Today’s Lectures:The Laws of Gravity

• Speed, velocity, acceleration, force

• Mass, momentum and inertia• Newton’s three laws of motion• The Force of Gravity

Assigned Reading

• Chapter 5.1

Before Newton• Kepler understood the phenomenology

of planetary motions, I.e. the three laws, but never understood *why* planets move the way they do– He thought of magnetic force from the Sun– He even thought (and dismissed) that Angels

pull planets along their orbits

• Galileo understood inertia, force and acceleration very well, but fell short of understand the causal relationship between force and acceleration. He also did not propose a universal law for the force of gravity

Describing Motion

• Motion is when the position of an object changes in time

• If position does not change, the object is at rest

• The describe motions we need to monitor position and time

• The rate at which an objects covers a given amount of space in a given amount of time is called speed

– v = s/t

Vectors,or things with a sense of

direction• There are physical quantities in nature

for which only one number, their intensity, tells the whole story: e.g. temperature, mass, luminosity, color

• Other quantities need both an intensity and a direction to be fully described: e.g. speed, force, acceleration.

• These quantities with a “direction” are called VECTORS

Galileo and the Concept of Inertia

Aristotle held that objects at rest remained at rest unless a force acted on them, but that objects in motion did not remain in motion unless a force acted constantly on them: F = v WRONG.

Galileo concluded that an object in a state of motion possesses an ``inertia'' that causes it to remain in that state of motion unless an external force acts on itRIGHT.

Galileo’s Law of Inertia

• But velocity cannot not the whole story: we need a more general concept to describe motions: momentum P = m·v

• An object maintains its “quantity of motion” (momentum), unless a force is acted upon it

• Only a force can change the “quantity of motion” (momentum) of an object, either by changing its speed, or by changing its direction of motion, or both

Sir Isaac Newton and the Unification of Physics & Astronomy

• Newton was by many standards the most important figure in the development of modern science.

• He demonstrated that the laws that govern the heavens are the same laws that govern the motion on the surface of the Earth.

• Newton's Three Laws of Motion. • Theory of Universal Gravitation

(1642-1727)

Newton’s First Law(really, Galielo’s Inertia Law)

• In the absence of a net force, an object moves with constant velocity, or it conserves its momentum.

• (paraphrased) If nothing acts on an object, the object will keep moving in a straight line and at a constant speed.

• The same is true for zero velocity.

There must be a force acting on the apple. What force?

More importantly, if the force of gravity reaches to the tree, might it not reach even further; in particular, might it not reach all the way to the orbit of the

Moon!

Vocabulary Words• Speed is the distance traveled in each

second – it’s measured in meters per second (m/s).

• Velocity is the speed in a particular direction – it’s measured in meters per second (m/s).

• Acceleration is the change in velocity in each second – it’s measured in meters per second per second (or m/s2)

Acceleration

• An acceleration is a change in velocity.

• Acceleration occurs when either the magnitude or direction of the velocity (or both) are altered.

• Uniform Circular Motion is Accelerated Motion

How many ways can your car be accelerated?

Newton’s Second Law

• Acceleration is caused by force but also related to the mass of the object

Force = Mass x Acceleration

F = m·a

Or a = F/m

Question: How do objects accelerate dueto the force of gravity?

The gravitational force on an object nearthe surface of Earth is:

Fgrav = m·g (g = 9.8m/s2)

Newton’s Third Law

• For every ACTION (I.e. application of a force) there is an equal and opposite re-ACTION

F1 = -F2

Newton’s Third Law

For any force, there always is an equal and opposite reaction force.

Table pushesback onbox

Box pushes downon table due to gravity.

Example: The Jet Engine

• What makes a jet-propelled airplane move forward?

Gravity

• What force is responsible for motions in the universe?

• What force makes objects fall?• What keeps us on the rotating Earth?• Why don’t planets move in straight lines,

but orbit around the Sun instead?

Gravity• We can summarize the universal law of

gravitation with the following statements:– Every mass attracts every other mass through

the force of gravity.– If mass #1 exerts force on mass #2, and

mass#2 exxerts force on mass#1, the force must depend o both masses, namely:

– The force of attraction is directly proportional to the product of the two masses.

– The force of attraction is inversely proportional to the square of the distance between the masses.

The Law of Gravity

221

d

MMGFg

d

M1M2

G = 6.67x10-11 m3/kg/s2

2

21

2

9.8m/s

d

MGg

gMFg

Near Earth’s surface

Mass and Weight• Mass is a measure of how much

material is in an object.• Weight is the force exterted by gravity

on a massive body (body with mass), e.g. placed on the surface of Earth

• Weight is a measure of the gravitational force exerted on that material.

• Thus, mass is constant for an object, but weight depends on the location of the object.

• Your mass is the same on the moon, but your weight on the surface of the moon is smaller

221

d

MMGFg Survey Question

Two equal masses, m, separated by a distance, d, exert a force, F, on each other due to their gravitational attraction. How large is the gravitational force between an object of mass m and an object of mass 2m separated by the same distance d?

¼ F

½ F

F

2F

4F

221

d

MMGFg Survey Question

Two equal masses, m, separated by a distance, d, exert a force, F, on each other due to their gravitational attraction. How large would their gravitational attraction be if the distance between them was doubled?

1) ¼ F

2) ½ F

3) F

4) 2F

5) 4F

… so why don’t planets just fall into the sun?

M1M2

… because they miss (that is, they have enough tangential

velocity to always miss)

M1M2

v

This is the concept of an orbit.

Fg Fg

Why doesn't the earth fall to the sun?

• It has a velocity and it has inertia!

• Force of gravity causes change in the direction of velocity --- acceleration.

• The earth is falling towards the sun all the time!

V=8km/s

Why don't they fall?

They are circuling Earth at a speed of 8 km/s!