2223-03 PH Physics II
Dr. David L. Monts 223 Hilbun, 325-2931 Tu/Th 1-2:30 p.m. (office hours) [e-mail] Text: University Physics, 12th Ed. with MasteringPhysics Course ID: MSUMONTSPH2223F08 http://www.masteringphysics.com/ Lab: http://newton.ph.msstate.edu/labs/
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Chapter 12 Gravitatio
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Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the
Fg= gravitational force (N) m1 = mass of object # 1 (kg) m2 = mass of object # 2 (kg) r = distance between #1
Newtons Law of Gravitation
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Newtons Law of Gravitation
Gravitation is action-at-a-distance force. Objects do NOT need to touch. Gravitational interaction is always attractive ( F is negative, which indicates attraction). Gravitational interaction is pairwise. If more than 2 objects, then there is contribution to total Fg from each pair of objects.
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Newtons Law of Gravitation
Magnitude of force on mass 1 due to mass 2 EQUALS magnitude of force on mass 2 due to mass 1 even if masses are different. Inverse-square law F ~ 1/(distance2) f(x) 0 as x f(x) as x 0
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Questio n mass of the Moon is 1/81 of the The 1
mass of the Earth. Compared to the gravitational force that the Earth exerts on the Moon, the gravitational force that the Moon exerts on the Earth A. 812= 6561 times greater. B. 81 times greater. C. equally strong. D. 1/81 as great. E. (1/81)2 = 1/6561 as great.
G vs g
G and g are different. G is the (universal) gravitational constant. It is the same everywhere. g is the acceleration due to gravity. g can be vector to indicate direction. g will vary by location. g = 9.80 m/s2 at the surface of the earth.
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Use Newtons 2nd law to find acceleration. Consider two point objects r apart. What is acceleration (magnitude) of object #1?
How to Get g from G
The gravitational force exerted by a finite-size, spherical body on a particle outside the distribution is the same as if the entire mass of the distribution were concentrated at the center (acts like point mass). Point mass is an idealization has mass, but no volume (size); acts as if spherical.
Gravitational Force due to Distribution of Mass
For the Earth, the force on m at surface
g above Earths Surface
If an object is some distance h above the Earths surface, r becomes RE + h
This shows that g decreases with increasing altitude.
As h , the gravitational acceleration of the object approaches zero.
Variation of g with Height above Earth
International Space Station orbits at about 400 km altitude.
Compared to the Earth, Planet X has twice the mass and twice the radius. This means that compared to the Earths gravity, surface the surface gravity on Planet X is A. 4 times as much. B. twice as much. C. the same. D. 1/2 as much. E. 1/4 as much.
Questio n2
Four identical masses of 800 kg each are placed at the corners of a square whose side length is 10.0 cm. What is the net gravitational force (magnitude and direction) on one of the masses (A) due to the A other three? B
Problem 12.10
C
D
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Gravitational Field The gravitational field is the gravitational force
that would be felt by unit test mass. Force is vector so gravitational field is also vector quantity. Can describe gravitational interaction between 2 masses as 2-step process: 1.) Mass #1 modifies the space surrounding it by establishing a gravitational field at all points in space. 2.) Mass # 2 (test mass) experiences the gravitational force due to its presence in this field at that point.
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Gravitational Field
Arrows show direction of force of mass M on another mass. A field gives a way to visualize the effect of the gravity of one object (such as the
Gravitational Field
m is the test mass
Field created by single point mass:
Units of gravitational field: N/kg N/kg is same units as m/s2 , same units as gravitational Note field is independent of size (mass) of the test
an isolated system, energy is conserved, i.e., gain (loss) of kinetic energy equals loss (gain) of potential energy. The change in the potential energy is the negative of the work done by the force.
Consider a mass m moving from point A to point B in the gravitational field of the
Gravitational Potential Energy When only conservative forces act upon
The work done for any force is
Gravitational Potential Energy
Gravitational force always along r direction in this example: Units of U are Joules!
Gravitational Potential Energy
Only differences in potential energy matter we can choose the reference point ri anywhere (as long as we are consistent).
The most common choice is ri (infinitely far away from any masses in the problem). Then:
Questio n3 Compared to the Earth, Planet X has
twice the mass and twice the radius. This means that compared to the amount of energy required to move an object from the Earths surface to infinity, the amount of energy required to move that same object from Planet A. 4 times as much. B. twice as much. C. the same. D. 1/2 as much.
Questio n4 A satellite is moving around the
Earth in a circular orbit. Over the course of an orbit, the Earths gravitational force A. does positive work on the satellite. B. does negative work on the satellite. C. does positive work on the satellite during part of the orbit and negative work on the satellite during the other part. D. does zero work on the satellite at all points in the orbit.