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8/10/2019 Chapter 4 Lec Newton
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Newtons Laws
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what have been discussed so far
Everything about kinematics In 1D
In 2D (such as projectile motion)
Circular motion -> later
Chapter 3
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Sir Isaac Newton, English Physicist, 1643-1727
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What are they and what do they
do?
A Force is a pull(an attraction)
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Or, a push (a repulsion)
What are they and what do they
do?
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Forces can also cancel each other out!
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The Meaning of Force
To a layman:
A forceis a push or pull upon an object
To a physics student:
A forceis that which causes the velocity of an
object to change
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Force
It is a vector quantity(with both magnitudeanddirection)
The combined effect of all forceson an objectdetermines its acceleration.
To combine forces means to add vectors, i.e.
Superposition of Forces
Chapter 4
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Principle of Superposition
The sum of the x-components of forces Fxaffects only ax
The sum of the y-components of forces Fyaffects only ay
The sum of the z-components of forces Fzaffects only az
x
y
F1xF2x
F1yF2y
F1F2
1 2F F F
1 2
1 2
22
x x x
y y y
x y
F F F
F F F
F F F
Chapter 4
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SI Unit of Force
Newton (N)
1 N is the required force to accelerate a 1kg object by 1
m/s2, i.e.
21 1 1
mN kg
s
Typical Force Magnitudes
Suns gravitational force on the Earth
Weight of a large blue whaleWeight of a medium-sized apple
Electric attraction between the proton
and the electron in a hydrogen atom
3.5 x 1022N
1.9 x 106
N1 N
8.2 x 10-8N
Chapter 4
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Thought Experiment
If an object sitting on a level surface is given a swiftkick, how will you describe its motion?
The Big Misconception:
The object will start to move but will eventually slow
down or stop because there is no more force to sustain
its motion.
Newtonian Mechanics Explain:
The slowing down of an object is caused by other forces
(i.e. frictional force exerted by the surface on the moving
object).
Chapter 4
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Newtons First Law
0F ma
Consider a body on which NOnet force acts. If the bodyis at rest, it will remain at rest. If the body is moving, it willcontinue to move with constant velocity.
This is also called the Law of Inertia
A constant velocity implies that its acceleration is zero.Hence, the body is in equilibrium.
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The motion of an object does not change unless it is acted upon by a net
force.
If v=0 it remains 0
If v is some value it stays at that value
Another way to say the same thing:
No net force
velocity is constant
acceleration is zero
no change of direction of motion
Newtons First Law
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Law of Inertia
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An airplane is flying from Buffalo airport to O'Hare. Many forces act
on the plane, including weight (gravity), drag (air resistance), the
trust of the engine, and the lift of the wings. At some point during its
trip the velocity of the plane is measured to be constant (which
means its altitude is also constant). At this time, the total (or net)
force on the plane:
1. is pointing upward2. is pointing downward
3. is pointing forward
4. is pointing backward
5. is zero
lift
weight
drag thrust
correct
Newtons First Law
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Newton's first law states that if no net force acts on anobject, then the velocity of the object remains
unchanged. Since at some point during the trip, the
velocity is constant, then the total force on the plane
must be zero, according to Newton's first law.
lift
weight
drag thrustF= ma = m0 = 0
Newtons First Law
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Newtons Second Law
Fa
m
If a NETexternal forceacts on an object, it willcause that object to accelerate in the same direction
as the net force.
The amount of acceleration is given by the force
divided by the objects mass.
F ma
Chapter 4
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Ch t 4
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Newtons Second Law
Fa
m
F ma
Chapter 4
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F = ma
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the bigger the mass, the
greater the inertia, loweracceleration
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Newtons 2ndLaw in Multiple Dimensions
Forces (or its components) in perpendiculardimensions are independent and separable.
Fx = max along the x-axis
Fy = may
Fz = maz
along the y-axis
along the z-axis
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Example #1
What acceleration will result when a 12-N net forceapplied to a 3-kg object? A 6-kg object?
A net force of 16 N causes a mass to accelerate at a
rate of 4 m/s2. Determine the mass.
a
=4 m/s2 ; 2 m/s2
m=4 kg
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Example #2
Three forces act on a particle that moves withunchanging velocity v = (2 m/s)i (7 m/s)j.Two
of the forces are FA= (2N) i +(3 N)jand F
B= (-
5N) i +(8 N)j. What is the third force?
FC=(3 N)i + (-11 N)j
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Defining the Mass
Mass is a quantitative measure of inertia The greater the mass, the more a body resists at
being accelerated
SI Unit kilogram
Gravitational Mass : based on the gravitational interaction of
the earth to an object
1 kg is the mass of a platinum-iridium alloy kept in a vault inParis
Inertial mass: based on the 1N amount of force that gives an
acceleration of 1 m/s2
Chapter 4
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Mass vs. Weight
Massis an inertial property of a body
Does not change with location
Measured in kilograms (SI)
Weightis a force due to local gravitational attraction
exerted by the Earth or some other massive
astronomical object (such as the moon) on the body
Measured in newton May vary with location W mg
Chapter 4
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Newtons Third Law
If one object is exerting a force on a second object,then the second object is also exerting a force back
on the first object. The two forces have exactly the
same magnitude but act in opposite directions.
A B B AF F
Chapter 4
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Types of Forces
Contact Forces Long-range/Non-contact
Normal force
Tension
Frictional force
Air resistance
Spring force
Applied force
Weight
Electrical/Coulomb Force
Magnetic Force
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Interaction of Forces
WEIGHT
FRICTION
APPLIED FORCE
NORMAL
FORCE
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What is the Normal Force?
Comes from the Latin word norma whichmeansperpendicular
When an object exerts a force with a component thatis perpendicular to the surface of another object, that
object deforms and pushes back on the first object
with an opposing force that is perpendicular to the
surfaces in contact.
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Frictional force
When an object exerts a force to a surface ofanother object, that object deforms and
pushes back on the first object with opposing
force that is parallel to the surfaces in contact.
Static friction
Kinetic friction
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Action-Reaction Pairs in Nature
The propulsion of a fish through the water.
The flying motion of birds.
The motion of vehicles.
The propulsion of rockets.
Chapter 4
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Free-body Diagram
1. These are diagrams used to show the relativemagnitudeand directionof all forces acting uponan object, free of its surrounding.
2. The size of the arrow in a free-body diagram isreflective of the magnitude of the force. Itsdirection reveals the direction which the force isacting.
3. Each force arrow in the diagram is labeled toindicate the exact type of force.
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Example
A loaded elevator has a total mass of 2500 kg, andthat it can accelerate upwards or downwards at2.5m/s2.
Find the Tension of the elevator
(a) if it is at rest
(b) if it is accelerating upwards at a = 2.5 m/s2.
(c) if it is accelerating downwards at a = -2.5 m/s2.
Chapter 4
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Example
A loaded elevator with very worn cables has a totalmass of 1800 kg, and the cables can withstand amaximum tension of 28,000 N.
(a) What is the maximum upward acceleration for theelevator if the cables are not to break?
(b) How would the answer differ if the elevator is to betaken to the moon where g = 1.62 m/s2.
Chapter 4
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Example
Two blocks are connected by a heavy rope with a massof 4.00 kg. The upper box has a mass of 6.00 kg and thelower box of mass 5.00 kg. An upward force of 200 N isapplied.
(a) Draw a free-body/force diagram for the upper box,rope, and the lower box.
(b) What is the acceleration of the system?
(c) What is the acceleration of the boxes and rope?
(d) What is the tension at the top of the heavy rope?
Chapter 4
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