BellworkBellwork• Why do objects of different mass

accelerate at the same rate at the surface of the earth?

• The more massive object has a greater force of gravity (weight) but also more inertia (mass) and these balance each other out.

Newton's Law of Newton's Law of Universal GravitationUniversal Gravitation

12/10/1212/10/12

Objects in EquilibriumObjects in Equilibrium• If an object is being pushed to right at a

constant velocity (Fnet = 0 N):

• (-) Fg = (+) Fsurf and (+) Fapp = (-) Ff

Inverse Square LawInverse Square Law

• Inverse Square Law: A physical quantity that is inversely proportional to the square of the distance from quantity.

Inverse Square Law

Inverse Square Law Plot

Background InformationBackground Information

• Newton knew that the force that caused the apple's acceleration (gravity) must be dependent upon the mass of the apple.

• And since the force acting to cause the apple's downward acceleration also causes the earth's upward acceleration (Newton's third law), that force must also depend upon the mass of the earth.

Background InformationBackground Information

• So for Newton, the force of gravity acting between the earth and any other object is directly proportional to the mass of the earth, directly proportional to the mass of the object, and inversely proportional to the square of the distance that separates the centers of the earth and the object.

Universal Law of GravitationUniversal Law of Gravitation

• Gravitational interactions exist between ALL objects directly depending on their masses.

• And, the inverse square of their distances.

Background InformationBackground Information

Universal Law of GravitationUniversal Law of Gravitation

• This Law applies everywhere or universally.

Gravitational ConstantGravitational Constant

• Gravitational constant (Big G) is the measurement of the gravitational force’s strength

• Aside: Henry Cavendish (1789) was the first person to measure it

• Acceleration of gravity (little g) rate at which an object changes it velocity

Universal Law of GravitationUniversal Law of Gravitation

• Universal Law of Gravitation and the acceleration of gravity

Universal Law of GravitationUniversal Law of Gravitation

• Example

• Homework

Objects in EquilibriumObjects in Equilibrium• If an object is being pushed to right at a

constant velocity (Fnet = 0 N):

• (-) Fg = (+) Fsurf and (+) Fapp = (-) Ff

• (on the y-axis) Fnet = Fsurf + Fg will be,

• (-) Fg = (+) Fsurf

• (on the x-axis) Fnet = Fapp + Ff will be,

• (+) Fapp = (-) Ff

Newton’s 2Newton’s 2ndnd Law Law

Newton 2nd Law equation:

• Fnet = m • a

Equation in terms of the force of gravity:

• Fg = m • g