Download Forces - Chabot College

Chapter 4
Newton’s Laws of
Motion
PowerPoint® Lectures for
University Physics, Thirteenth Edition
– Hugh D. Young and Roger A. Freedman
Copyright © 2012 Pearson Education Inc.
Goals for Chapter 4
• To understand the meaning of force in physics
• To view force as a vector and learn how to
combine forces
• To understand the behavior of a body on which
the forces “balance”:
• Newton’s First Law of Motion:
if there is no NET force on an object it will
remain in the same state of motion
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Goals for Chapter 4
• To learn the relationship between mass,
acceleration, and force:
Newton’s Second Law of Motion: F = ma
a = F/m
• To relate mass (quantity of matter) and weight
(force on that matter from gravity)
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Goals for Chapter 4
• To see the effect of action-reaction pairs:
Newton’s Third Law of Motion
Force on object a from object b
is EQUAL in magnitude
(and opposite in direction) to
Force on object b from object a
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What are some properties of a force?
• A force is a push or a pull
• A force is an interaction between two objects, or
between an object and its environment
• A force is a VECTOR quantity, with magnitude and
direction.
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There are four common types of forces
• #1: The normal force:
When an object pushes on a surface, the surface
pushes back on the object perpendicular to the
surface.
• This is a contact force.
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There are four common types of forces
• #2: Friction force:
This force occurs when a surface resists sliding
of an object and is parallel to the surface.
• Friction is a contact force.
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There are four common types of forces II
• #3: Tension force:
A pulling force exerted on an object by a rope or
cord.
• This is a contact force.
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There are four common types of forces II
• #4: Weight:
The pull of gravity on an object.
• This is a long-range force, not a contact force, and is
also a “field” force.
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What are the magnitudes of common forces?
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Drawing force vectors
• Use a vector arrow to indicate the magnitude
and direction of the force.
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Superposition of forces
• Several forces acting at a point on an object have
the same effect as their vector sum acting at the
same point.
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Decomposing a force into its component vectors
• Choose coordinate system with perpendicular x and y axes.
• Fx and Fy are components of force along axes.
• Use trigonometry to find force components.
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Notation for the vector sum
• Vector sum of all forces on an object is resultant of forces
• The net force.
R= F1+F2 +F3+ = F
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Superposition of forces
• Force vectors are added using components:
Rx = F1x + F2x + F3x + …
Ry = F1y + F2y + F3y + …
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Newton’s First Law
“An object at rest tends
to stay at rest, an object
in motion tends to stay
in uniform motion.”
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Newton’s First Law
Mathematically,
“A body acted on by
zero net force moves
with constant velocity
and zero
acceleration.”
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Newton’s First Law II
• In part (a) net force acts,
causing acceleration.
• In part (b) net force = 0
resulting in no
acceleration.
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When is Newton’s first law valid?
• You are on roller skates
in a stopped BART
car…
• The car starts to
accelerate forwards.
• What happens to you?
• If no net force acts on
you, you maintain a
constant velocity (0!)
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When is Newton’s first law valid?
• You are on roller skates
in a moving BART car…
• The car starts to slow accelerate backwards.
• What happens to you?
• If no net force acts on
you, you maintain a
constant velocity
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When is Newton’s first law valid?
• If no net force acts on you,
you maintains a constant
velocity (a vector!)
• But as seen in the noninertial frame of the
accelerating vehicle, it
appears that you are being
pushed to the outside!
• Newton’s first law is valid
only in non-accelerating
inertial frames.
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Newton’s Second Law
•
If the net force on an object is zero, the object will not accelerate.
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Newton’s Second Law
•
If the net force on an object is not zero, it causes the object to accelerate.
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Newton’s Second Law
•
If the net force on an object is not zero, it causes the object to accelerate.
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An object undergoing uniform circular motion
• An object in uniform
circular motion is
accelerated toward
the center of the
circle.
• So net force on
object must point
toward the center of
the circle.
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Force and acceleration
• Magnitude of acceleration
of an object is directly
proportional to the net force
 F on the object.
• | a | = F/m
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Mass and acceleration
• Magnitude of acceleration
of an object is
inversely proportional
to object’s mass if net
force remains fixed.
• |a | = F/m
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Newton’s second law of motion
• The acceleration of an object is directly
proportional to the net force acting on it, and
inversely proportional to the mass of the object.
F  ma
• The SI unit for force is the newton (N).
1 N = 1 kg·m/s2
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Using Newton’s Second Law Ex. 4.4
• Worker pushes box of mass 40 kg, with constant
force of 20N. What is acceleration?
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Using Newton’s Second Law Ex. 4.4
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Using Newton’s Second Law II—Example 4.5
• Shove bottle of mass 0.45 kg at initial speed of 2.8
m/s a distance of 1 m before it stops. What is the
magnitude and direction of force on bottle?
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Using Newton’s Second Law II—Example 4.5
• Shove bottle of mass 0.45 kg at initial speed of 2.8
m/s a distance of 1 m before it stops. What is the
magnitude and direction of force on bottle?
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Using Newton’s Second Law II—Example 4.5
• We know:
• Displacement in x = +1.0 m
• Initial x velocity = +2.8 m/s
• Final x velocity = 0 m/s
• THREE THINGS!
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Using Newton’s Second Law II—Example 4.5
• vf2 = vi2 + 2aDx
• So…
• a = (vf2 - vi2)/2Dx
+x
• a = - 3.9 m/s2
•
NOTE
a
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points in the direction of
f
!
Systems of units (Table 4.2)
• In MKS (SI) system
• force is measured in Newtons, distance in meters,
mass in kilograms.
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Systems of units (Table 4.2)
• In British system, force is measured in pounds, distance in
feet, mass in slugs.
• In cgs system, force in dynes, distance in centimeters, and
mass is in grams.
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Mass and weight
• The weight of an object (on Earth) is
gravitational force that Earth exerts on it.
• The weight W of an object of mass m is
W = mg
• The value of g depends on altitude.
• On other planets, g will have an entirely
different value than on the earth.
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A euro in free fall
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A bit coin in free fall?
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Don’t confuse mass and weight!
• Keep in mind that the Newton is a unit of
force, not mass.
• A 2.49 x 104 N Rolls-Royce Phantom traveling
in +x direction makes an emergency stop; the
x component of the net force acting on its -1.83
x 104 N. What is its acceleration?
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Newton’s Third Law
• If you exert a force on a body, the body always
exerts a force (the “reaction”) back upon you.
• A force and its reaction
force have the same
magnitude but
opposite directions.
• These forces act on
different bodies.
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Applying Newton’s Third Law: Objects at rest
• An apple rests on a table. Identify the forces that act
on it and the action-reaction pairs.
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Applying Newton’s Third Law: Objects at rest
• An apple rests on a table. Identify the forces that act
on it and the action-reaction pairs.
Copyright © 2012 Pearson Education Inc.
Applying Newton’s Third Law: Objects at rest
• An apple rests on a table. Identify the forces that act
on it and the action-reaction pairs.
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Applying Newton’s Third Law: Objects at rest
• An apple rests on a table. Identify the forces that act
on it and the action-reaction pairs.
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Applying Newton’s Third Law: Objects in motion
• A person pulls on a block across the floor. Identify
the action-reaction pairs.
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Applying Newton’s Third Law: Objects in motion
• A person pulls on a block across the floor. Identify
the action-reaction pairs.
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Applying Newton’s Third Law: Objects in motion
• A person pulls on a block across the floor. Identify
the action-reaction pairs.
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Applying Newton’s Third Law: Objects in motion
• A person pulls on a block across the floor. Identify
the action-reaction pairs.
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A paradox?
• If an object pulls back on you just as hard as you
pull on it, how can it ever accelerate?
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Free-body diagrams
A
free-body
diagram
is a sketch
showing all the
forces acting
on an object.
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Free-body diagrams
A
free-body
diagram
is a sketch
showing all the
forces acting
on an object.
Copyright © 2012 Pearson Education Inc.
Free-body diagrams
A free-body diagram is a sketch showing all the forces
acting on an object.
Copyright © 2012 Pearson Education Inc.