PES 1110 Fall 2013, Spendier
Lecture 36/Page 1
Today:
- Gravity (13.1-13.4)
- Quiz 5,
There is one more force/energy we will talk about this semester.
So far we have considered the gravitational force and gravitational potential energy only
on/near the surface of the earth. Then the acceleration due to gravity is constant:
g = 9.8 m/s2 towards the center of the Earth
But what is this value on space? Or on another planet?
Acceleration due to Gravity
Newton proposed that the acceleration due to gravity is given by
Gm planet
aG 
(towards the center of the planet)
r2
ag = acceleration
G = Gravitational constant = 6.67 x 10-11 N m2 kg-2 (m3 kg-1 s-2)
mplanet = mass of planet
r = distance from center of planet
-
if the mass of the planet increases, the acceleration is larger.
If the object moves further away from the planet (r increases), then the
acceleration is smaller.
Example 1: Compute the acceleration on the surface of the Earth.
So g = 9.8 m/s2 is just a special case.
Example 2: Compute acceleration on the surface of the moon.
PES 1110 Fall 2013, Spendier
Lecture 36/Page 2
Newton’s Law of Gravitation
Every object with mass exerts a gravitational force on every other object with mass.
For an object with mass M1 located r away from mass M2 (before we called this mass
mplanet)
FG  M1 aG
GM 1 M 2
FG 
(call this an inverse square law)
r2
r = separation distance, center-to-center for spherical objects
Direction:
The gravitational force is an “attractive" force  each object feels a force towards the
other.

m1 feels a force due to m2 ( F1 - Force on m1 due to m2)

m2 fells a force due to m1 ( F2 - Force on m2 due to m1)
Here geometry determines direction
PES 1110 Fall 2013, Spendier
Lecture 36/Page 3
Weight: Force due to gravity
To relate what we used before (Mg) to Newton’s law of gravity:
So F = Mg is just a special case of this equation on the surface of the earth.
Example 3:
Let’s calculate the force between 2 people standing 0.5 m apart.
Compare this to the maximum static friction that can oppose motion:
Gravity is one of the weakest forces. It is only when we have giant massive objects like
planets and suns/stars that it becomes important. So we can ignore interactions with all
masses on the surface of the Earth, apart from the Earth itself.
PES 1110 Fall 2013, Spendier
Lecture 36/Page 4
What happens if we have an object of mass m between two other objects of mass M1 and
M2? We need to calculate the net Force on the object of mass m.
Example 4:
An 8.00 kg point mass and a 15 kg mass are held in place 50 cm apart. A particle of mass
m is released from a point between the two masses 20.0 cm from the 8.00 kg mass along
the line connecting the two fixed masses. Find the magnitude and direction of
acceleration of the particle.