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Force and Motion
The Laws of Motion
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Classical Mechanics
Describes the relationship between the motionof objects in our everyday world and the forcesacting on them
Conditions when Classical Mechanics does not
apply very tiny objects (< atomic sizes)
objects moving near the speed of light
Quantum and relativistic mechanics
Kinetics analyzes the cause of motion force
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Sir Isaac Newton
1642 1727 Formulated basic
concepts and laws ofmechanics
Universal Gravitation
Calculus
Light and optics
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Natural characteristicof an object
Tendency tocontinue in motion
Tendency toremain at rest
inertia momentum
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Inertia
The natural tendency of an object toremain at rest.
Measured by its mass
In order to move the object you need aforce (eg push or pull) acting on theobject.
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Momentum
Common meaning:tendency of a body to continue in motion
Physics definition:the quantity to measure the tendency tooppose change of motion
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Momentum
The natural tendency of an object tomaintain uniform motion (constant velocity).
This tendency is dependent on the mass ofthe object and its velocity
Define momentum,
Momentum = mass velocity,
A vector quantity
In order to change the velocity of the objectyou need a force acting on the object.
vmp
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Force
Effect of force - change of velocity
From rest to move increase/ decrease in value change in direction both
Other effect of force - change of shape
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External and Internal Forces
External forceAny force that results from the interaction
between the object and its environmentexample: push, pull, gravitational force, magnetic force
Internal forces Forces that originate within the object itself
They cannot change the objects velocity
example: vibration of atoms
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Forces on an object
Usually think of a force as a push or pull Vector quantity
May be a contact force or a field force (non-contact)
Contact forces result from physical contact betweentwo objects
Field forces act between disconnected objectsAlso called action at a distance
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The forces can be: contact forces field (non-contact) forces
Forces on an object
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Single or many forces
Net effect is due to the net force (sum of allforces)
Forces on an object
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Newtons First Law
An object will remain at rest or moveswith a constant velocity (that is constantin magnitude and direction) unless actedon by a nonzero net force
The net force (also known as resultant force) isdefined as the vector sum of all the external forcesexerted on the object
Newtons First LawAlso known as Law of Inertia
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Newtons First Law
Nonzero net force
No force act on the object
Sum of the forces act on the object is zero
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Newtons First Law
As long as no net force acting on an object An object at rest remains at rest
An object moving with constant velocity continuesmoving with the same velocity
The object are said to be in equilibrium.
If Fnet = 0 thenv = 0
v = constant
or acceleration a = 0
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Newtons First Law
First condition of equilibriumThe net (external) force acting on the object is zero.
0F
1F
2F
4F
3F
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Newtons First Law
The object are in equilibrium if:
It is at rest ( v = 0) static equilibrium.
It is in uniform motion ( v = constant ) dynamic equilibrium
First condition of equilibrium
The net (external) force acting on the object is zero.
0F
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Newtons First Law
First condition of equilibriumThe net (external) force acting on the object is zero.
0F
yx
yx
yx
yx
FFF
FFF
FFFFFF
444
333
222
111
0xF
0yF
and
then
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Force and momentum
Object can change its velocity only whenthere is a force (eg push or pull) acting onthe object.
A force will change the velocity of anobject.
A force can move an object initially at rest
A force can stop a moving object
A force can make object to move faster orslower.
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Force and momentum
Everyday experience: Force depends on mass
Force depends on velocity
Momentum : p = m v
What is the relationship between forcewith momentum?
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Newtons Second Law
The rate of change of momentum of an object isdirectly proportional to the net force acting on it.
F D tnetDp
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Newtons Second Law
Change of momentum Dp
Change of mass Change of velocity
D t
Dp= m D t
Dv + v DmD t
Rate of Change of momentum
F D t
Dpnet
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Newtons Second Law
Assume: no change in mass.
Change in momentum change in velocity only
Rate of change of momentum
D tDp = m D tDv
= m a
Newtons Second Law
Fnet m a
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Units of Force
SI unit of force is a Newton (N)
The force to change 1 kg of mass to
accelerate at 1 m s-1.
2s
m
kg1N1 1
Newtons Second Law
Fnet = m aThis equation is only true if the mass is constant
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Newtons Second Law
If there is change in mass.
Rate of change of momentum
Newtons Second Law
Fnet = m a
D t
Dp
= m D t
Dv
+v
Dm
D t
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Newtons Third Law
If object 1 and object 2 interact, the forceexerted by object 1 on object 2 is equal inmagnitude but opposite in direction to theforce exerted by object 2 on object 1.
Equivalent to saying a single isolated force
cannot exist
12 21 F F
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Newtons Third Law
F12 may be called theactionforce and F21 thereactionforce
Actually, either force can
be the action or thereaction force
The action and reactionforces
act on different objects
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Newtons Law of motion
Summary: First law
Second law
Third law
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Newtons Law of motion
Application:
First law
Particle in equilibrium
Acceleration, a = 0
Velocity, v = 0 or v = constant
Second law
Particle in motion
Acceleration a 0
Third law
What are
the forcesacting on
the object?
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Forces on an object
1. Gravitational Force
2. Normal reaction force
3. Friction4. Tension of string
5. Other external force ( push/ pull)
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Forces on an object
1. Gravitational Force Mutual force of attraction between any
two objects
Expressed by Newtons Law of UniversalGravitation:
2
21g
rmmGF
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The magnitude of the gravitational forceacting on an object of mass mnear theEarths surface is called the weightWof the object
W = m g is a special case of NewtonsSecond Law gis the acceleration due to gravity
Forces on an object
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The acceleration due to gravity gdependsupon location (altitude above the Earth).
Near the Earth, g taken as constant
g = 9.81 m s-1
Direction of g is vertically downward (directedtowards the centre of the Earth).
Gravitational Force
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Forces on an object
2. Normal Reaction forceNormal Reaction Force alwaysexists when two objects are in
contactIt is the reaction of thesurface of the second objectdue to the force (action) by
the first object. (Newtonsthird law)
12
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Normal (Reaction) Force
Normal Reaction Force always existswhen two objects are in contact It is the reaction of the surface of the
second object due to the force (action) bythe first object. (Newtons third law)The direction of Normal Reaction Force isalways perpendicular to the surface
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Normal (Reaction) Force
R
R
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Normal (Reaction) Force
RR
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Forces on an object
3. Friction forceNormal Reaction Force alwaysexists when two objects are in
contact
This is due to theinteractions between the
object and the surface
1
2
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Force of Friction
When an object is in motion (tends tomove) on a surface or through a viscousmedium, there will be a resistance to themotion
This is due to the interactions between theobject and its environment
This is resistance is called friction Static friction (stationary object)
Kinetic friction (moving object)
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Forces of Friction
This is due to theinteractions betweenthe object and itsenvironment
The force ofstaticfriction is generallygreater than the forceofkinetic friction
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Forces of Friction
Friction is proportional tothe normal force
Ffriction = m R m is the coefficient of friction
The direction of thefrictional force is parallelto surface opposite thedirection of motion
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Forces of Friction
The direction of the frictional force isopposite the direction of motion
Friction is proportional to the normal(reaction) force, parallel to surface
Ffriction = m R The coefficient of friction () depends on
the surfaces in contact
The coefficients of friction are nearlyindependent of the area of contact
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Forces of Friction
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Forces on an object
4. Tension forceTension Force always existswhen the object is
connnected by a rope/ string/cable etc
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Tension Force
The force exerted by a rope, string, wire.
The direction is always towards the centre ofthe rope.
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Tension Force
The force exertedby a rope, string,wire.
The direction isalways towards thecentre of the rope.
If pulley is smooth,tension on bothsides are equal inmagnitude
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Tension Force
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Free Body Diagram
Treat the object as a particle (representedby a point).
Treat each object separately.
Only forces acting directly on the objectare included in the free body diagram
Indicate the direction of each force.
If the free body diagram is incorrect, the
solution will likely be incorrect
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Free Body Diagram
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Free Body Diagram
F B d Di
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Free Body Diagrams
Free Body Diagram
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Free Body Diagram Multiple Objects
Draw free diagram separately for each object
Free Body Diagram
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Free Body Diagram Multiple Objects
Draw free diagram separately for each object
A li ti N t L f ti
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Need to identify the forces acting on the
object Weight of object (gravitational force)
Normal (reaction) force
Frictional force Tension of string/ rope
Other external force
Need to draw a free body diagramA rough sketch to show all the forces on the
object
Application Newtons Law of motion
Object in contact
with a surface
Connected objects
A li ti N t L f ti
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Need to find the NET FORCE (addition of
vectors) Resolve vectors into components.
Parallel component
Perpendicular component
Apply the Newton law of motion equationApply separately for each object component
by component
Solve the equations Simultaneous equation
Application Newtons Law of motion
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