Chapter 3 Newton’s Laws Newton’s Laws

Classical Mechanics Describes the relationship between the motion of objects in our everyday world and the forces acting on them Describes the relationship between the motion of objects in our everyday world and the forces acting on them Conditions when Classical Mechanics does not apply Conditions when Classical Mechanics does not apply very tiny objects (< atomic sizes)very tiny objects (< atomic sizes) objects moving near the speed of lightobjects moving near the speed of light

Forces Usually think of a force as a push or pull Usually think of a force as a push or pull Vector quantity Vector quantity May be a contact force or a field force May be a contact force or a field force Contact forces result from physical contact between two objects: pushing, pullingContact forces result from physical contact between two objects: pushing, pulling Field forces act between disconnected objectsField forces act between disconnected objects Also called “action at a distance” Also called “action at a distance” Gravitational force: weight of object Gravitational force: weight of object

Contact and Field Forces

Force as vector Magnitude + Direction Magnitude + Direction Components F x, F y Components F x, F y Units: Newton (N), pound(lb) Units: Newton (N), pound(lb) 1lb=4.45N 1lb=4.45N

Addition of Forces Graphical method Graphical method Components method Components method

Newton’s First Law An object moves with a velocity that is constant in magnitude and direction, unless acted on by a nonzero net force An object moves with a velocity that is constant in magnitude and direction, unless acted on by a nonzero net force The net force is defined as the vector sum of all the external forces exerted on the objectThe net force is defined as the vector sum of all the external forces exerted on the object

External and Internal Forces External force External force Any force that results from the interaction between the object and its environmentAny force that results from the interaction between the object and its environment Internal forces Internal forces Forces that originate within the object itselfForces that originate within the object itself They cannot change the object’s velocityThey cannot change the object’s velocity

Inertia Is the property of a material to resist changes in motion. Is the property of a material to resist changes in motion. Is the tendency of an object to continue in its original motionIs the tendency of an object to continue in its original motion

Mass A measure of the resistance of an object to changes in its motion due to a force A measure of the resistance of an object to changes in its motion due to a force Scalar quantity Scalar quantity SI units: kg SI units: kg

Condition for Equilibrium Net force vanishes Net force vanishes No motion No motion

Newton’s Second Law The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. F and a are both vectorsF and a are both vectors

Units of Force SI unit of force is a Newton (N) SI unit of force is a Newton (N) US Customary unit of force is a pound (lb) US Customary unit of force is a pound (lb) 1 N = lb1 N = lb

Sir Isaac Newton 1642 – – 1727 Formulated basic concepts and laws of mechanics Formulated basic concepts and laws of mechanics Universal Gravitation Universal Gravitation Calculus Calculus Light and optics Light and optics

Newton’s Third Law If object 1 and object 2 interact, the force exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force exerted by object 2 on object 1. If object 1 and object 2 interact, the force exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force exerted by object 2 on object 1. Equivalent to saying a single isolated force cannot existEquivalent to saying a single isolated force cannot exist

Newton’s Third Law cont. F 12 may be called the action force and F 21 the reaction force F 12 may be called the action force and F 21 the reaction force Actually, either force can be the action or the reaction forceActually, either force can be the action or the reaction force The action and reaction forces act on different objects The action and reaction forces act on different objects

Weight vs Mass Weight is not mass but they are related Weight is not mass but they are related Weight is a force Weight is a force Consider a Falling object Consider a Falling object Weight w=mg Weight w=mg Object on a table? Object on a table?

Weight The magnitude of the gravitational force acting on an object of mass m near the Earth’s surface is called the weight w of the object The magnitude of the gravitational force acting on an object of mass m near the Earth’s surface is called the weight w of the object w = m g is a special case of Newton’s Second Laww = m g is a special case of Newton’s Second Law g is the acceleration due to gravity g is the acceleration due to gravity g can also be found from the Law of Universal Gravitation g can also be found from the Law of Universal Gravitation

More about weight Weight is not an inherent property of an object Weight is not an inherent property of an object mass is an inherent propertymass is an inherent property Weight depends upon location Weight depends upon location

Using Second Law F=ma F=ma Net Force Net Force

Method Isolate object of interest Isolate object of interest Draw picture, show all forces Draw picture, show all forces Decide if the object is accelerating Decide if the object is accelerating Choose appropriate coordinate system Choose appropriate coordinate system find force components find force components Use F=ma Use F=ma

Example (prob. 23) 1200 kg car going 20 m/s collides head on with a tree and stops in 2.0m. What is the average stopping force?What is the average stopping force?

Example (Atwood’s Machine) Two masses, 2.0 kg and 2.05 kg, … 0.5 m above ground. Find acceleration and the time the 2.05 kg mass takes to reach the ground.

Example Force of 10 N gives a mass acceleration of 1 m/s². How large a force is needed to accelerate to 0.25 m/s²?How large a force is needed to accelerate to 0.25 m/s²? If the mass is increased by a factor of two, how large of a force will give an acceleration of 2 m/s²?If the mass is increased by a factor of two, how large of a force will give an acceleration of 2 m/s²?

Example Two masses m 1 (5kg) and m 2 (10kg) are connected by a rope on a table top. Friction forces on m 1 and m 2 are 15N and 30N respectively. A pulling force P acts on m 2 at 45° above horizontal and accelerates the system with 0.2m/s² acc. Find tension in the ropeFind tension in the rope Force PForce P

Newton’s law of Gravitation Mutual force of attraction between any two objects Mutual force of attraction between any two objects Expressed by Newton’s Law of Universal Gravitation: Expressed by Newton’s Law of Universal Gravitation:

Universal Gravitation, 2 G is the constant of universal gravitational G is the constant of universal gravitational G = x N m² /kg² G = x N m² /kg² This is an example of an inverse square law This is an example of an inverse square law

Universal Gravitation, 3 The gravitational force exerted by a uniform sphere on a particle outside the sphere is the same as the force exerted if the entire mass of the sphere were concentrated on its center The gravitational force exerted by a uniform sphere on a particle outside the sphere is the same as the force exerted if the entire mass of the sphere were concentrated on its center This is called Gauss’ LawThis is called Gauss’ Law

Gravitation Constant Determined experimentally Determined experimentally Henry Cavendish Henry Cavendish The light beam and mirror serve to amplify the motion The light beam and mirror serve to amplify the motion

Applications of Universal Gravitation Weighing the Earth Weighing the Earth

Applications of Universal Gravitation Acceleration due to gravity Acceleration due to gravity g will vary with altitude g will vary with altitude

Apparent Weight The weight of object in an accelerating frame. The weight of object in an accelerating frame. Consider inside a elevator Consider inside a elevator Why do we need 1 st law? Why do we need 1 st law?

Example An object weighing 500 N is uniformly accelerated upward during a short elevator ride. If the object’s apparent weight was 625 N during the trip, how long did the ride take to move 40 m upward?