Physics 2111
Unit 25
Today’s Concept:
a) Newton’s Law of Gravity
b) Gravitational Potential Energy
c) A bit of cosmology and the fate of the universe
Mechanics Lecture 25, Slide 1
A bit of history on the forces
What makes
moon orbit the earth
What makes
apples fall
electricity
magnetism
Gravity!
(1687)
General
Relativity
(1915)
Electro-magnetic force
(1862)
??
??
Mechanics Lecture 25, Slide 2
A bit of history on the forces (part II)
Gravity!
(1687)
??
??
Electro-magnetic force
(1862)
Weak force
(nuclear decay)
(~1930)
Electro-weak force
(1968)
Strong force
(holds nuclei together)
(~1960)
Standard Model
(~1970)
Mechanics Lecture 25, Slide 3
Newton’s Law of Gravity
Gravity is always
attractive - Why??
𝐹𝐺𝑅𝐴𝑉 12 =
𝑚1 𝑚2
-G 2 𝑟12
𝑟
A really small number
6.7X10-11 Nm2/kg2
Mechanics Lecture 25, Slide 4
Example 25.1 (Two point particles)
Two small rocks with
masses of 2kg and a 4kg
are 0.5m apart. What is the
gravitational force between
them?
𝐹𝐺𝑅𝐴𝑉 12 =
2kg
4kg
0.5m
𝑚1 𝑚2
-G 2 𝑟12
𝑟
Mechanics Lecture 25, Slide 5
Example 25.2 (superposition)
2kg
A third 6kg rock is now
added 0.5m to the right
of the 4kg rock. What is
the total gravitation force
on this rock?
𝐹𝐺𝑅𝐴𝑉 12 =
4kg
0.5m
6kg
0.5m
𝑚1 𝑚2
-G 2 𝑟12
𝑟
Mechanics Lecture 25, Slide 6
Example 25.3 (uniform rod)
A uniform rod with a
mass of 10kg and a
length of 2m, is 3m to
the left of a 6kg rock.
What is the gravitation
force on the rod?
𝐹𝐺𝑅𝐴𝑉 12 =
6kg
10kg
2m
3m
𝑚1 𝑚2
-G 2 𝑟12
𝑟
Mechanics Lecture 25, Slide 7