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MOTION & FORCE: DYNAMICS

MOTION & FORCE: DYNAMICS. Terminology - Recap. Mechanics = Study of objects in motion. 2 parts to mechanics. Kinematics = Description of HOW objects move. Chapters 2 & 3 Dynamics = WHY objects move. Introduction of the concept of FORCE . Causes of motion, Newton ’ s Laws

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MOTION & FORCE: DYNAMICS

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  1. MOTION & FORCE: DYNAMICS

  2. Terminology - Recap • Mechanics= Study of objects in motion. • 2 parts to mechanics. • Kinematics =Description of HOWobjects move. • Chapters 2 & 3 • Dynamics =WHYobjects move. • Introduction of the concept of FORCE. • Causes of motion, Newton’s Laws • Most of the course from Chapter 4 & beyond.

  3. Force A Forceis “A push or a pull” on an object. Usually, for a force, we use the symbol F. F is a VECTOR! Obviously, vector addition is needed to add forces!

  4. Classes of Forces “Pushing” Forces “Pulling” Forces 1. “Contact”Forces: 2. “Field”Forces: Physics II: Electricity & Magnetism Physics I: Gravity

  5. Classes of Forces • Contact Forces involve physical contactbetween two objects • Examples (in the pictures): spring forces, pulling force, pushing force • Field Forcesact through empty space. • No physical contact is required. • Examples (in the pictures): gravitation, electrostatic, magnetic

  6. The 4 Fundamental Forces of Nature • Gravitational Forces • Between objects • Electromagnetic Forces • Between electric charges • Nuclear Weak Forces • Arise in certain radioactive decay processes • Nuclear Strong Forces • Between subatomic particles Note: These are all field forces!

  7. Sir Isaac Newton 1642 – 1727 • Formulated the basic laws of mechanics. • Discovered the Law of Universal Gravitation. • Invented a form of Calculus • Made many observations dealing with light & optics.

  8. Newton’s Laws of Motion In the 21st Century, this is still a common MISCONCEPTION!!! • The ancient (& wrong!) view (of Aristotle): A force is needed to keep an object in motion. The “natural” state of an object is at rest. . • THE CORRECT VIEW(Galileo & Newton): • It’s just as natural for an object to be in motion at constant speed in a straight line as to be at rest. • At first, imagine the case of NO FRICTION • Experiment:If NO NET FORCEis appliedto an object moving at a constant speed in straight line, it will continuemovingat the same speed in a straight line! l • Overcoming the wrong, ancient misconception & understanding the correct view is one of the main goals of this chapter! Proven by Galileo in the 1620’s!

  9. Newton’s Laws • Galileo laid the ground work for Newton’s Laws. • Newton: Built on Galileo’s work • Now, Let us examine Newton’s 3 Laws, one at a time.

  10. Newton’s First Law Newton was born the same year Galileo died! • Newton’s First Law(The “Law of Inertia”): “Every object continues in a state of rest or uniform motion (constant velocity) in a straight line unless acted on by a net force.”

  11. Newton’s First Law A Mathematical Statement of Newton’s 1st Law If v = constant(a=0) , ∑F = 0 OR If v ≠ constant(a ≠ 0), ∑F ≠ 0

  12. Newton’s First LawAlternative Statement • In the absence of external forcesan object at rest remains at rest & an object in motion continues in motion with a constant velocity. • Newton’s 1st Lawdescribes what happens in the absence of a net force. • It also tells us that when no force acts on an object, the acceleration of the object is zero.

  13. Conceptual Example Newton’s First Law. A school bus comes to a sudden stop, and all of the backpacks on the floor start to slide forward. What causes them to do this?

  14. Inertia & Mass • InertiaThetendency of a body to maintain its state of rest or motion. • MASSA measure of the inertia of a body. • The quantity of matter in a body. • The SI System quantifies mass by having a standard mass = Standard Kilogram (kg) (Similar to the standards for length & time). • The SI Unit of Mass = The Kilogram (kg) • The cgs unit of mass = the gram (g) = 10-3 kg • Weight is NOT the same as mass! • Weight is the force of gravity on an object. • Discussed later.

  15. Newton’s Second Law • Newton’s 1st Law: If no net force acts, an object remains at rest or in uniform motion in straight line. • What if a net force acts? That is answered by doing Experiments. • It is found that, if the net force ∑F  0  Thevelocity v changes (in magnitude, in direction or both). • A change in the velocity v (Δv). There is an acceleration a = (Δv/Δt) OR A net force acting on a body produces an Acceleration!!! ∑F  a

  16. Newton’s Second Law Experiments Show That: The net force ∑F on a body & the accelerationa of that body are related. • How are they related? Answer this by doing more EXPERIMENTS! • Thousands of experiments over hundreds of years find (for an object of massm):a  ∑F/m (proportionality) • The SI system chooses the units of force so that this is not just a proportionality but an Equation:a  ∑(F/m) OR(total force!)  Fnet ∑F = ma

  17. Newton’s 2nd Law:Fnet = ma Fnet =the net (TOTAL!) force acting on mass m m =mass (inertia) of the object. a = acceleration of the object. OR, a = a description of the effect of F. OR, F is the cause of a. • To emphasize that F in Newton’s 2nd Lawis the TOTAL(net) force on the mass m, we write: ∑F = ma ∑ = a math symbol meaning sum (capital sigma)  The Vector Sum of all Forces on mass m!

  18. Based on experiment! Not derivable mathematically!! • Newton’s 2nd Law: ∑F = ma A VECTOREquation!! It holds component by component. ∑Fx = max, ∑Fy = may, ∑Fz = maz ll THIS IS ONE OF THE MOST FUNDAMENTAL & IMPORTANT LAWS OF CLASSICAL PHYSICS!!!

  19. Summary • Newton’s 2nd Lawis the relation between acceleration & force. • Acceleration is proportional to force and inversely proportional to mass. • It takes a force to change either the direction of motion or the speed of an object. • More force means more acceleration; the same force exerted on a more massive object will yield less acceleration.

  20. Now, a more precise definition of Force: Force  An action capable of accelerating an object. Force is a vector & is true along each coordinate axis. The SI unitof forceis The Newton (N) ∑F = ma, unit = kg m/s2  1N = 1 kg m/s2

  21. F1 F2 Recap We’ve been learning kinematics; describing motion without understanding what the cause of the motion is. Now we are going to learn dynamics!! FORCE is what causes an object to move. Can someone tell me what FORCE is? The above statement is not entirely correct. Why? Because when an object is moving with a constant velocity no force is exerted on the object!!! FORCEs are what cause changes to the velocity of an object!! When there is force, there is change of velocity!! What does this statement mean? What does force cause? It causes an acceleration.!! What happens if there are several forces being exerted on an object? Forces are vector quantities, so vector sum of all forces, the NET FORCE, determines the direction of the acceleration of the object. When the net force on an object is 0, it has constant velocity and is at its equilibrium!! NET FORCE, F= F1+F2

  22. More on Force There are various classes of forces Contact Forces: Forces exerted by physical contact of objects Examples of Contact Forces: Baseball hit by a bat, Car collisions Field Forces: Forces exerted without physical contact of objects Examples of Field Forces: Gravitational Force, Electro-magnetic force What are possible ways to measure strength of the force? A calibrated spring whose length changes linearly with the force exerted . Forces are vector quantities, so the addition of multiple forces must be done following the rules of vector additions.

  23. Newton’s First Law Aristotle (384-322BC): A natural state of a body is rest. Thus force is required to move an object. To move faster, ones needs larger forces. Galileo’s statement on natural states of matter: Any velocity once imparted to a moving body will be rigidly maintained as long as the external causes of retardation are removed!! What does this statement tell us? • When no force is exerted on an object, the acceleration of the object is 0. • Any isolated object, the object that do not interact with its surroundings, is either at rest or moving at a constant velocity. • Objects would like to keep its current state of motion, as long as there are no forces that interfere with the motion. This tendency is called the Inertia. Galileo’s statement is formulated by Newton into the 1st law of motion (Law of Inertia):In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity. A frame of reference that is moving at a constant velocity is called theInertial Frame NO! Is a frame of reference with an acceleration an Inertial Frame?

  24. Mass Mass: A measure of the inertia of a body or quantity of matter • Independent of the object’s surroundings: The same no matter where you go. • Independent of the method of measurement: The same no matter how you measure it. The heavier the object, the bigger the inertia !! It is harder to make changes of motion of a heavier object than a lighter one. The same forces applied to two different masses result in different acceleration depending on the mass. Note that the mass and the weight of an object are two different quantities!! Weight of an object is the magnitude of the gravitational force exerted on the object. Not an inherent property of an object!!! Weight will change if you measure on the Earth or on the moon but the mass won’t!! Unit of mass?

  25. Newton’s Second Law of Motion The acceleration of an object is directly proportional to the net force exerted on it and is inversely proportional to the object’s mass. How do we write the above statement in a mathematical expression? From this we obtain Newton’s 2nd Law of Motion Since it’s a vector expression, each component must also satisfy:

  26. Unit of the Force From the vector expression in the previous page, what do you conclude the dimension and the unit of the force are? The dimension of force is The unit of force in SI is For ease of use, we define a new derived unit called, Newton (N)

  27. Example: Estimate the net force needed to accelerate (a) a 1000-kgcar at a = (½)g (b) a 200-g appleat the same rate. Example: The force to stop a car. What average net force is required to bring a1500-kgcar to rest from a speed of 100 km/h (27.8 m/s) within a distance of 55 m?

  28. Force to Stop a Car What constant net force is required to bring a 1500kg car to rest from a speed of 100km/h within a distance of 55m? Acceleration!! What do we need to know to figure out the force? Initial speed: Final speed: What are given? Displacement: This is a one dimensional motion. Which kinetic formula do we use to find acceleration? Acceleration Thus, the force needed to stop the car is • Linearly proportional to the mass of the car • Squarely proportional to the speed of the car • Inversely proportional to the force by the brake Given the force how far does the car move till it stops?

  29. Free Body Diagram A free-body-diagram is a diagram that represents the object and the forces that act on it.

  30. Ex. Pushing a stalled car What is the net force in this example? F= 275 N + 395 N – 560 N = +110 N Which direction? The + x axis of the coordinate system.

  31. What is the acceleration the car receives? If the mass of the car is 1850 kg then, by Newton’s second law, the acceleration is Since the motion is in 1 dimension Now we solve this equation for a

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