chapter 4 force; newton’s laws of motion. classical mechanics describes the relationship between...
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Chapter 4Chapter 4
Force; Newton’s Laws of Force; Newton’s Laws of MotionMotion
Classical MechanicsClassical Mechanics
Describes the relationship between Describes the relationship between the motion of objects in our everyday the motion of objects in our everyday world and the forces acting on themworld and the forces acting on them
Conditions when Classical Mechanics Conditions when Classical Mechanics does not applydoes 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
ForcesForces
Usually think of a force as a push or pullUsually think of a force as a push or pull Vector quantityVector quantity May be a May be a contact forcecontact force or a or a field forcefield force
• Contact forces result from physical contact Contact forces result from physical contact between two objects: pushing, pullingbetween 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 objectGravitational force: weight of object
Contact and Field ForcesContact and Field Forces
Force as vectorForce as vector
Magnitude + DirectionMagnitude + Direction Components FComponents Fx, x, FFyy
Units: Newton (N), Units: Newton (N), pound(lb)pound(lb)
1lb=4.45N1lb=4.45N
F
sin
cos
FF
FF
y
x
22
tan
yx
x
y
FFF
F
F
F
yF
xF
x
y
Addition of ForcesAddition of Forces
Tail-to tip methodTail-to tip method
Parallelogram methodParallelogram method
Components methodComponents method
A
BAC
B
A
B
A
B
ExamplesExamples
Parallel forcesParallel forces
FF11=150N, F=150N, F22=100N and 53° to F=100N and 53° to F11
Newton’s First LawNewton’s First Law
An object moves with a velocity that An object moves with a velocity that is constant in magnitude and is constant in magnitude and direction, unless acted on by a direction, unless acted on by a nonzero net forcenonzero net force• The net force is defined as the vector The net force is defined as the vector
sum of all the external forces exerted on sum of all the external forces exerted on the objectthe object
External and Internal ForcesExternal and Internal Forces
External forceExternal force• Any force that results from the Any force that results from the
interaction between the object and its interaction between the object and its environmentenvironment
Internal forcesInternal forces• Forces that originate within the object Forces that originate within the object
itselfitself• They cannot change the object’s They cannot change the object’s
velocityvelocity
InertiaInertia
Is the tendency of an object to Is the tendency of an object to continue in its original motioncontinue in its original motion
MassMass
A measure of the resistance of an A measure of the resistance of an object to changes in its motion due object to changes in its motion due to a forceto a force
Scalar quantityScalar quantity SI units are kgSI units are kg
Condition for EquilibriumCondition for Equilibrium
Net force vanishesNet force vanishes No motionNo motion
0...321 FFFF
0...321 xxxx FFFF
0...321 yyyy FFFF
Newton’s Second LawNewton’s Second Law
The acceleration of an object is The acceleration of an object is directly proportional to the net force directly proportional to the net force acting on it and inversely acting on it and inversely proportional to its mass.proportional to its mass.
• F and a are both vectorsF and a are both vectors
amF
Units of ForceUnits 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 US Customary unit of force is a pound (lb)pound (lb)• 1 N = 0.225 lb1 N = 0.225 lb
2s
mkg1N1
Sir Isaac NewtonSir Isaac Newton
1642 – 17271642 – 1727 Formulated basic Formulated basic
concepts and laws concepts and laws of mechanicsof mechanics
Universal Universal GravitationGravitation
CalculusCalculus Light and opticsLight and optics
WeightWeight
Falling objectFalling object
Weight w=mgWeight w=mg Object on a table?Object on a table?
mgF
WeightWeight
The magnitude of the gravitational The magnitude of the gravitational force acting on an object of mass force acting on an object of mass mm near the Earth’s surface is called the near the Earth’s surface is called the weight weight ww of the object of the object• w = m gw = m g is a special case of Newton’s is a special case of Newton’s
Second LawSecond Law gg is the acceleration due to gravity is the acceleration due to gravity
g g can also be found from the Law of can also be found from the Law of Universal GravitationUniversal Gravitation
More about weightMore about weight
Weight is Weight is notnot an inherent property of an inherent property of an object an object • mass mass isis an inherent property an inherent property
Weight depends upon locationWeight depends upon location
Newton’s Third LawNewton’s Third Law
If object 1 and object 2 interact, the If object 1 and object 2 interact, the force exerted by object 1 on object 2 force exerted by object 1 on object 2 is equal in magnitude but opposite in is equal in magnitude but opposite in direction to the force exerted by direction to the force exerted by object 2 on object 1.object 2 on object 1.•
• Equivalent to saying a single isolated Equivalent to saying a single isolated force cannot existforce cannot exist
12 21F F
Newton’s Third Law cont.Newton’s Third Law cont.
FF1212 may be called the may be called the actionaction force and F force and F2121 the the reactionreaction force force• Actually, either force Actually, either force
can be the action or can be the action or the reaction forcethe reaction force
The action and The action and reaction forces act reaction forces act on on differentdifferent objects objects
Example: Force TableExample: Force Table
Three forces in equilibrium!Three forces in equilibrium!
Find tension in each cable supporting Find tension in each cable supporting the 600N signthe 600N sign
ExamplesExamples
Calculate the acceleration of the boxCalculate the acceleration of the box
A 50 kg box is pulled across a 16m A 50 kg box is pulled across a 16m drivewaydriveway
Projectile Motion(Ch. 5)Projectile Motion(Ch. 5)
Example of motion in 2-dimExample of motion in 2-dim An object may move in both the x An object may move in both the x
and y directions simultaneouslyand y directions simultaneously• It moves in two dimensionsIt moves in two dimensions
The form of two dimensional motion The form of two dimensional motion we will deal with is called we will deal with is called projectile projectile motionmotion
vvo o and and o o
Assumptions of Projectile Assumptions of Projectile MotionMotion
We may ignore air frictionWe may ignore air friction We may ignore the rotation of the We may ignore the rotation of the
earthearth With these assumptions, an object in With these assumptions, an object in
projectile motion will follow a projectile motion will follow a parabolic pathparabolic path
Rules of Projectile MotionRules of Projectile Motion
The horizontal motion (x) and vertical of The horizontal motion (x) and vertical of motion (y) are completely independent of motion (y) are completely independent of each othereach other
The x-direction is uniform motionThe x-direction is uniform motion• aaxx = 0 = 0
The y-direction is free fallThe y-direction is free fall• aayy = -g = -g
The initial velocity can be broken down The initial velocity can be broken down into its x- and y-componentsinto its x- and y-components• cos sinOx O O Oy O Ov v v v
Projectile MotionProjectile Motion
Projectile Motion at Various Projectile Motion at Various Initial AnglesInitial Angles
Complementary Complementary values of the values of the initial angle result initial angle result in the same rangein the same range• The heights will be The heights will be
differentdifferent The maximum The maximum
range occurs at a range occurs at a projection angle projection angle of 45of 45oo
Some Details About the RulesSome Details About the Rules
Horizontal motion Horizontal motion • vvx x =v=vxo xo =v=vo o coscosoo
• x = xx = xoo+v+vxoxott
This is the only operative equation in the x-This is the only operative equation in the x-direction since there is uniform velocity in direction since there is uniform velocity in that directionthat direction
constantvcosvv xooxo
More Details About the RulesMore Details About the Rules
Vertical motion-- free fall problemVertical motion-- free fall problem• vvyy=v=voosinsinoo-gt-gt
• y=y=yoo+ (v+ (voosinsinoo)t-(1/2)gt)t-(1/2)gt22
• the positive direction as upwardthe positive direction as upward• uniformly accelerated motion, so the uniformly accelerated motion, so the
motion equations all holdmotion equations all hold
ooyo sinvv
Velocity of the ProjectileVelocity of the Projectile
The velocity of the projectile at any The velocity of the projectile at any point of its motion is the vector sum point of its motion is the vector sum of its x and y components at that of its x and y components at that pointpoint
• Remember to be careful about the Remember to be careful about the angle’s quadrantangle’s quadrant
2 2 1tan yx y
x
vv v v and
v
ExampleExample
Superman hits a home run with Superman hits a home run with vvoo=15m/s and =15m/s and oo=60°=60°
Some useful resultsSome useful results
TrajectoryTrajectory
Maximum HeightMaximum Height
RangeRange
222 cos2
)(tan xv
gxy
ooo
g
vh oo
2
sin 22
g
vR oo
)2sin(2
ExampleExample
A daredevil jumps a canyon 15m wide A daredevil jumps a canyon 15m wide by driving a motorcycle up an incline by driving a motorcycle up an incline sloped at an angle of 37° with the sloped at an angle of 37° with the horizontal. What minimum speed horizontal. What minimum speed must she have in order to clear the must she have in order to clear the canyon? How long will she be in the canyon? How long will she be in the air?air?
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