Physics 117

Chapter 2

Explaining motion

Extra Material

Heavier bodies go down faster

It is common experience that heavier body go down faster.

This one of the reason why you have the other three guys…

Aristotle

Aristotle lived from 384-322BC, and is universally considered as one of the great thinkers of the ancient world. He was born in the city of Stagira in Macedonia.

Aristotle was a student of Plato and world-class philosopher in his own right.

Aristotle had a tremendous influence on western culture. His work covered: Logic,Physics,Psychology, Natural History, Philosophy, Politics.

Galileo Galilei

Galileo was born in Pisa, Italy on February 15, 1564. His father, Vincenzo Galilei, was a musician.

At the University of Pisa, Galileo learned the physics of the Ancient Greek scientist, Aristotle. However, Galileo questioned the Aristotelian approach to physics.

Galileo eventually disproved this idea by asserting that all objects, regardless of their density, fall at the same rate in a vacuum.

To determine this, Galileo performed various experiments in which he dropped objects from a certain height.

He wrote down his discoveries about motion in his book, De Motu, which means "On Motion."

The leaning tower of Pisa

Would you go up there to throw rocks down?

Do you believe Galileo really did? Did he really need to?

Free fall law

In the absence of friction (e.g. by air) all the bodies fall at the same rate independently of

their mass

Summary of Lecture 2: Falling Bodies

Aristotle’s view: heavier bodies fall faster Galileo’s observations led him to a new word view. Using

the inclined plane he studied how bodies fall under the influence of gravity. He observed that1. Bodies fall with a constant acceleration independent of

their mass (but which was increasing with the increasing steepness of the inclined plane)

2. In the absence of friction bodies tends to remain in their state of motion which can be at rest or at constant speed along a straight line (constant velocity)

3. The distance, d, covered by a falling body was proportional to the the square of the time lapsed. Indeed:

€

v = at, d =1

2at 2 (a = const)

In the case of vertical inclination (free fall)

€

a = 9.8m

s2≡ g

Inertia

QuickTime™ and aSorenson Video decompressorare needed to see this picture.

Newton

Isaac Newton was born on Xmas day of 1642 in Woolsthorpe, England.

As a child he did not show particular signs of brightness but he managed to graduate at the University of Cambridge (although without particular distinction).

When he was 23 the plague swept trough London and Newton retreated to his mother farm. Here in few months he laid the foundations for the work that made him immortal among men.

Newton is responsible (among other things) for: The discovery of the law of universal

gravitation. The invention of calculus The first theory of light The formulation of the three laws of

dynamics

Newton’s First Law of Dynamics

“Every object continues in a state of rest, or of uniform motion on a straight line

(constant velocity), unless it is compelled to change that state by an unbalanced

force impressed upon it.”

The property of material objects to resist changes in their state of motion is called inertia

Newton’s First Law of Dynamics

“Every object continues in a state of rest, or of uniform motion on a straight line

(constant velocity), unless it is compelled to change that state by an unbalanced

force impressed upon it.”

The property of material objects to resist changes in their state of motion is called inertia

Newton’s Second Law of Dynamics

“The net force on an object is equal to its mass times its acceleration and

points in the direction of the acceleration

€

F = ma

The acceleration is inversely proportional to the mass

Newton’s Second Law of Dynamics

“The net force on an object is equal to its mass times its acceleration and

points in the direction of the acceleration”

€

rF = m

r a

Summary of the previous lecture

• Newton’s second law:

• Units: [m]=kg, [F]=N=kg·m/s2

• Gravitational force:

• Air resistance:

• Terminal velocity: it is velocity such that •For skydivers once the chute is opened R=v2

€

rF = m

r a

€

rF grav =

r W = m

r g

€

rR = β

r v (viscous media, no turbulence) or

r R = γ

r v 2 (turbulence, generally fast fall)

€

ra = 0 =

r W −

r R (v)

m

Newton’s Third Law of Dynamics

“If an object exerts a force on a second object, the second object exerts an equal force back on the first object”

Engine pushed forward

Flow pushed backward