devil physics the baddest class on campus ib physics...
TRANSCRIPT
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DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS
IB PHYSICS
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LSN 2-11: MOTION IN A GRAVITATIONAL FIELD
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Questions From Reading Activity?
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Assessment Statements
Gravitational Field, Potential and Energy
9.2.7. Explain the concept of escape speed from a planet.
9.2.8. Derive an expression for the escape speed of an object from the surface of a planet.
9.2.9. Solve problems involving gravitational potential energy and gravitational potential.
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Objectives
State the definitions of gravitational potential energy, and gravitational potential.
Understand that the work done as a mass m is moved across two points with gravitational potential difference ∆V is, W = mΔV
r
MGV
r
MMGEp
21
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Objectives
Understand the meaning of escape velocity and solve related problems using the equations for escape speed from a body of mass M and radius R,
R
GMvesc
2
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Objectives
Solve problems of orbital motion using the equation for orbital speed at a distance r from a body of mass M,
Understand the term weightlessness.
R
GMv
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Newton’s Law of Universal Gravitation
Last year we learned,
This year we look at it from an energy standpoint
2
21
r
MMGF
r
MMGFdWE 21
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Gravitational Potential Energy
The gravitational force is an attractive force
Work must be done to separate two bodies in space a certain distance R
This work is converted to potential energy called the gravitational potential energy
r
MMGEp
21
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Gravitational Potential Energy
For a satellite orbiting a body, its total energy is the sum of its kinetic and potential energy
r
MMGmvE 212
2
1
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Gravitational Potential Energy
For a satellite orbiting a body, its total energy is the sum of its kinetic and potential energy
r
MMGmvE 212
2
1
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Gravitational Potential Energy
If the satellite is in a stable, continuous orbit, the kinetic energy is equal to its potential energy
r
MMGmv 212
2
1
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Gravitational Potential Energy
Newton’s Second Law tells us that the gravitational force will be balanced by the centripetal acceleration
2
2
2
vr
GM
r
vm
r
MmG
maF c
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Gravitational Potential Energy
Substituting into the traditional value for kinetic energy gives us
r
GMmE
mvE
vr
GM
k
k
2
1
2
1 2
2
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Gravitational Potential Energy
And total energy becomes
r
GMmE
r
GMm
r
GMmE
EEE
r
GMmE
pk
k
2
2
1
2
1
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Gravitational Potential Energy
Graph of kinetic, potential, and total energy as a function of distance for a circular orbit
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Gravitational Potential
The gravitational potential at any point P in the gravitational field is the work done per unit mass in bringing a small point mass m from infinity to point P
If the work done is W, then the gravitational potential is the ratio of the work done to the mass m
m
WV
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Gravitational Potential
The gravitational potential due to a single mass M a distance r from the center of M is
Gravitational potential is a scalar quantity
Its units are J/kg r
GMV
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Gravitational Potential
If we know the gravitational potential at some point P, then the potential energy of a mass m will be
And work will be defined as
r
GMV
mVEp
VmW
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Escape Velocity
Total energy of a mass m moving near a large mass M is given by
We assume the only force acting on m is the gravitational force created by M
r
MMGmvE 212
2
1
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Escape Velocity
We want to know if a mass m is launched from the surface of M, will it escape M’s gravitational field?
22
02
1
2
1 mv
r
MmGmv
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Escape Velocity
If total energy is greater than zero, m escapes
If total energy is less than zero, m will eventually return to the surface of M
r
MMGmvE 212
2
1
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Escape Velocity
The separation point is when V∞ is equal to zero
r
GMv
r
MmGmv
mvr
MmGmv
2
2
1
02
1
2
1
0
2
0
22
0
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Escape Velocity
This is the minimum velocity needed to exceed the gravitational attraction of M and is called the escape velocity
What happens if we double the value of m?
r
GMvesc
2
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Orbital Motion
The law of gravitational attraction combined with Newton’s second law show that the orbit of any body due to gravitational attraction will follow the path of an ellipse or a circle (circles are ellipses with both foci at the same point).
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Orbital Speed
2
2
2
vr
GM
r
vm
r
MmG
maF c
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Period of Motion
The period of a planet is proportional to the 3/2 power of the orbit radius
Kepler’s Third Law of Planetary Motion
32
2
2
2
4
2
2
rGM
T
T
r
r
GM
T
rv
vr
GM
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Period of Motion
For two planets orbiting the same body, the ratio of their periods squared to their mean distance from the attracting body cubed, will be equal
3
2
2
2
3
1
2
1
2
3
2
32
2
4
4
r
T
r
T
GMr
T
rGM
T
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Equipotential Surfaces
Gravitational potential is given by
An equipotential surface consists of those points that have the same potential
r
GMV
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Equipotential Surfaces
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Equipotential Surfaces
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Equipotential Surfaces
The magnitude of the gravitational field is the rate of change of with distance of the gravitational potential.
r
Vg
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Equipotential Surfaces
Equipotential surfaces and field line are normal (perpendicular) to each other
r
Vg
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Equipotential Surfaces
If we have a graph showing the variation with distance of the gravitational potential, the slope (gradient) of the graph is the magnitude of the gravitational field strength
r
Vg
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Σary Review
Can you state the definitions of gravitational potential energy, and gravitational potential?
Do you understand that the work done as a mass m is moved across two points with gravitational potential difference ∆V is, W = mΔV ?
r
MGV
r
MMGEp
21
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Σary Review
Do you understand the meaning of escape velocity and can you solve related problems using the equations for escape speed from a body of mass M and radius R ?
R
GMvesc
2
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Σary Review
Can you solve problems of orbital motion using the equation for orbital speed at a distance r from a body of mass M ?
Do you understand the term weightlessness?
R
GMv
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Assessment Statements
Gravitational Field, Potential and Energy
9.2.7. Explain the concept of escape speed from a planet.
9.2.8. Derive an expression for the escape speed of an object from the surface of a planet.
9.2.9. Solve problems involving gravitational potential energy and gravitational potential.
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QUESTIONS?
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Part A, #1-15
Part B, #16-29
Homework