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Transcript
Chapter 4 FORCES AND NEWTON’S LAWS OF MOTION Sir Isaac Newton 1642 – 1727 Formulated basic laws of mechanics Discovered Law of Universal Gravitation Invented form of calculus Many observations dealing with light and optics 4.1 The Concepts of Force and Mass • Force is a push or pull; the cause of an acceleration, or a change in an object’s velocity. • Kinds of forces: • 1. contact forces- arise from the physical contact between 2 objects. • Examples: • Frictional Force, Tensional Force, Normal Force, Air Resistance Force, Applied Force Spring Force • e.g. in basketball, the player launches a shot and pushed the ball when he shoot. Kinds of forces • 2. non contact forces are also called action at a distance force because they arise without physical contact between two objects. • e.g. when a skydiver is pulled toward the earth because of the force of gravity. Gravitational Force, Electrical Force, Magnetic Force Classes of Forces Contact and Field forces Forces cause changes in velocity • • • • Force can cause object to: A. start moving B. stop moving C. change direction C A B Fundamental Forces •Gravitational force – Between objects •Electromagnetic forces – Between electric charges •Nuclear force – Between subatomic particles •Weak forces – Arise in certain radioactive decay processes •Note: These are all field forces. Give at least 3 examples of each of the following • 1. force causing an object to start moving • 2. force causing an object to stop moving • 3. force causing an object to change direction. Mass is a property of matter that determines how difficult it is to • accelerate or decelerate an object. It is a scalar quantity. • There are 3 important laws that deal with force and mass and they are called Newton’s Laws of Motion. Inertia and Mass • Inertia is the natural tendency of an object to remain at rest or in motion at a constant speed along a straight line. • Mass of an object is a quantitative measure of inertia. • The larger the mass, the greater is the inertia. • SI unit: kilogram (kg) 4.2 Newton’s First Law of Motion (Law of Inertia) • An object continues in a state of rest or in the state of motion at a constant speed along a straight line, unless compelled to change that state by a net force. • Example: If friction and other opposing forces are absent, a car could travel forever at 60km/hr in a straight line, without using any gas after it has come up to speed. • When an object moves at a constant speed along a straight line, its velocity is constant. More About Mass •Mass is an inherent property of an object. •Mass is independent of the object’s surroundings. •Mass is independent of the method used to measure it. •Mass is a scalar quantity. – Obeys the rules of ordinary arithmetic •The SI unit of mass is kg. Newton’s 1st law indicates that a state of rest (zero velocity) and • a state of constant velocity are completely equivalent, in the sense that neither one requires the application of a net force to sustain it. • Consider a car traveling at a constant velocity, Newton’s FLM tells us that the external force on the car must be equal to zero. Units of mass, acceleration and force System Mass Acceleration Force SI kg m/s2 N= kg.m/s2 Cgs g cm/s2 dyne=g.cm/s2 ft/s2 lb=slug.ft/s2 avoirdupois slug 4.3 Newton’s Second Law of Motion • Newton’s First Law indicates that if no net force acts on an object, then the velocity of the object remains unchanged. • The 2nd law deals with what happens when a net force does act on it. • The 2nd law: The acceleration a, of an object is directly proportional to the net external force F, acting on an object and inversely proportional to the object’s mass, m • a = ΣF= ma or a = ΣF/m Units for Mass, Acceleration and Force System Mass Acceleration Force SI Kilogram (kg) meter/sec2 (m/s2) Newton (N) CGS Gram (g) centimeter/sec2 Dyne (dyn) (cm/s2) BE Slug (sI) foot/sec2 (ft/s2) Pound (lb) Example 3: • An airplane has a mass of 3.1 x 104 kg and take off under the influence of a constant net force of 3.7 x 104 N. What is the net force that acts on the plane’s 78 kg pilot? • Solution: • a = ΣF/m ΣF = ma More About Newton’s Second Law • is the net force – This is the vector sum of all the forces acting on the object. • May also be called the total force, resultant force, or the unbalanced force. •Newton’s Second Law can be expressed in terms of components: ΣFx = m ax ΣFy = m ay ΣFz = m az •Remember that ma is not a force. – The sum of the forces is equated to this product of the mass of the object and its acceleration. Conceptual Challenge • 1. A truck loaded with sand accelerates at 0.5 m/s2 on the highway. If the driving force on the truck remains constant, what happens to the truck’s acceleration if sand leaks at a constant rate from a hole in the truck bed? • 2. Gravity and Rocks. The force of gravity is twice as great as on a 2 kg rock as it is on a 1 kg rock. Why doesn’t the 2 kg rock have a greater free fall acceleration? Gravitational Force •The gravitational force, Fg , is the force that the earth exerts on an object. •This force is directed toward the center of the earth. •From Newton’s Second Law: •Its magnitude is called the weight of the object. Weight = Fg= mg 4.4 The Vector Nature of Newton’s Second Law of Motion • Application of Newton’s 2nd law always involve the net external force which is the vector sum of all the external forces that act on an object. Each component of the net force leads to a corresponding components of the acceleration. • ΣFx= max ΣFy = may Example 2 • A vector force has a magnitude of 720 N and a direction of 380 north of east. Determine the magnitude and direction of the components of the force that point along the north-south line and along the east-west line? Equilibrium, Example •A lamp is suspended from a chain of negligible mass. •The forces acting on the lamp are: – the downward force of gravity – the upward tension in the chain •Applying equilibrium gives ∑F y = 0 → T − Fg = 0 → T = Fg Section 5.7 4.5 Newton’s Third Law of Motion • Whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body. • This law is often called “action-reaction”. Example: The Acceleration Produced by Action Reaction Forces • Suppose that the mass of the spacecraft is ms = 11000 kg and that the mass of the astronaut is ma = 92 kg. Assume that the astronaut exerts a force of P = + 36 N on the spacecraft. Find the acceleration of the spacecraft and the astronaut? Analysis: According to Newton’s 3rd law, when the astronauts applies • The force P = + 36 N to the spacecraft, the spacecraft applies the reaction • force –P = -36N to the astronaut. • Therefore, the spacecraft and the astronaut accelerate in opposite directions. Although the action and reaction forces have the same magnitude, they don’t have the same acceleration because they don’t have the same mass. (smaller mass, larger acceleration) • There is a clever application of Newton’s third law in some rental trailer. • The tow bar connecting the trailer to the rear bumper of a car contains a mechanism that can automatically actuate brakes on the trailer wheels. • When the driver applies the car brakes, the car slows down. Because of inertia, the trailer continues to roll forward and begins pushing against the bumper. In reaction, the bumper pushes back on the tow bar. The reaction force is used by the mechanism in the tow bar to “ push the brake pedal” for the trailer. 4.6 Types of Forces: An Overview • Newton’s law of motion make it clear that forces play a central role in determining the motion of an object. • 3 Fundamental force: • 1. Gravitational force• 2. Strong nuclear force- stability of the nucleus in atom (Chapter 31) • 3. Electroweak force- single force that manifests itself in 2 ways (Chapter 32) •Homework: p 125127, # 1 - 14 4.7 The Gravitational Force Newton’s Law of Universal Gravitation • Objects fall down because of gravity. • Every particle in the universe exerts an attractive force on every other particle. A particle is a piece of matter, small enough in size to be regarded as a mathematical point. For 2 particles that have masses m1 and m2 and are separated by distance r, the force that each exerts on the other hand is directed along the line joining the particles and has a magnitude given by F = G m 1 r m 2 2 • The symbol G denotes the universal gravitational constant, whose value is found experimentally to be • G= 6.673 x 10-11 N.m2/kg2 Example: Gravitational Attraction • What is the magnitude of the gravitational force that acts on earth particle assuming m1 = 12 kg (approximately the mass of a bicycle), m2 = 25 kg, and r = 1.2 m? • Solution: Weight • The weight of an object arises because of the gravitational pull of the earth. • The weight of an object on or above the earth is the gravitational force that the earth exerts on the object. The weight always acts downward, toward the center of the earth. On or above another astronomical body, the weight is the gravitational force exerted on an object by that body. • SI Unit: newton (N) The gravitational force that each uniform sphere of matter exerts On the other is the same as if each sphere were a particle with Its mass concentrated at its center. The earth (mass ME) and The moon (mass MM) approximate such uniform spheres. W =G • • • • M Em r2 W= weight m = mass of the object ME= mass of the earth r = radius Example: The Hubble Space Telescope • The mass of the Hubble Space Telescope is 11600 kg. Determine the weight of the telescope • (a) when it was resting on the earth (b) as it is in its orbit 598 km above the earth’s surface. (Earth’s radius = 6.38 x106m and Earth’s mass = 5.98 x 1024 kg)) The weight of the Hubble telescope decreases as the telescope gets further from the earth. The distance from the center of the earth to The telescope is r. Class work: Do exercises on page 127 • # 18, 19, 21, 23, 25, 27, 29, 31, 33 Relation Between Mass and Weight • Mass is an intrinsic property of matter and does not change as an object is moved from one location to another while • Weight is the gravitational force acting on an object and can vary, depending on how far the object is above the earth’s surface or whether it is located near another body such as the moon. M Em W =G 2 r W = mg • The weight of an object whose mass is m depends on the values for the universal gravitational constant G, the mass ME of the earth and the distance r. These 3 parameters together determine the acceleration g due to gravity (g= 9.8 m/s2). • The g decreases as the distance r increases means that the weight likewise decreases. The mass of the object however, does not depend on these effects and does not change. 4.8 The Normal Force • The normal force FN is one component of the force that a surface exerts on an object with which it is in contact- namely, the component that is perpendicular to the surface. • The normal force is the support force exerted upon an object which is in contact with another stable object. For example, if a book is resting upon a surface, then the surface is exerting an upward force upon the book in order to support the weight of the book. On occasion, a normal force is exerted horizontally between two objects which are in contact with each other. The magnitude of these 2 forces are equal accdg. to Newton’s 3rd law • If other forces in addition to weight W and normal force Fn act in the vertical direction, the magnitudes of the normal force and the weight are no longer equal. Example: Balancing Act • In a circus balancing act, a woman performs a headstand on top of the man’s head. The woman weights 490N, and the man’s head and neck weigh 50N. It is primarily the seventh cervical vertebra in the spine that supports all the weight above the shoulders. What is the normal force that this vertebra exerts on the neck and head of the man (a) before the act • (b) during the act? Fn Solution: x 50N • A) The only forces acting are the FN and 50N weight. These 2 forces must be balance for the man’s neck and shoulder to remain at rest. Therefore, the 7th cervical vertebra exerts a normal force of FN = 50 N (BEFORE THE ACT) • B)W of the 7th vertebrae + weight of the woman (DURING THE ACT) • Fn = 50 N + 490N = 540 N Summary: • 1. The normal force does not necessarily have the same magnitude as the weight of the object. • 2. The value of the normal force depends on what other forces are present. • 3. It also depends on whether the objects in contact are accelerating. In situation that involves accelerating objects, the magnitude of the normal force can be regarded as apparent weight. • Apparent weight is the force that the object exerts on the scale with which it is in contact. • The discrepancies between true weight and apparent weight can be understood by Newton 2nd law. Applying Newton's 2nd law in the vertical direction gives • ΣFy = +Fn – mg = ma When the elevator is not accelerating the true weight registers. The apparent weight is zero if the elevator falls freely. Solving for a normal force then will give us • Fn = mg + ma • • (Fn is the apparent weight and mg is the true weight) • A free body diagram showing the forces acting on the person riding in the elevator. 4.9 Static and Kinetic Frictional Forces • A surface exerts a force on an object with which it is in contact. The component of the force perpendicular to the surface is called the normal force. • The component parallel to the surface is called friction. Static Frictional Force: • The magnitude fs of the static frictional force can have any value from zero up to a maximum value of fsmax, depending on the applied force. In other words, fs ≤ fsMAX. The equality holds only when fs attains its maximum value, which is fsMAX = µsFN. • µ = coefficient of static friction • FN = magnitude of the normal force. Example1 : A Force Needed to Start a Sled Moving • A sled is resting on a horizontal patch of snow, and the coefficient of static friction is µ= 0.350. The sled and its rider have a total mass of 38 kg. What is the magnitude of the maximum horizontal force that can be applied to the sled before it just begin to move? Kinetic Frictional Force • The magnitude fk of the kinetic frictional force is given by fk = µkFn • µk is the coefficient of kinetic friction • Example: A 24 kg crate initially at rest on a horizontal floor requires a 75 N horizontal force to set it in motion. Find the coefficient of static friction between the crate and the floor? 4.10 The Tension Force • Tension is commonly used to mean the tendency of a rope to be pulled apart due to forces that are applied at each end. • Because of tension, a rope transmits a force from one end to the other. When a rope is accelerating, the force is transmitted only if the rope is mass less. • Tension is the force which is transmitted through a string, rope, or wire when it is pulled tight by forces acting at each end. The tensional force is directed along the wire and pulls equally on the objects on either end of the wire. The force T applied at one end of a mass less rope is transmitted undiminished to the other end, even when the rope bends Around a pulley, provided the pulley is also mass less and Friction is absent. 4.11 Equilibrium Applications of Newton’s Law • An object is in equilibrium when it has a zero acceleration. • Questions: • Can an object be in equilibrium if only one force acts on it? Prepare for a Chapter Test • Do exercises on page 125 – Conceptual Questions: • # 1, 4, 6, 7, 8, 17