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Transcript
Forces and Newton’s Laws Unit Lecture Notes - Forces Part 1 Introduction to Newton’s Laws The laws codified by Isaac Newton organize our understanding of why objects move (or do not move), (as long as they are not very, very small and not moving too close to the speed of light ) Newton wrote his laws as follows: Law 1 Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it. Law 2 The change of motion is proportional to the motive force impressed and is made in the direction of the right line in which that force is impressed. Law 3 To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal and directed to contrary parts. A. Newton’s Laws explained 1. First Law of Motion - the law of inertia Inertia – resistance to change in state of motion. inertia, more resistance. 1 More Forces and Newton’s Laws Unit If a body has more inertia, more force will be required to “compel” it to a) Speed up b) Slow down c) Change direction Inertia is the same as mass. Inertia is a property of a body, NOT a force that acts upon a body. 2. Second Law of Motion - A net force is the cause of a change in motion. a a force mass ∑F = ma What variables are held constant in each of these plots? 3. Newton’s third Law Forces come in action-reaction pairs. Forces come in interaction pairs. F1,2 = - F2,1 2 Forces and Newton’s Laws Unit B. What are forces? Where do forces come from? 1. There are several different types of forces. The important skill is to sketch a free-body diagram, which consists of: a) The body b) The forces acting upon the body The forces are represented by arrows: http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Drawing-Free-Body-Diagrams 2. Types of Forces Forces come in two general types Contact forces and Non-contact or field forces Contact forces include – a) Normal force – surface support force; perpendicular to the surface 3 Forces and Newton’s Laws Unit b) Friction force – sliding resistance between surfaces in relative motion c) Tension force - pull from rope or similar d) Applied force – direct push or pull e) Drag or air resistance – mechanical resistance to a body’s passage, provided by a low-density medium such as air. Non –contact forces include field forces: a) Gravitational force b) Electromagnetic force And Nuclear forces: a) Strong force b) Weak force These field forces are non-contact, however in the standard model that explains their existence, they are considered to be transmitted by particles called bosons. Gravitational force – graviton Electromagnetic force – photon Strong force – gluon Weak force – W, Z boson 3. Forces come from interactions Recall that forces are always part of an interaction pair. The forces in that pair are equal in magnitude and opposite in direction, but importantly, they Do not act upon the same object. parts”. 4 They act upon “contrary Forces and Newton’s Laws Unit Consider again the free-body diagram: Where did each of the forces arise and what are the pairs? a) Fgrav is the field force of the earth’s gravitational field acting upon the mass. The interaction pair is the mass’s gravitational field acting upon the Earth. They are EQUAL in magnitude. b) FNorm is the support force of the table on the mass. This is the reaction force due to the mass’s force on the table (NOT its weight) The table can do this due to its intermolecular structure. c) Fapp is the direct pull, which has an interaction pair that would be the same force acting on whatever is doing the pulling. That is why it might hurt your hand when you pull something along. d) Ffriction is the force of the ground on the mass due to their relative motion. The interaction pair is the force of the mass on the ground, which would cause the ground to be disturbed. 5 Forces and Newton’s Laws Unit 4. The horse and cart problem: How can a horse move a cart if whenever he pulls on the cart, the cart pulls back on him with an equal and opposite force? C. What is Weight? Weight is not mass. Consider a mass in free-fall: Assume no air M Weight = force due to position in Earth’s gravitational field. According to Newton’s second law: Fnet = ma There is only one force, weight. Therefore: Weight = ma In free- fall, the mass experiences acceleration equal to a = 𝑊𝑒𝑖𝑔ℎ𝑡 𝑚𝑎𝑠𝑠 This ratio is defined as the gravitational field strength ‘g’. Therefore: g = 𝑊𝑒𝑖𝑔ℎ𝑡 𝑚𝑎𝑠𝑠 (no air resistance) Weight is therefore defined as: Weight = mg. (Close to the surface) 6 Forces and Newton’s Laws Unit While mass is a measure of inertia and unaffected by gravitational force, weight is a function of the gravitational field strength at the location of the mass. D. Newton’s Second Law: Constant force and constant acceleration ∑𝐹 = 𝑚𝑎 If the vector sum of the forces acting upon a body is equal to zero (left side of the relation), then the acceleration must always equal zero (right side of the relation). An object is in equilibrium when the vector sum of the forces acting on the object is zero. a = 0 Therefore, the object is either at rest or moving at constant velocity (in straight line at constant speed) 1. Some statements to keep in mind! -A body is in a natural state of motion when it is at rest, or moving at constant velocity. 7 Forces and Newton’s Laws Unit -As a consequence of its inertia, it has a tendency to remain at rest or to move at constant velocity. - A body does not have a tendency to slow down or speed up! - The more inertia (mass) the more force required to move a body from its natural state of motion to a different state. - A change in motion includes speeding up, slowing down or changing direction 2. Solve: Newton’s Second Law. F = ma problems Two canoe paddlers paddle together in their 300-kg canoe. One exerts 225 N, the other exerts 375 N. What is the acceleration of the canoe? Suppose air resistance supplies 50 N of force to a freefalling, 50-kg object. What is the resulting acceleration? E. Friction – force that acts between surfaces to impede their relative sliding motion 1. Static friction – when the surfaces are stationary with respect to each other 8 Forces and Newton’s Laws Unit 2. Kinetic friction – when one or both surfaces are in motion. 3. For a given pair of surfaces, usually static frictional force is greater than kinetic. 4. Frictional force depends on two factors which are characteristics of the system being analyzed: Ff = µFN Where µ = the coefficient of friction, a measure of how “sticky” two surfaces when in contact. Typical coefficients of friction Surface µs µK Rubber tires on 0.80 0.65 0.60 0.40 0.78 0.58 0.15 0.06 dry concrete Rubber tires on wet road Steel on steel, dry Steel on steel with oil Normal shoes on 0.68 concrete 9 Forces and Newton’s Laws Unit Shoes on 0.40 (less than linoleum 0.5 is a slip hazard) Zitzewitz, Paul W., Todd George. Elliott, David G. Haase, Kathleen A. Harper, Michael R. Herzog, Jane Bray. Nelson, Jim Nelson, Charles A. Schuler, and Margaret K. Zorn. Physics: Principles and Problems. New York: Glencoe/McGraw-Hill, 2005. Print. Coefficients of friction can be greater than 1.0 for objects that have some adhesion, such as with tape, sticky surfaces and special tires used in drag racing. FN = the Normal force that acts perpendicular to the surfaces: Normal Force motion Normal force 10 Forces and Newton’s Laws Unit mg 11