Download Gravitational Fields and Force

IB Physics Power Points
Topic 6 SL
Fields and Forces
www.pedagogics.ca
Gravitational
Fields
Defining Mass
Inertial mass
A measure of an object’s inertia (tendency to resist a
change in motion)
Expressed as a ratio of net force
and acceleration – Newton’s 2nd
Law
minertial
F

a
Gravitational mass
The property of matter that gives rise to the
gravitational attraction between objects.
The gravitational force is proportional to the product
of the two object’s masses.
Newton’s Universal Law of Gravitation
Consider – two masses A and B
There is a gravitational attraction between A and B.
FB on A = - FA on B
(think Newton’s 3rd)
This gravitation attraction can be calculated by
m1m2
F G 2
r
The gravitational constant G = 6.67×10-11 N m2 kg-2
The gravitational force is:
Proportional to the product of the two masses.
Inversely proportional to the square of the distance
between the center of mass of each object.
NULOG  “an inverse square law”
How could we determine G experimentally?
Practice: Find the gravitational force of attraction between a 75 kg physics
student and her 1 500 kg car when their centers are 10.0 m apart.
A. 7.5 x10-8 N
B. 7.5 x10-7 N
C. 740 N
D. 1.5 x103 N
Falling objects and the force of gravity
Free-body diagrams and elevators – what do scales measure?

Draw free body diagrams (including annotations and
calculated values) representing the following situations
(consider g = 10 ms-2)
i.
ii.
A 50 kg student in an elevator at rest
A 50 kg student in an elevator moving
downwards at 2 ms-1.
iii. A 50 kg student in an elevator moving upwards
at 5 ms-1.
iv. A 50 kg student in an elevator accelerating
upwards at 1 ms-2.
v. A 50 kg student in an elevator accelerating
downwards at 3 ms-2
vi. A 50 kg student in an elevator falling freely
Consider an object (mass m) at some point P, in the
Earth’s gravitational field.
The object will feel a force (Fe) that can be calculated
using:
me m
Fe  G 2
r
Gravitational Field Strength
Defined – the force per unit mass acting on an object
placed in a gravitational field.
F
g
m
In the example, the force on the object at point P in the
Earth’s gravitational field can be calculated by:
me m
Fe  G 2
r
So by substitution
Mm
G 2
F
M
r
g 
G 2
m
m
r
The gravitational field strength (FORCE PER UNIT MASS)
at distance r from the center of mass M (the object
creating the gravitational field)
At the surface of a planet (like Earth), the gravitational
field strength can be determined by:
Mm
G 2
F
M
r
g0  
G 2
m
m
r
Where M is the mass of the planet. For Earth:
ME
g G 2
rE
Given
Earth’s mass: 5.97 x 1024 kg
Earth radius: ~ 6.38 x 103 km
Determine a value for the gravitational field strength at
the Earth’s surface.
Gravitational Fields
Gravity is a field force. It exists between objects without
contact and cannot be shielded or blocked.
Gravitational fields are
depicted by drawing field
diagrams. Field lines show
the direction of the force
acting on a particle placed in
the field (toward the center
of mass)
The density of field lines indicates the strength of
the field.
Gravitational Field Strength – More than one point mass
Consider the following diagram and determine the
gravitational field strength at point P, located 3.45 x 108 m
from the centre of the Earth.
Moon mass: 7.35 x 1022 kg
Earth-Moon distance: 384 x 103 km
The gravitational
fields of the earth
and moon
superpose.
Note how the fields
cancel at one point,
and how there is no
boundary between
the interpenetrating
fields surrounding
the two bodies.