2.
Must be true from
Newton’s 3rd Law
The gravitational force on you is half of a Newton’s 3rd Law pair:
Earth exerts a downward force on you, & you exert an upward
force on Earth. When there is such a large difference in the 2
masses, the reaction force (force you exert on the Earth) is
undetectable, but for 2 objects with masses closer in size to each
other, it can be significant.
The gravitational force one body exerts
on a 2nd body , is directed toward the first
body, and is equal and opposite to the
force exerted by the second body on the
first
3. G = the Universal Gravitational constant
Measurements in SI Units:
The force given above is strictly valid only for:
› Very small masses m1 & m2 (point asses)
› Uniform spheres
For other objects: Need integral calculus!
4. Comments
F12 Force exerted by particle 1
on particle 2
F21 Force exerted by particle 2
on particle 1
This tells us that the forces form a Newton’s 3rd Law
action-reaction pair, as expected.
The negative sign in the above vector equation tells us
that
particle 2 is attracted toward particle 1
F21 = - F12
5. The Law of Gravitation
• You exert an attractive force on everything
around you and everything is exerting an
attractive force on you.
• This attractive force is called gravity.
• Anything that has mass is attracted by the
force of gravity.
• The Law of Gravitation states that any two
masses exert an attractive force on each
other.
6. The Law of Gravitation
• Gravitation force depends on two things:
– The mass of the two objects
– The distance between the two objects
• Why do you suppose the Earth exerts a
force on you that you can feel, but you
can’t feel the force the desk is exerting on
you?
7. Gravity – a basic force
• There are four basic forces:
–Gravity
–Electromagnetic force
–Nuclear force = Strong
–Nuclear force = Weak
Apply to
an atom
only
Caused by
electricity and
magnetism
8. Gravitational Acceleration
• When objects fall, the
gravitational pull is 9.8 m/s2
• When a falling object is only
affected by gravity it is said
to be in free fall.
9. Gravitational Acceleration
• If you drop a bowling ball and
a marble off a bridge, which
would hit the water first?
• Things to consider…
10. Gravitational Acceleration
– Force of gravity is greater on the bowling ball
because of its larger mass.
– The larger mass means it has a larger inertia
so more force is needed to change its
velocity.
– Gravitational force on the marble is smaller
because it has a smaller mass
– The inertia on the marble is less and less
force is needed to change the velocity.
– Therefore, all objects fall with the same
acceleration!
11. QUESTIONS
Choose the correct option:
1. Two objects of different masses falling freely near the surface of moon would
(a) have same velocities at any instant
(b) have different accelerations
(c) experience forces of same magnitude
(d) undergo a change in their inertia
2. The value of acceleration due to gravity
(a) is same on equator and poles (c)is least on equator
(b) is least on poles (d) increases from pole to
equator (c)
3. The gravitational force between two objects is F. If masses of both objects
are halved without changing distance between them, then the gravitational
force would become
(a) F/4 (b) F/2 (c) F (d) 2 F
(a)
4. A boy is whirling a stone tied with a string in an horizontal circular path. If
the string breaks, the stone
(a) will continue to move in the circular path
(b) (b) will move along a straight line towards the centre of the circular path
(c) will move along a straight line tangential to the circular path
(d) will move along a straight line perpendicular to the circular path away
from the boy
12. Gravity Factors
• The acceleration due to gravity
is directly proportional to the
mass of the objects and
inversely related to the
distance squared.
13. Inverse Square Law
When a quantity varies as
the inverse square of its
distance from its source.
14. Universal Gravitation
• To find the Fg
between any two
objects in the
universe.
• G is the
gravitational
constant of
proportionality
• G = 6.67 x 10-11 N m2/kg2
• F = G m1m2/r2
16. Applications of Gravity
Education
• Acceleration at a Height
• Acceleration at a Depth
• Comparison of acceleration due to gravity
• Rotation of Earth
• Comparison of gravitational acceleration
• Rate of change of gravity
17. 5. In the relation F = G M m/d2, the quantity G
(a) depends on the value of g at the place of observation
(b) is used only when the earth is one of the two masses
(c) is greatest at the surface of the earth
(d) is universal constant of nature
6. Law of gravitation gives the gravitational force between
(a) the earth and a point mass only (b) the earth and Sun only
(c) any two bodies having some mass (d) two charged bodies only
7. The value of quantity G in the law of gravitation
(a) depends on mass of earth only
(b) depends on radius of earth only
(c) depends on both mass and radius of earth
(d) is independent of mass and radius of the earth
8. The atmosphere is held to the earth by
(a) gravity (c) clouds
(b) wind (d) earth’smagnetic field
9. The force of attraction between two unit point masses separated by a unit
distance is called
(a) gravitational potential (c)gravitational field
(b) acceleration due to gravity (d)universal gravitational constanT
10. The gravitation force between two bodies varies with distance r as
a) 1/r b) 1/r²
c) r d) r²
