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Phy 201: General Physics I Chapter 4: Forces & Newton’s Laws of Motion Lecture Notes Newton’s 1st Law Every object continues in its state of rest, or of motion unless compelled to change that state by forces impressed upon it. • Also known as the “Law of Inertia” • Key Points: – When an object is moving in uniform linear motion it has no net force acting on it – When there is no net force acting on an object, it will stay at rest or maintain its constant speed in a straight line • This property of matter to maintain uniform motion is called inertia F=0 a = 0 {v = constant} • Stated a simpler way: Nature is lazy! {i.e. matter resists changes in motion} Newton’s 2nd Law • • When a net force is exerted on an object its velocity will change: dv F=F F F ... 1 2 3 dt The time rate of change of motion (acceleration) is related to: – Proportional to the size of the net force – Inversely proportional to the mass of the object (i.e. its inertia) • The relationship between them is F 1 a= = Fx xˆ + Fyyˆ or F = ma= m ax xˆ + ayyˆ m m • The direction of a will always correspond to the direction of F Newton’s 3rd Law When an object exerts a force on a second object, the second object exerts an equal but oppositely directed force on the first object Body 1 where: F2 on 1 F1 on 2 Body 2 F2 on 1 F1 on 2 Consequences: • Forces always occur in action-reaction pairs (never by themselves) • Each force in an action-reaction pair acts on a different object Important: • Newton’s 3rd law identifies the forces produced by interactions between bodies • Newton’s 2nd law defines the accelerations that each object undergoes Free-Body Diagrams • Simplified drawing of a body with only the forces acting on it specified • The forces are drawn as vectors • Free-Body diagrams facilitate the application of Newton’s 2nd Law Examples: Joey getting slapped Joey standing on a floor while standing on a floor Joey in “Free Fall” Joey W Ffloor Joey W Ffloor Joey W Fslap Types of Forces In our world, forces can be categorized as one of 2 types: • Non-Contact: force is exerted over a distance of space with out direct contact (a.k.a. “action-at-a-distance” forces) • Contact: forces is exerted due to direct contact (Note: at the microscopic level, ALL forces are non-contact) • In either case, Newton’s 3rd law still applies to the forces present Examples of each type of force: Non-Contact: • Gravitational • Electric • Magnetic Contact: • Normal • Frictional • Tension Mass vs. Weight • The “weight” of an object is the gravitational force exerted on it by the gravitational attraction between the object and its environment: FG=maG=maGyˆ FG =m aG FG=maG • On the surface of the Earth, the gravitational force is referred to as weight: FG = W = (-mg)yˆ FG = W = mg • Mass is a measure of an object’s inertia (measured in kg) – Independent of object location • Weight is the effect of gravity on an object’s mass (measured in N) – Determined by the local gravitational acceleration surrounding the object Notes: • Mass is a measure of an object’s inertia (measured in kg) – Independent of object location • Weight is the effect of gravity on an object’s mass (measured in N) – Determined by the local gravitational acceleration surrounding the object Normal Force • The “support” force between 2 surfaces in contact • Direction is always perpendicular (or normal) to the plane of the area of contact Example: the force of floor that supports your weight Consider standing on a scale on the floor of an elevator. The reading of the scale is equal to the normal force it exerts on you: Task: Construct free body diagrams for the scale: 1. 2. 3. 4. At rest Constant velocity Accelerating upward Accelerating downward Examples of Normal Force Surface Frictional Forces • When an object moves or tends to move along a surface, there is an interaction between the microscopic contact points on the 2 surfaces. This interaction results in a frictional force, that is – parallel to the surface – opposite to the direction of the motion • There are 2 types of surface friction: – Static (sticking) – Kinetic (sliding) Static Friction • Static (or sticking) friction ( fs ) is the frictional force exerted when the object tends to move, but the external force is not yet strong enough to actually move the object. • Increasing the applied force, the static frictional force increases as well (so the net force is zero) . The force just before breakaway is the maximum static frictional force. • The direction of the static friction force is always in opposition to the external forces(s) acting on the body • The magnitude of the maximum static friction force is: fsmax =μmax FN s Where: – μmax is the coefficient (maximum) of static friction s – FN is the normal force Kinetic Friction • Kinetic frictional force ( fk ) is the frictional force exerted by the surface on an object that is moving along the surface • Kinetic frictional force: – always opposes the direction of the motion – the direction is along the surface (parallel to the surface) • The magnitude of the kinetic frictional force depends only on the normal force and the properties of the 2 surfaces in contact fk =μk FN Where: – mk is the coefficient of kinetic friction – FN is the normal force Notes: – Kinetic friction is independent to the rate of travel of the sliding body – Kinetic friction is independent to the surface area of contact Tension Force • Force applied through a rope or cable • When the rope or cable is mass-less (negligible compared to the bodies it is attached to) it can be treated as a connection between 2 bodies – No mass means no force needed to accelerate rope – Force of pull transfers unchanged along the rope – Action force at one end is the same as the Reaction force at the other end • When attached to a pulley the tension force can be used to change the direction of force acting on a body • Calculation of a tension force is usually an intermediate step to connecting the free-body diagrams between 2 attached objects Tension Applications M2 • With Pulley (flat surface): M1 • Inclined Plane: q M1 • Atwood Machine: M1 M2 Sir Isaac Newton (1642-1727) • Greatest scientific mind of the late 17th century • Invented the “calculus” (independently but simultaneously with Gottfried Wilhelm Leibnitz) • Among his accomplishments included: – A Particle Theory Light & Optics – A Theory of Heat & Cooling • Established 3 Laws of Motion • Proposed the Law of Universal Gravitation (to settle a parlor bet proposed by Christopher Wren!!) – The competition was actually between Edward Haley & Robert Hooke – This theory successfully explained planetary motion and elliptical orbits “If I have seen further it is by standing on the shoulders of giants.”