Chapter 2, 4 &5 Newton’s Laws of Motion

Aristotle ( )BC

Aristotelian School of Thought Natural Motion Every Object in the universe has a proper place, determined by its nature. Heavier objects strive harder to be in their proper place. This implies that heavier objects fall faster than lighter objects.

Violent Motion: All motion results from a push or pull. Except for celestial objects (the realm of the Gods), the normal “natural” state of an object was to be at rest. Aristotle’s school of thought dominated western culture for the next 2000 years, until the 16 th century. The Earth does not move.

Celestial Spheres

Copernicus and the Moving Earth

Ptolemaic Model

Copernican Model

Copernicus asserts that the Sun is at the center of the solar system instead of the Earth. This runs contrary to the Aristotelian school of thought – Copernicus publishes De Revolutionibus

Galileo Galilei

Galileo is considered to be the father of experimental science. Galileo demolished the Aristotelian model by doing experiments and proving it wrong. Inclined plane demo

Galileo’s Inclined Planes Inertia The tendency of a body to resist changes in its motion. Mass is a measure of inertia – A more massive body has more inertia.

Chapter 3 Linear Motion

Description of Motion -Kinematics Average Speed = total distance/time Total distance = (Average speed) x (time)

Velocity Speed in a particular direction 70mi/h due north --- is a velocity Examples 70mi/h is a speed

Approximate Speeds in Different Units 20km/h12 mi/h6 m/s 40 km/h25 mi/h11 m/s 60 km/h37 mi/h17 m/s 65 km/h40 mi/h18 m/s 80 km/h50 mi/h22 m/s 88 km/h55 mi/h24 m/s 100 km/h 62 mi/h28 m/s 120 km/h75 mi/h33 m/s

Velocity is proportional to the time

Acceleration Acceleration = change in velocity/change in time How quickly how fast changes

Constant Acceleration – Free Fall Near the surface of the earth, all objects fall with the same acceleration baring effects from air friction. In this case, a = g = 9.8m/s/s or 32 ft/s/s or a = g = 9.8m/s 2 or 32 ft/s 2

Distance traveled Assume a= 2 m/s/s and is constant. 1 sec3 sec2 sec 1m 4m 9m

The distance traveled is proportional to the time squared.

Distance vs time d = ½ gt 2

If a is constant

If the particle starts with an initial velocity of V o at zero seconds (t o = 0 sec) then:

Assume V o = 1m/s and a = 10m/s 2 0 s1 m/s 1 s11 m/s 2 s21 m/s 3 s31 m/s 4 s41 m/s 5 s51 m/s 6 s61 m/s 7 s71m/s 8 s81 m/s 9 s91m/s 10 s101 m/s t(sec)V(m/s)

For free-fall

Newton’s Laws of Motion

Newton’s First Law of Motion Every object continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.

Newton’s Second law of Motion The acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object.

Newton’s Third Law of Motion For every action, there is always opposed an equal reaction. By “action”, we mean a force. Action/reaction forces do not act on the same object.

Types of Forces Gravitational Friction Electromagnetic Nuclear Forces between masses Contact force Forces between charges. Forces between nuclear particles (protons, neutron) NormalContact force SpringRestoring Forces

When the acceleration is g we have Free Fall m F 2m 2F

When acceleration is zero - Equilibrium mg N

When acceleration is zero - Equilibrium mg N FaFa f v = constant

Action/Reaction pairs Action:Tire Pushes on Road Reaction:Road pushes on Tire

Action/Reaction Action:Rocket pushes on gas Reaction:Gas pushes on rocket

Nonlinear Motion Velocity : A vector quantity A B A+B

A B Vector quantities have magnitude and direction R = A + B R is called the resultant vector

A B R = A + B R 2 = A 2 + B 2 The Pythagorean Theorem

Projectile Motion Any object that is projected by some means and continues in motion under the influence of gravity and air resistance is called a projectile. The path of a projectile is called the trajectory

Projectile Motion -g vector

Projectile Range At 30 degrees At 15 degrees

Fast Moving Projectiles Satellites The Earth’s curvature drops a vertical distance of 5 meters every 8,000 meters horizontally

Circular Motion V = r   r