Transcript Gravitation - abaphysics

Gravitation
AHL 8.2
F=
2
GMm/r
• All objects exert a force
on each other
• If either mass increases
the force increases
• Double the mass
doubles the force
• If the distance
decreases the force
increases
• Half the distance gives
4 times the force
Gravitational field
strength
• Gravitational field strength is the
force per unit mass
• g = F/m
• On Earth g = 10Nkg-1
• How much force wil the Earth’s
gravity exert on 3 kg
• 30N
• The force on 10kg on the moon is
17N. Calculate g on the moon
• g = F/m = 1.7 Nkg-1
g=
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2
GM/r
F = GMm/r2
g = F/m = GM/r2
Mass of Earth = 6x1024kg
Radius of Earth = 6.4 x106m
Calculate g on Earth
g = GM/r2
= 6.67x10-11 x 6x1024/ (6.4 x 106)2
= 9.8 Nkg-1
g is a vector
g from star
g from planet
Total g = Vector
sum
planet
Star
Gravitational PE
F
S
N
N
S
F
PE
• These magnets have no energy when they
are separated
• You do work when you push them together
• When they are close together potential
energy is stored
• Let them go and the energy is released
Gravitational PE
F
S
N
S
F
N
- PE
• The magnets have zero energy when they are
apart.
• They slide together and have less energy (negative)
• A force must do work to pull them back to zero
• When objects attract each other they have negative
potential energy
Gravitational Potential
Amount of work
needed to remove
object
Zero energy
Attracted by
gravity
Negative PE
planet
A distant object
has zero PE
• Gravitational
potential is
always
negative
• The potential
at a point is
the amount
ofBack
energy
to zero
needed
energy to
move 1 kg
from infinity
to that point
• V = -GM/r
Gravitational Potential
Energy V = -GMm/r
Amountof
of work
work
Amount
neededto
toremove
remove
needed
2 kg
1kg
Zero energy
Attracted by
gravity
Negative PE
The potential at a point is
the energy needed to move
1 kg from infinity to that
point
The potential energy of an
object Back
is theto
energy
zero needed
to move
the object from
energy
infinity to that point
PE = mV = -GMm/r
1 kg 2kg
planet
Escape velocity
planet
• How fast must an object
go so that it doesn’t
come back?
• It must have enough KE
to overcome the
negative PE (-GMm/r) and
get to zero energy
• 1/2mv2 = GMm/r
• V2 = 2GM/r
• V = (2GM/r)
Calculate the escape velocity of Earth
r= 6.4 x106m m =6 x 1024 kg
v = (2GM/r) =  (2 x 6.67 x 10-11 x 6 x1024 / 6.4 x106)
= 11 000 ms-1 = 11kms-1