2-Dimensional Motion & Newton Laws of Motion

2-Dimensional Motion & Newton Laws of Motion (sections 5.1-5.4)

Kinematics: Assumptions, Definitions and Logical Conclusions What have we done so far? • Defined displacement, velocity, acceleration (also position, distance, speed)... • Defined scalers (like speed) and vectors (like velocity) • Laid out assumptions about free-fall • noticed that 2-dimensional motion is really just two, simultaneous, 1-dimensional motions. Used this to shoot a monkey, range out a small cannon, etc. This wasn’t physics. This was preparing the language needed to talk about physics.

Newton’s Laws How can we consistently and generally describe the way objects move and interact?

Newton in a 1702 portrait by Godfrey Kneller Newton in a 1689 portrait by Godfrey Kneller Isaac Newton 1643-1727

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me. Nature and nature's laws lay hid in night;God said "Let Newton be" and all was light. Newton’s epitaph, Alexander Pope from a memoir by Newton

Force Force: push or pull Force is a vector – it has magnitude and direction

Mass Mass is the measure of how hard it is to change an object’s velocity. Mass can also be thought of as a measure of the quantity of matter in an object. 7

Newton’s First Law of Motion If you stop pushing an object, does it stop moving? Only if there is friction! In the absence of any net external force, an object at rest will remain at rest. In the absence of any net external force a moving object will keep moving at a constant speed in a straight line. This is also known as the Law of Inertia.

Inertia

Newton’s First Law A hockey puck slides on ice at constant velocity. What is the net force acting on the puck? a) more than its weight b) equal to its weight c) less than its weight but more than zero d) depends on the speed of the puck e) zero

Newton’s First Law a) more than its weight b) equal to its weight c) less than its weight but more than zero d) depends on the speed of the puck e) zero A hockey puck slides on ice at constant velocity. What is the net force acting on the puck? The puck is moving at a constant velocity, and therefore it is not accelerating. Thus, there must be no net force acting on the puck. Follow-up: Are there any forces acting on the puck? What are they?

Newton’s First Law a) a net force acted on it b) no, or insufficient, net force acted on it c) it remained at rest d) it did not move, but only seemed to e) gravity briefly stopped acting on it You put your book on the bus seat next to you. When the bus stops suddenly, the book slides forward off the seat. Why?

Newton’s First Law a) a net force acted on it b) no, or insufficient, net force acted on it c) it remained at rest d) it did not move, but only seemed to e) gravity briefly stopped acting on it You put your book on the bus seat next to you. When the bus stops suddenly, the book slides forward off the seat. Why? The book was initially moving forward (because it was on a moving bus). When the bus stopped, the book continued moving forward, which was its initial state ofmotion, and therefore it slid forward off the seat.

Calibrating force Two equal weights exert twice the force of one; this can be used for calibration of a spring:

Experiment: Acceleration vs Force Now that we have a calibrated spring, we can do more experiments. Acceleration is proportional to force:

Experiment: Acceleration vs Mass Acceleration is inversely proportional to mass:

Newton’s Second Law of Motion Acceleration is proportional to force: Acceleration is inversely proportional to mass: Combining these two observations gives Or, more familiarly,

Newton’s Second Law of Motion An object may have several forces acting on it; the acceleration is due to the net force: SI unit for force Newton is defined using this equation as: 1 N is the force required to give a mass of 1 kg an acceleration of 1 m/s2

Units of force: Newtons

The weight of an object is the force acting on it due to gravity Weight: W = Fg = ma = mg vertically downwards Since , the weight of an object in Newtons is approximately 10 x its mass in kg adult human 70 kg 700 N ~ 160 lbs. Force of Gravity Weight is not mass! WHERE? There is no “conversion” from kg to pounds! (Unless you specify what planet you are assuming)

In order to change the velocity of an object – magnitude or direction – a net force is required. (I) (II) Newton’s First and Second Laws

In order to change the velocity of an object – magnitude or direction – a net force is required. (I) (II) Inertial Reference Frames Newton’s First and Second Laws do not work in an accelerating frame of reference An inertial reference frame is one in which the first and second laws are true. Accelerating reference frames are not inertial. Is the earth an inertial reference frame? No, but acceleration due to earth’s rotation around Its axis (0.034 m/s2), and due to earth’s rotation around sun (smaller) are negligible compared to g; so approximately yes.

Analyzing the forces in a system Free-body diagrams: A free-body diagram shows every force acting on an object. • Sketch the forces • Isolate the object of interest • Choose a convenient coordinate system • Resolve the forces into components • Apply Newton’s second law to each coordinate direction

Free-body Diagram Example of a free-body diagram:

Newton’s First Law a) there is a net force but the book has too much inertia b) there are no forces acting on it at all c) it does move, but too slowly to be seen d) there is no net force on the book e) there is a net force, but the book is too heavy to move A book is lying at rest on a table. The book will remain there at rest because:

Newton’s First Law a) there is a net force but the book has too much inertia b) there are no forces acting on it at all c) it does move, but too slowly to be seen d) there is no net force on the book e) there is a net force, but the book is too heavy to move A book is lying at rest on a table. The book will remain there at rest because: There are forces acting on the book, but the only forces acting are in the y-direction. Gravity acts downward, but the table exerts an upward force that is equally strong, so the two forces cancel, leaving no net force.

Newton’s Third Law of Motion Forces always come in pairs, acting on different objects: If object 1 exerts a force on object 2, then object 2 exerts a force – on object 1. These forces are called action-reaction pairs.

Some action-reaction pairs 28

Newton’s 3rd: F12 = - F21 action-reaction pairs are equal and opposite, but they act on different bodies Action-reaction pair? a) Yes b) No

Newton’s Third Law of Motion Although the forces are the same, the accelerations will not be unless the objects have the same mass. Q: When skydiving, do you exert a force on the earth? Does the earth accelerate towards you? Is the magnitude of the acceleration of the earth the same as the magnitude of your acceleration?

Newton’s Third Law of Motion Contact forces: The force exerted by one box on the other is different depending on which one you push. Assume the mass of the two objects scales with size, and the forces pictured are the same. In which case is the magnitude of the force of box 1 on box 2 larger? 32

Truck on Frozen Lake a) it is too heavy, so it just sits there b) it moves backward at constant speed c) it accelerates backward d) it moves forward at constant speed e) it accelerates forward A very large truck sits on a frozen lake. Assume there is no friction between the tires and the ice. A fly suddenly smashes against the front window. What will happen to the truck?

Truck on Frozen Lake a) it is too heavy, so it just sits there b) it moves backward at constant speed c) it continuously accelerates backward d) it moves forward at constant speed e) it continuously accelerates forward A very large truck sits on a frozen lake. Assume there is no friction between the tires and the ice. A fly suddenly smashes against the front window. What will happen to the truck? When the fly hit the truck, it exerted a force on the truck (only for a fraction of a second). So, in this time period, the truck accelerated (backward) up to some speed. After the fly was squashed, it no longer exerted a force, and the truck simply continued moving at constant speed. Follow-up: What if the fly takes off, with the same speed in the direction from whence it came? 34

A 71-kg parent and a 19-kg child meet at the center of an ice rink. They place their hands together and push. (a) Is the force experienced by the child more than, less than, or the same as the force experienced by the parent? (b) Is the acceleration of the child more than, less than, or the same as the acceleration of the parent? Explain. (c) If the acceleration of the child is 2.6 m/s2 in magnitude, what is the magnitude of the parent’s acceleration? 35

On vacation, your 1300-kg car pulls a 540-kg trailer away from a stoplight with an acceleration of 1.9 m/s2 (a) What is the net force exerted by the car on the trailer? (b) What force does the trailer exert on the car? (c) What is the net force acting on the car? 37

2-Dimensional Motion & Newton Laws of Motion