Law of universal Gravitation

Section 5.6 - 5.8

The force of gravity:

• All objects accelerate towards the earth. Thus the earth exerts a force on these objects - this is called the force of gravity.

• By Newton's third law, such objects must also exert a force on the earth.

• As the earth is a special case of an object, it must be that any two objects exert an attractive gravitational force on one another.

• Newton postulated that this force between two objects was due to the masses of the objects and that it was proportional to the product of the masses of the two objects. He also deduced that gravitational force was inversely proportional to the square of the distance, r, between the centers of the objects:

• The force is directed along a line joining the centers of the objects

The universal law of gravitation:

"Every particle in the universe attracts every other particle in the universe with

a force that is proportional to the product of the masses and inversely

proportional to the square of the distance between the particles."

Example

• Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is standing at sea level, a distance of 6.37 x 106 m from earth's center

The acceleration due to gravity

Satellites

• When a satellite orbits the Earth, it is being pulled on by the gravity of the earth. That is why it follows a circular orbit. – It stays in orbit because of its speed. If it goes too

slow it will fall to earth. If it has too much speed it can fly out to space.

– The acceleration due to gravity is the acceleration of the satellite. So the use the law of Gravitation and set equal to the Radial Force equation. R = radius of the earth + the height above the earth

Apparent Weight (w) and Weightlessness

• On a scale in the elevator, if there is a constant speed, the apparent weight = mg

• If the acceleration is up, the scale will read more than mg

• If the acceleration is down, the scale will read less than mg

• If the elevator falls at gravity the scale will read zero. (weightless) even though gravity is still acting.

Elevator Problem

Weightless when cable breaks