Chapter 4 Force; Newton’s Laws of Motion

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  x y

Addition of Forces Tail-to tip method Tail-to tip method Parallelogram method Parallelogram method Components method Components method

Examples Parallel forces Parallel forces F 1 =150N, F 2 =100N and 53° to F 1 F 1 =150N, F 2 =100N and 53° to F 1

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 tendency of an object to continue in its original motion Is 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 are kg SI units are 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

Weight Falling object 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

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

Example: Force Table Three forces in equilibrium! Find tension in each cable supporting the 600N sign

Examples Calculate the acceleration of the box Calculate the acceleration of the box A 50 kg box is pulled across a 16m driveway A 50 kg box is pulled across a 16m driveway

Projectile Motion(Ch. 5) Example of motion in 2-dim Example of motion in 2-dim An object may move in both the x and y directions simultaneously An object may move in both the x and y directions simultaneously It moves in two dimensionsIt moves in two dimensions The form of two dimensional motion we will deal with is called projectile motion The form of two dimensional motion we will deal with is called projectile motion v o and  o v o and  o

Assumptions of Projectile Motion We may ignore air friction We may ignore air friction We may ignore the rotation of the earth We may ignore the rotation of the earth With these assumptions, an object in projectile motion will follow a parabolic path With these assumptions, an object in projectile motion will follow a parabolic path

Rules of Projectile Motion The horizontal motion (x) and vertical of motion (y) are completely independent of each other The horizontal motion (x) and vertical of motion (y) are completely independent of each other The x-direction is uniform motion The x-direction is uniform motion a x = 0a x = 0 The y-direction is free fall The y-direction is free fall a y = -ga y = -g The initial velocity can be broken down into its x- and y-components The initial velocity can be broken down into its x- and y-components

Projectile Motion

Projectile Motion at Various Initial Angles Complementary values of the initial angle result in the same range Complementary values of the initial angle result in the same range The heights will be differentThe heights will be different The maximum range occurs at a projection angle of 45 o The maximum range occurs at a projection angle of 45 o

Some Details About the Rules Horizontal motion Horizontal motion v x =v xo =v o cos ov x =v xo =v o cos o x = x o +v xo tx = x o +v xo t This is the only operative equation in the x- direction since there is uniform velocity in that direction This is the only operative equation in the x- direction since there is uniform velocity in that direction

More Details About the Rules Vertical motion-- free fall problem Vertical motion-- free fall problem v y =v o sin o -gt v y =v o sin o -gt y= o + (v o sin o )t-(1/2)gt 2 y=y o + (v o sin o )t-(1/2)gt 2 the positive direction as upward the positive direction as upward uniformly accelerated motion, so the motion equations all holduniformly accelerated motion, so the motion equations all hold

Velocity of the Projectile The velocity of the projectile at any point of its motion is the vector sum of its x and y components at that point The velocity of the projectile at any point of its motion is the vector sum of its x and y components at that point Remember to be careful about the angle’s quadrantRemember to be careful about the angle’s quadrant

Example Superman hits a home run with v o =15m/s and  o =60° Superman hits a home run with v o =15m/s and  o =60°

Some useful results Trajectory Trajectory Maximum Height Maximum Height Range Range

Example A daredevil jumps a canyon 15m wide by driving a motorcycle up an incline sloped at an angle of 37° with the horizontal. What minimum speed must she have in order to clear the canyon? How long will she be in the air?