November 18, 2020

Chapter 5 – Gravitation

Chapter 6 – Work and Energy

Chapter 5

• (5.6) Newton’s Law of Universal Gravitation

• (5.7) Gravity Near the Earth’s Surface

Chapter 6 (today)

• Work Done by a Constant Force

• Kinetic Energy, and the Work-Energy Principle

Old assignments can be picked up

in my office

(LB-212)

Recalling Recalling

LastLast

LectureLecture

Recalling Recalling

LastLast

LectureLecture

Newton’s Law of Universal GravitationNewton’s Law of Universal Gravitation

Newton’s law of universal gravitation:

“ Every particle in the universe attracts every other particle with a force that is

proportional to the products of their masses and inversely proportional to the

square of the distance between them. This forces acts along the line joining the

square of the distance between them. This forces acts along the line joining the

two particles.”

Newton’s Law of Universal GravitationNewton’s Law of Universal Gravitation

The magnitude of this force is given by:

Where:

(4.7)

Newton’s Law of Universal GravitationNewton’s Law of Universal Gravitation

If m2is the object exerting a force on m1, then the gravitational acceleration felt

by object 1 can be identified as:

And vice-versa: object 2 will feel an acceleration

(4.8)

⇒⇒

due to the gravitational force applied by object 1.

You can then write for the force acting on m1and for the

force acting on m2.

Gravity Near the Earth’s SurfaceGravity Near the Earth’s Surface

An object of mass mON the surface of the Earth will feel a force given by:

Where,

mE= mass of the Earth ;

r

E

= 6.38 x 10

6

m

= radius of the Earth

.

(4.9)

r

E

= 6.38 x 10

6

m

= radius of the Earth

.

ghas been measured and it is known to be 9.80 m/s2.

In fact, the value of g can be considered constant at any position near the Earth’s

surface

Accurate measurements yield: mE= 5.974 x 1024 Kg

Newton’s Law of Universal GravitationNewton’s Law of Universal Gravitation

Problem 5-31 (textbook): A hypothetical planet has a radius 1.5 times that of Earth,

but has the same mass. What is the acceleration due to gravity near its surface?

Solution:

The acceleration due to gravity at any location on or above the surface of a planet is

given by

2

planet Planet

g G M r

=

where ris the distance from the center of the planet to the location in question.

( )

2

2

Planet Earth Earth

planet Earth

2

2 2 2 2 2

Earth

Earth

1 1 9.8 m s

4.4 m s

1.5 1.5 1.5

1.5

M M M

g G G G g

r R

R

= = = = = =

Newton’s Law of Universal GravitationNewton’s Law of Universal Gravitation

Problem 5-34 (textbook): Calculate the effective value of g, the acceleration of

gravity, at (a) 3200 m, and (b) 3200 km, above the Earth’s surface.

Solution:

P P

P P

y

θ

θ

y

x

m

g

r

N

F

r

f r

F

r

P

F

r

P P