Classic Mechanics : Dynamics. Dynamics Newton’s laws Work and energy Momentum & angular momentum Momentum & angular momentum Newton’s laws Newton’s laws.

Slides:



Advertisements
Similar presentations
Chapter 5 – Force and Motion I
Advertisements

Chapter 4 The Laws of Motion.
Forces and Newton’s Laws of Motion Chapter 4. All objects naturally tend to continue moving in the same direction at the same speed. All objects resist.
1 Chapter Four Newton's Laws. 2  In this chapter we will consider Newton's three laws of motion.  There is one consistent word in these three laws and.
Dr. Steve Peterson Physics 1025F Mechanics NEWTON’S LAWS Dr. Steve Peterson
III. Newton’s Laws of Motion A.Kinematics and Mechanics B.Newton’s Laws of Motion C.Common Forces in Nature D.Problem Solving Using Newton’s Laws E.Frictional.
Force and Motion Force Newton’s First Law Newton’s Second Law Newton’s Third Law Gravitational Force Weight Normal Force pps by C Gliniewicz.
AP Physics Chapter 5 Force and Motion – I.
PHYS 218 sec Review Chap. 4 Newton’s laws of motion.
Forces and the Laws of MotionSection 4 Click below to watch the Visual Concept. Visual Concept Everyday Forces.
Chapter 5 Force and Motion (I) Kinematics vs Dynamics.
Chapter 5 The Laws of Motion.
Chapter 5 The Laws of Motion.
Chapter 4 Forces and Mass.
Circular Motion and Other Applications of Newton’s Laws
Physics Instructor: Dr. Tatiana Erukhimova Lecture 6.
Newton’s Laws.
Chapter 4 The Laws of Motion. Forces Usually think of a force as a push or pull Usually think of a force as a push or pull Vector quantity Vector quantity.
Forces and The Laws of Motion
Classical Mechanics Review 4: Units 1-19
Chapter everyday forces.
Forces and Newton’s Laws of Motion
Chapter 4 The Laws of Motion. Classical Mechanics Describes the relationship between the motion of objects in our everyday world and the forces acting.
Chapter 4 Preview Objectives Force Force Diagrams
Chapter 4 Section 1 Changes in Motion Force.
Classical Mechanics Describes the relationship between the motion of objects in our everyday world and the forces acting on them Conditions when Classical.
Dynamics Chapter 4. Expectations After Chapter 4, students will:  understand the concepts of force and inertia.  use Newton’s laws of motion to analyze.
Chapter 4 Preview Objectives Force Force Diagrams
Forces Contact Forces - those resulting from physical contact between objects –Normal Force –Friction –Tension (spring/rope) –Compression Action at a Distance.
© Houghton Mifflin Harcourt Publishing Company The student is expected to: Chapter 4 Section 1 Changes in Motion TEKS 4E develop and interpret free-body.
Forces and the Laws of Motion Chapter Changes in Motion Objectives  Describe how force affects the motion of an object  Interpret and construct.
Newton’s Laws The Study of Dynamics.
What is the normal force for a 500 kg object resting on a horizontal surface if a massless rope with a tension of 150 N is acting at a 45 o angle to the.
Mechanics Topic 2.2 Forces and Dynamics. Forces and Free-body Diagrams To a physicist a force is recognised by the effect or effects that it produces.
Chapter 4 The Laws of Motion. Classical Mechanics Describes the relationship between the motion of objects in our everyday world and the forces acting.
Mechanics 105 Kinematics – answers the question “how?” Statics and dynamics answer the question “why?” Force Newton’s 1 st law (object at rest/motion stays.
Chapter 4 Dynamics: Newton’s Laws of Motion
Forces of Friction When an object is in motion on a surface or through a viscous medium, there will be a resistance to the motion This is due to the interactions.
Monday, Sept. 18, 2002PHYS , Fall 2002 Dr. Jaehoon Yu 1 PHYS 1443 – Section 003 Lecture #5 Monday, Sept. 18, 2002 Dr. Jaehoon Yu 1.Newton’s Laws.
Chapter 4 The Laws of Motion. Classes of Forces Contact forces involve physical contact between two objects Field forces act through empty space No physical.
Dynamics: Newton’s Laws of Motion. Concepts Force Newton’s First Law of Motion Mass Newton’s Second Law of Motion Newton’s Third Law of Motion Weight.
Force and Motion This week – This week – Force and Motion – Chapter 4 Force and Motion – Chapter 4.
Physics 111: Mechanics Lecture 4
Dynamics: Newton’s Laws of Motion
Exam 2 Review 8.02 W08D1. Announcements Test Two Next Week Thursday Oct 27 7:30-9:30 Section Room Assignments on Announcements Page Test Two Topics: Circular.
Chapter 4 The Laws of Motion. Classical Mechanics Describes the relationship between the motion of objects in our everyday world and the forces acting.
Section 4–4: Everyday Forces Coach Kelsoe Physics Pages 135–143.
The tendency of objects to resist change in their state of motion is called inertia  Inertia is measured quantitatively by the object's mass.  Objects.
Physics 211 Force and Equilibrium Hookes Law Newtons Laws Weight Friction Free Body Diagrams Force Problems 4: Classical Mechanics - Newtons Laws.
Chapter 5 The Laws of Motion.
© Houghton Mifflin Harcourt Publishing Company Preview Objectives Force Force Diagrams Chapter 4 Section 1 Changes in Motion.
Chapter 4 Dynamics: Aim: How can we describe Newton’s Laws of Motion? © 2014 Pearson Education, Inc.
Chapter 4 & 5 Dynamics: Newton's Laws and Its Application.
FORCES Chapter 5. Mechanics The study of Motion Isaac Newton, 1600’s The father of mechanics.
1 Chapter 4 The Laws of Motion Classes of Forces Contact forces involve physical contact between two objects Field forces act through empty.
Chapter 4 The Laws of Motion.
1 Chapter 5 The Laws of Motion. 2 Force Forces are what cause any change in the velocity of an object A force is that which causes an acceleration The.
Raymond A. Serway Chris Vuille Chapter Four The Laws of Motion.
Forces & The Laws of Motion Ideas of Sir Isaac newton.
Force and Motion–I Chapter 5. Newton's First and Second Laws A force: o Is a “push or pull” acting on an object o Causes acceleration We will focus on.
The Laws of Motion. Classical Mechanics Describes the relationship between the motion of objects in our everyday world and the forces acting on them Describes.
Chapter 5 Force and Motion I. Classical Mechanics Describes the relationship between the motion of objects in our everyday world and the forces acting.
Dynamics: Newton’s Laws of Motion
Chapter 4 Preview Objectives Force Force Diagrams
Dr.Mohammed Abdulrazzaq Mechanical Department College of Enginerring
Chapter 4 Newton’s Laws.
Chapter 5 The Laws of Motion.
The Laws of Motion (not including Atwood)
Presentation transcript:

Classic Mechanics : Dynamics

Dynamics Newton’s laws Work and energy Momentum & angular momentum Momentum & angular momentum Newton’s laws Newton’s laws application Work and energy Work and energy Momentum and angular momentum Momentum and angular momentum Conservation of energy Conservation of energy Conservation of Momentum and angular momentum Conservation of Momentum and angular momentum

"Nature and Nature's laws lay hid in night; God said, Let Newton be! and all was light." Newton, Sir Isaac ( ), mathematician and physicist, one of the foremost scientific intellects of all time.

a profound impact: astronomy, physics, and mathematics achievements: reflecting telescope three laws of motion; the law of universal gravitation the invention of calculus

Key terms: dynamics force mass superposition net force Newton’s law of motion Inertia equilibrium action-reaction pair elasticity tension friction force gravitational interaction free-body diagram Chapter4-5 Newton’s Laws of Motion

1. Newton’s law of motion 1.1 Newton’s first law A body acted on by no net force moves with constant velocity and zero acceleration inertial force 1.2 Newton’s second law If a net external force acts on a body, the body accelerates. The direction of acceleration is the same as the direction of the net force. The net force vector is equal to the mass of the body times the acceleration of the body. Chapter4-5 Newton’s Laws of Motion

If m is a constant, then: Caution: This is a vector equation used for a instant. We will use it in component form. (net force) In the natural coordinate axis: In the rectangular coordinate axis: m

1.3 Newton’s third law Whenever two bodies interact, the two forces that they exert on each other are always equal in magnitude and opposite indirection. 1.4 Application area of Newton’s law low speed macroscopic practicality inertial frame

2. What is a force? Forces are the interactions between two or more objects.

unified field theory:gravity and electromagnetic interaction Einstain : S.L.Glashow physicists Grand Unification Theory weak and electromagnetic interaction 2.1 Fundamental Forces:

x 2.2 the Common forces in mechanics 1) Gravitation o k: force constant x: elongation 2) elasticity 3) Frictional force Static friction Kinetic friction

3. Applications of Newton’s law * Identify the body  Examine the force, draw a free body diagram  Construct a coordinate * Write the Newton’s law in component form * Calculate the equation Problem-solving strategy

Example: A wedge with mass M rests on a frictionless horizontal table top. A block with mass m is placed on the wedge, and a horizontal force F is applied to the wedge. What must be the magnitude of F if the block is to remain at a constant height above the table top? Solution: x y F M  m N mg For m: x:Nsin  =ma y:Ncos  =mg a=g.tg  For (M+m): F=(M+m)a =(M+m)g.tg 

a m m N mg FsFs Discussion:What must be the magnitude of a if the block does not slide down the wedge? Draw a free body diagram of m. horizontal: N=ma perpendicular:  N=mg So: a=g/  。 If a ,then N , then  N>mg, will the m go up?

 m R m N mg FsFs Discussion:What must be the  if the block does not slide down the cylinder? Draw a free body diagram of m. horizontal: N=mR  2 perpendicular:  N=mg

Example: A man pulls a box by a rope with constant speed along a straight line, known:  k =0.6, h=1.5m. Find how long the rope is when F=F min.  L m h F fkfk N mg Solution: horizontal : Fcos  - f k =0 perpendicular : Fsin  + N - mg=0 f k = µN So: tg  = µ 。 that is: when L=h/sin  =2.92m F=F min F=F min :

Example: A parachute man drop into air, the resisting force is approximately proportional to the man’s speed v, find the velocity in any instantaneous time and the final velocity? Solution: o y Draw a free body diagram of the man, establish Newton’s law in y direction: Suppose: mg f

o y f final velocity: Can you describe the man’s motion? Suppose:

Example: Try to find the path of the particle according to the picture. x y m F=f 0 t i v0v0 O Solution:

x y m F=f 0 t i v0v0 O

Example: A small bead can slide without friction on a Circular hoop that is in a vertical plane and has a radius of R=0.1m. The hoop rotates at a constant rate of  =4.0rev/s about a vertical diameter. a) Find the angle  at which the bead is in vertical equilibrium. b) Is it possible for the bead to “ride” at the same elevation as the center of the loop? c) What will happen if the hoop rotates at 1.00rev/s p. 161, Solution: a) For the bead normal : Nsin  =m  2 Rsin  perpendicular : Ncos  =mg cos  =g/ (  2 R)  =  =4.0rev/s R=0.1m  N mg

b) N can not balance mg, so… c) When  =1.0rev/s=2  rad/s, cos  =2.5, so the bead stay at the bottom of the loop Example: A small bead can slide without friction on a Circular hoop that is in a vertical plane and has a radius of R=0.01m. The hoop rotates at a constant rate of  =4.0rev/s about a vertical diameter. a) Find the angle  at which the bead is in vertical equilibrium. b) Is it possible for the bead to “ride” at the same elevation as the center of the loop? c) What will happen if the hoop rotates at 1.00rev/s  =4.0rev/s R=0.1m  N mg

Example: A small bead at rest slide down a frictionless bowl of radius R from point A. Find N, a n, a t at this position.  R o A N mg  Solution: tangential : mgsin  = ma t = m normal : N-mgcos  = ma n = m so : a t =gsin  f n =ma n, f t =ma t

4. Noninertial Frame of reference B A a m k B: mass m is accelerating. A: mass m is at rest. Which one is right? The bus is not a inertial frame of reference. A frame of reference in which Newton’s first law is valid is called an inertial frame of reference. Any frame of reference will also be inertial if it moves relative to earth with constant velocity. Newton’s laws of motion become valid in non-inertial system by applying a inertial force on the object.

B A a m k Transposition: : real force : inertial force : acceleration of A relative to B Then:

Example: A wedge rests on the floor of a elevator. A block with mass m is placed on the wedge. There is no friction between the block and the wedge. The elevator is accelerating upward. The block slides along the wedge. Try to find the acceleration of the block with respect to the elevator. a  m a  mg ma N m a Solution: The elevator is the frame of reference, there are three forces acts on the block. m(g+a)sin  =ma a=(g+a)sin 

Example: A wedge with mass M rests on a frictionless Horizontal table top. A block with mass m is placed on The wedge. There is on friction between the block and the wedge. The system is released from rest. a) Calculate the acceleration of the wedge and the Horizontal and vertical components of the acceleration of the block. b) Do your answer to part (a) reduce to the correct results When M is very large? c) As seen by a stationary observer, what is the shape of the trajectory of the block? (see page 182, 5-108) M  m x y

Tracing problem Plane: x=x 0 +vt, y=h Missile: dY/dX=(y-Y)/(x-X) h v x y O u So: dY/dt=k(y-Y) dX/dt=k(x-X) And: k 2 [(y-Y) 2 +(x-X) 2 ]=u 2 k=u/[(y-Y) 2 +(x-X) 2 ] -1/2 So: Y(n+1)=Y(n)+k(y-Y)  t X(n+1)=X(n)+k(x-X)  t Y(0)=0, X(0)=0