Newton's Laws of Motion

Chapter 4: Newtons laws of motion Starting with a review 1

So far: We described motion using mathematics We saw one bit of physics a = constant Coordinate system = + fv v at 0 Defined position, velocity, and acceleration 1 2 = + + 2 fx x v t at 0 0 Organization of information ( ) = + 2 f 2 0 1-D kinematics 2 v v a x x 0 f Key to 2-D kinematics: treat the x and y components independently 2

One statement about the natural world: Near the surface of the earth, things spontaneously accelerate towards the center of the earth at approximately 9.8 m/sec2, unless something prevents it from doing so. 3

Now: Newtons laws more statements about the natural world This is the core of the course Their discovery ranks among the greatest achievements of the human intellect! They are not quaint or obvious! Apply across an enormous range of scales The idea that there are laws of nature at all was hugely influential physics & science in general economics political philosophy design of English estate gardens 4

Newtons task: Given a particle whose characteristics are known, in an environment for which we have a complete description, what is the motion of the particle? 1. What characteristics of the particle are relevant? Concept of mass 2. How do you describe the environment? Concept of force 3. How do you describe the resulting motion? Invented calculus! 5

Older question: What is the natural state of motion of an object? Aristotle (384 BC 322 BC) Natural state eudaemonium is to be at rest. Galileo (1564 1642) The natural state of motion of an object is to be either at rest or be moving with a constant velocity. 6

Videos showing motion in zero gravity for intuition https://youtu.be/Q0Wz5P0JdeU?t=126 OK Go Upside Down & Inside Out https://www.youtube.com/watch?v=LWGJA9i18Co Play first minute 7

Newton (1642 1727) Q: How does the state of motion of an object change? A: Something pushes it! Q: What pushes it? A: A force! Q: What s a force? A: Good question! 8

Contact forces versus non-contact forces 9

Forces that arise from interaction with surfaces 10

Forces that arise from interaction with surfaces 11

12

This force arises without any contact! Spooky! 13

Force is a VECTOR 1F 2 F = + F F F 1 2 net = = If , F F 0 F 1 2 net 14

Force is a VECTOR = + F F F 1 2 net = = If , F F 0 F 1 2 net 15

Force is a VECTOR 1F 2 F = + F F F 1 2 net 16

Force is a VECTOR 1F 2 F = + F F F 1 2 net If , F F 0 F 2 1 net 17

Force is a VECTOR F net = + F F F 1 2 net If , F F 0 F 2 1 net 18

Force is a VECTOR 1F 2 F 3 F = + + F F F F 1 2 3 net 19

Force is a VECTOR 1F 2 F 2 F 3 F 3 F 1F = + + F F F F 1 2 3 net 20

Force is a VECTOR 1F 2 F 2 F F net 3 F 3 F 1F = + + F F F F 1 2 3 net 21

Force is a VECTOR 2 F F net F 3 F net 1F = + + F F F F 1 2 3 net 22

Newtons First Law of Motion 23

Newtons First Law of Motion Assume there is no net force on an object, then: 1. If it is at rest, then it will stay at rest 2. If it is moving, then its velocity will remain constant 24

Newtons first law of motion The book says: Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it 25

Space station video for intuition Motion with effectively zero gravity https://youtu.be/m1G4DsTJBtk?t=48 https://youtu.be/m1G4DsTJBtk?t=48 26

Newtons first law of motion The 1st law is really about inertial reference frames. I prefer: In an inertial reference frame, every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it 27

Newtons first law of motion The 1st law is really about inertial reference frames. I REALLY prefer: Inertial reference frames exist, in which every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it 28

What do things look like from an inertial reference frame? What do things look like from a non-inertial reference frame? 29

Roller skates means no friction This shows the view of someone standing on the ground 30

Roller skates means no friction This shows the view of someone standing on the ground 31

Roller skates means no friction This shows the view of someone standing on the ground 32

Roller skates means no friction This shows the view of someone standing on the ground The red person doesn t move! No net force on the red person, so he/she maintains zero velocity The view from outside: an inertial reference frame! (Talk about inside view) 33

Roller skates means no friction This shows the view of someone standing on the ground 34

Roller skates means no friction This shows the view of someone standing on the ground 35

Roller skates means no friction This shows the view of someone standing on the ground 36

Roller skates means no friction This shows the view of someone standing on the ground No net force on the red person, so he/she maintains a constant velocity The view from outside: an inertial reference frame! 37

This shows the view of someone in a helicopter hovering over one fixed spot on the ground 38

This shows the view of someone in a helicopter hovering over one fixed spot on the ground 39

This shows the view of someone in a helicopter hovering over one fixed spot on the ground No net force on the red person, so he/she maintains a constant velocity The view from outside: an inertial reference frame! 40

How do you know if you have an inertial reference frame? If Newton s first law applies, then you do! If all forces are associated with identifiable objects, then you do. An example of what it looks like in a non-inertial reference frame: (Coriolis free throw) https://youtu.be/7TjOy56-x8Q?t=19 41

Newtons second law of motion 42

Newtons second law of motion = F ma net This is a statement about how Nature behaves This can t be mathematically derived Must be checked via experiments Notice that it is a vector equation - no reference to any particular coordinate system 43

2nd law contains our statement of the 1st law as a special case = F ma net = = If 0, then 0. F a net = = 0 means constant. a v (1st law is really more of a statement about the existence of inertial reference frames) 44

= F ma net x component y component = net y F ma = net x F ma , y , x The vector equation contains two scalar equations 45

= F ma Units of force: m kgsec 2 m 1kg 1Newton 2 sec 1 Newton = the force magnitude that is required to accelerate 1 kilogram to a speed of 1 meter/second in 1 second. 46

Example calculation: A 5kg mass is at rest, and two constant forces act on it as shown. Find the subsequent motion. 2 F = = 20N F F 1 1 = = 15N F F 1F 2 2 =60o 47

= = = = cos sin F F F F F F F 1 1 2 2 x x = F ma y net 0 2 F 1 2 2 y y = = 20N = 15N 60o F F 1 2 = F 5 kg m 2y F x 1F 2x x component y component = net x F F + ma , x = 2cos F ma 1 x + 2cos F m ( F = a 1 x ) + o 20N 15Ncos 60 5kg m = = 5.5 x a 2 sec 48

(Aside) ( ) + o 20N 15Ncos 60 5kg m = = 5.5 x a 2 sec Note how the units work out: kg m sec 1 kg m N kg 2 2 sec 49

= = = = cos sin F F F F F F F 2 2 1 1 x x = F ma y net 0 2 F 2 2 1 y y = = 20N 15N F F 1 2 F =60o 2y 1F F x 2x x component y component F = = ma net x F F + ma , net y y , x = 2cos F ma + = 0 sin F ma 1 x 2 y + 2cos F m ( F = a 1 ( ) ( ) 5kg x o 15N sin 60 m y a = = 2.6 ) ( ) + o 2 20N 15N cos 60 5kg sec m = = 5.5 x a 2 sec 50