Last Time Kinematics TwoDimensional Motion Projectiles Relative Velocity

• Last Time: Kinematics: Two-Dimensional Motion Projectiles, Relative Velocity • Today: Dynamics: Forces Newton’s Laws of Motion HW #3 due Tuesday, Sept 21, 11: 59 p. m. (Last HW before Exam #1) Recitation Quiz #3 tomorrow Today: Have to end office hours at 3: 30 p. m. 1

• Recitation Quizzes : In general, formula sheets will not be provided. 2

Who Was Isaac Newton ? • English physicist, mathematician, astronomer, philosopher, and theologian, 1643 – 1727. • Widely considered to be perhaps the most influential scientist ever. • Developed calculus (with Gottfried Leibniz). • Developed theory of color. • Developed mechanics (study of motion) o Three Laws of Motion • Developed theory of gravitation. 3

Contact Forces • What is a force? Forces commonly thought of as a “pull” or a “push” on an object. • These are examples of “contact forces”. o Result from physical contact between two objects. 4

Field Forces • There also forces in physics which do NOT arise from actual physical contact between objects. o Gravity is one example of an “action-at-a-distance” force. • Gravity is an example of a “field force”. o Objects are said to interact with a “field”. o “Field” concept due to Michael Faraday (1791 – 1867). 5

Fundamental Forces of Nature Strong Electromagnetic quarks, gluons, < 10 – 15 m electric, magnetic, Weak Gravity radioactivity, < 10 – 15 m planet orbits, etc. , 6

Newton’s First Law of Motion • Before Galileo, it was thought that the natural state of matter was the state of rest (i. e. , no motion). • By considering thought experiments of frictionless surfaces, Galileo concluded, instead, an object will tend to continue in its current state of motion. Newton’s First Law of Motion An object moves with a velocity that is constant in magnitude and direction, unless acted on by a non-zero net force. Net Force The vector sum of all external forces exerted on an object. 7

External vs. Internal Forces • External forces originate from the object’s environment. o If an object’s velocity is constant (i. e. , not changing in either magnitude or direction), then the acceleration is zero, meaning the net external force acting on it must be zero. • Internal forces originate within the object itself, and cannot change the object’s velocity. o They can, however, change the object’s rate of rotation (discuss later when we study rotational motion …) 8

Mass and Inertia • Inertia is the tendency of an object to continue in its original state of motion. vs. • Mass is a measure of an object’s resistance to change in motion due to a force. The greater the mass, the less it accelerates under a given force. • SI unit of mass is the kilogram (kg). • An object’s mass is the same, no matter where in the universe. Mass is NOT equivalent to weight ! 9

Newton’s Second Law of Motion • First Law: Tells us what happens to an object with no net force acting on it NOTHING !! • Second Law: Describes what happens to an object that DOES have a net force acting on it. Newton’s Second Law of Motion The acceleration a of an object is directly proportional to the net force acting on it, and inversely proportional to its mass. Σ: “sum of” acceleration vector sum of all external forces 10

What F = m a Means • What Newton’s Second Law of Motion tells us is that a net force causes a CHANGE in an object’s velocity (i. e. , in its motion). Ø If no net force, the object’s acceleration is zero, and so its velocity must be constant. 11

F = ma • Newton’s Second Law of Motion is a VECTOR equation. It can be decomposed into separate x-, y-, and z-components as: • What does this mean? For example, suppose net force only along y-axis (Fx = Fz = 0). This means ax = az = 0. Acceleration ONLY along y-direction ! • Acceleration will be in the direction of the net force. 12

F = ma • The VECTOR equation permits us to relate a net force in a particular direction to the acceleration in that same direction. Acceleration always along direction of force ! • If all we care about are the MAGNITUDES of the net force and the acceleration, we simply have: magnitude of force magnitude of acceleration 13

Units for Force and Mass Acceleration in m/s 2 SI unit force is the “Newton”. • Defined to be the force acting on a 1 kg mass that produces an acceleration of 1 m/s 2. SI unit for mass is the kilogram (kg). 1 Newton (N) = 1 kg m/s 2 14

Example: Multiple Choice #10 (p. 110) If an object moves with a constant velocity v , the magnitude of the net force on the object must be: (a) mg (b) mv (c) ma (d) 0 (e) Not enough information, need to know its mass. 15

Example: 4. 3 A 6. 0 -kg object undergoes an acceleration of 2. 0 m/s 2. (a) What must be the magnitude of the net force acting on it? (b) If this same force is applied to a 4. 0 -kg object, what would its acceleration be? 16

Example: 4. 12 Two forces are applied to a car: (a) What is the resultant (vector sum) of these two forces? (b) If the car has a mass of 3000 kg, what acceleration will it have? (ignore friction) 17

Gravitational Force • The gravitational force is the mutual force of attraction between any two objects in the universe. • It is the weakest of the four fundamental forces. Newton’s Law of Universal Gravitation Every object in the universe attracts every other object with a force that is proportional to the product of their masses, and inversely proportional to the square of the distance between them. Fg: gravitational force in Newtons G : universal gravitation constant = 6. 67 10− 11 N-m 2/kg 2 m 1, m 2 : masses (kg) ; r : distance (m) 18

“Weight” • The “weight”, w, of an object is defined to be the magnitude of the gravitational force acting on the object. w = mg [ just from F = ma ] Thus, weight has units of Newtons (in SI). • The above is only applicable near the surface of Earth (acceleration due to gravity = g near surface of Earth). More generally, at some distance r from the surface of the Earth: ME = Earth’s mass = 5. 98 1024 kg r = distance from center of Earth = RE + height above surface Note: On surface of Earth, r = RE = 6. 38 106 m !! 19

What is a Pound ? • When we calculate the gravitational force, or weight, of an object, in SI units the weight (a force) has units of Newtons. • The “pound” is a unit of force in the English system, where: 1 Newton = 0. 225 lb 20

Example • A person has a mass of 75 kg. What is the person’s weight in pounds on the surface of the Earth? • What would this person’s weight in pounds be on the Moon? ME = 5. 98 1024 kg r. E = 6. 38 106 m MM = 7. 36 1022 kg r. M = 1. 74 106 m 21

Example • A person lands on Planet X, whose mass is 3 times that of Earth’s, and radius half that of Earth’s. What is the person’s weight as a multiple of her Earth weight? 22

Newton’s Third Law of Motion • Newton recognized that a single isolated force doesn’t exist. Instead, forces always exist in “action/reaction” pairs. What would happen, instead, if you ran into a wall? Newton’s Third Law of Motion If objects 1 and 2 interact, the (action) force F 12 exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the (reaction) force F 21 exerted by object 2 on object 1. 23

Newton’s Third Law of Motion • Key Points: The action force is equal in magnitude to the reaction force, but opposite in direction. In all cases, the action/reaction forces act on different objects. They do NOT act on the same object. Example: Gravitational force between two objects #1 F 21 F 12 #2 Magnitude of two forces are equal in magnitude, but opposite in direction ! 24

“Normal Forces” • Suppose a book is sitting on a table. There is a downward gravitational force on it. Why doesn’t it fall through the table? mg 25

“Normal Forces” • Answer: The table exerts an opposite upward force on the book! This is called a “normal force”, n. upward “normal force” mg • Forces acting on the book: downward gravity, upward normal Equal Magnitude, Opposite Direction , Net Force = 0 !! • Reaction to upward normal: force exerted by book on table • Reaction to downward gravity: gravitational force exerted by the book on the Earth 26

Reading Assignment • Next two classes: 4. 5 – 4. 6 Applications of Newton’s Laws of Motion 27