertial mass - the mass of a body as determined by its
momentum, as opposed to gravitational mass. How it
accelerates
• m = Fnet/a
• Gravitational mass -the mass of a body determined by its
response to the force of gravity.
1. Show that the acceleration of gravity
g = GM/r2, where M is the mass of a
planet or star r is its radius.
Fg = m2g = GM1m2.
r 2.
g = GM1 is accl due to gravity
r 2.
Mass of the object cancels out.
Acceleration depends only on the mass of the
planet (or star).
Questions: Raise Hands.
• Is heavier body attracted to the Earth
with more force than a light body.
•Does the heavier object free fall faster?
•Explain.
Newton’s Universal Law of
Gravitation
• Fg = GMm.
R2.
Describes Force btw point masses.
What is a point mass?
Gravitational Field deals with
space around the large mass.
Gravitational Field Strength/Intensity Force per unit mass experienced by a
small “test mass” in space.
Gravitational Field Lines
drawn in direction of acceleration of small
mass.
Gravitational Field = g.
The value for acceleration, g, is also called the
gravitational field. Set the weight equal the Fg.
The units of the gravitational field are N/kg.
Since mg = GMm.
r2.
Grav Field
The small mass m cancels
g = GM
r2.
units N/kg.
Use to find acceleration or gravitational field.
2. What is the gravitational field
strength due to Earth at a point
450 km above the surface?
• g = GM
r2.
• (6.67 x 10-11)(6 x 1024kg)
(6.4 x 106m + 450 x 103m)2.
• 4 x 1014.
(6 850 000)2.
• 4 x 1014.
4.7 x 1013.
8.5 N/kg
Combining Fields
All fields are vectors. Forces resulting from more
than 1 field is the sum of the field strengths.
Write the equation for grav field strength that
involves planets mass and distance>
3. Two spheres lie along a straight line. The sphere on the left
has m = 1000-kg, and the right on the right has m = 100-kg.
The distance between their centers is 5-m.
Point A lies between the spheres at 2.5-m from the center of
each.
Point B lies 1 m to the left of m = 1000kg.
Calculate the field strength at A and B.
B
A
9.63 x 10 – 9 N/kg left
6.69 x 10-8 N/kg
Satellites in freefall not beyond grav field =
apparent weightlessness. The orbit is maintained
by gravity.
Newton’s Cannon Animation
http://waowen.screaming.net/revision/force&motion/ncananim.htm
4. Derive an equation to
express the minimum
velocity a satellite must have
to stay in orbit.
Fg keeps the satellite in orbit.
Set Fc equal to gravitational force.
Fg
=
GMem
r2
v=
Fc
=
mv2.
r
(GMe)1/2.
(r) 1/2.
5. What is the velocity needed
for a satellite to stay in orbit 200
km above the Earth’s surface?
• First find dtot between their centers – r:
• 2.0 x 105 m + 6.57 x 106m
• 6.57 x 106m
v=
(GMe)1/2.
(r) 1/2.
(6.67x10-11)(5.98x1024 kg)1/2
(6.57 x 106m )1/2.
7800 m/s.
Einstein vs. Newton
9.5 min
• http://www.youtube.com/watch?v=4yyb_R
NJWUM
Squeeze water in freefall
• http://apod.nasa.gov/apod/ap130424.html
• Squeeze water in space
Rd Hamper 127 – 129 do pg 129 - 131.
Purple boxes #1 – 5.
Show all work.
Einstein vs. Newton
9.5 min
•
http://www.youtube.com/watch?v=4yyb_RNJWUM
http://www.phy.ntnu.edu.tw/java/pro
jectileOrbit/projectileOrbit.html
• Newton’s Cannon Launch Satellite
• Apparent weightlessness. Satellites are in
freefall around the Earth! That is why
astronauts appear weightless. They are
constantly falling toward Earth. Their rate
of fall is balanced by their tangential
momentum.
The universe season 2
Gravity, Roller Coasters,
Space Travel & PEg.
https://www.youtube.com/watch?v=Eilj
zeDL0co 45 minutes