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PHYSICS 149: Lecture 3
• Chapter 2
– 2.1 Forces
– 2.2 Net Force
– 2.3 Newton’s first law
Lecture 3
Purdue University, Physics 149
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Forces
• Forces are interactions between objects
• Different type of forces:
– Contact vs. non-contact forces
– Contact forces are due to EM interactions
• Forces always exist in pairs
– When you push on the ground to walk, the ground pushes
back on your foot
• Measuring forces: Hooke’s law F = kx
• Forces are vectors: magnitude plus direction
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Force
• Force: a push or pull that one object exerts on
another
– Force can also be defined as any action that alters a
body’s state of rest or of constant speed motion in a
straight line.
• Forces always exist in pairs
– Anything that exerts a force also has a force exerted on it.
– For example, when you push on the ground to walk, the ground
pushes back on your foot.
• Two types of forces on macroscopic objects:
– Long-range forces: Forces that do not require the two objects to
be touching. Example:) gravity and electromagnetic forces.
– Contact forces: Forces that exist only as long as the objects are
touching one another. Example: kicking a ball.
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How to Measure a Force?
•
•
•
•
The SI unit for force is the Newton (N).
One way to measure forces is using springs (F ∝ x).
Hooke’s low for an ideal spring:
F = kx where k is the spring constant
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Net Force
•
•
•
•
More than one force can act on an object at once.
The “net” force means the “total force”.
Be careful since the force is a vector.
The sum is easy if all forces act in the same
direction.
• If Fnet = 0 we have “translational equilibrium”.
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Adding Vectors in 1-D
• If two vectors are in the same direction, their sum is in the
same direction and its magnitude is the sum for the
magnitudes of the two.
• If two vectors are in opposite directions, the magnitude of
their sum is the difference between the magnitudes of the
two vectors, and the direction of the vector sum is the
direction of the larger of the two.
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Forces
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Forces
• Quantifies the “interaction” between two objects
• 4 Fundamental Forces
–
–
–
–
Gravity
Electromagnetic
Strong Nuclear
Weak Nuclear
• Forces come in pairs, equal and opposite
• Vector
– Has magnitude and direction
– Be careful when you add two forces!
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Contact/Action-at-a-Distance
F
F
F
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ILQ 1
Which of these is not a long-range force?
A) The force that makes lightning flow between an
electrically charged cloud and an oppositely
charged area on the ground
B) The force that keeps the Moon in its orbital path
around the Earth
C) The force that a person exerts on a chair while
sitting
D) The force that makes the compass point North
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Isaac Newton (1643-1727)
• Newton’s Law of Motion
• The law of universal gravitation
• Principia
• Newton’s laws form the basis of classical
mechanics.
The Principia or Philosophiae naturalis
principia mathematica published 1687
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Newton’s Laws of Motion
1.
2.
An object at rest remains at rest
and an object in motion remains
in motion unless acted upon by
an unbalanced force (law of Inertia)
An unbalanced force is equal to
the rate of change of momentum
( F = ma )
3.
For every action, there is an equal
and opposite reaction.
Isaac Newton
(1643-1727)
Humans could explain/understand the most complex
phenomena with only 3 assumptions.
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Newton’s Laws
1. No forces → no change in velocity magnitude or
direction
2.
3. For TWO objects, forces on each other are equal
and opposite
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Newton’s Laws of Motion
1. If the sum of all external forces on an object is
zero, then its speed and direction will not
change. Inertia
2. If a nonzero net force is applied to an object its
motion will change. F = ma
3. In an interaction between two objects, the
forces that each exerts on the other are equal
in magnitude and opposite in direction.
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Newton’s First Law of Motion
• An object’s velocity (a vector) does not change if
and only if the net force acting on the object is zero.
• In other words, if there is no net force on an object,
its speed and direction of motion do not change
(including if it is at rest).
• Also called “the law of inertia.” Inertia means
resistance to changes in velocity.
– Example: the start or stop of a car’s motion, dusts on
clothes, a quarter on top of an index card on a cup.
– Note that circular motion is NOT a constant motion, that
is, net force is not zero. Why?
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Newton’s First Law
Objects at rest remain at rest and objects in motion remain in motion in
a straight line unless acted upon by an external agent
- External agents are called Forces
- Forces change the state of motion of an object
A force which causes a standard mass of 1 kg to have an
acceleration of 1 m/s2 is, by definition, a force of 1 newton (N)
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Newton’s First Law
• An object continues in a state of rest or in a state of
motion at a constant speed along a straight line,
unless compelled to change that state by a net force
• The state of rest and constant velocity are
“equivalent”
• If the object is in a circular trajectory there must be
a force
• Leads to the definition of inertia: the tendency of an
object to remain at rest
• Mass and Inertia are measured in kg
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Mass
• The mass of an object quantifies the amount of inertia that
an object possesses – an intrinsic property of the object
• Objects with a lot of inertia (large mass) are harder to
change the state of motion of compared to objects with a
small amount of inertia (small mass)
• The units of mass are grams, kilograms, or slugs
F
Small
acceleration
F
Lecture 3
Large
acceleration
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Weight
• Weight is the force of gravity on an object with mass
• Units of weight are Newtons or Pounds
Same mass but Different weight!
r
On earth W=mg where g=9.8 m/s2
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Weight
The weight (W) of an object is
equal to the magnitude of the
gravitational force acting on a
body of mass m
W = mg
Dropping an object causes it
to accelerate at free-fall
acceleration g
Fg = mg
W = Fg
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Weight on Earth
• Your weight on Earth is the magnitude of Earth’s
gravitational force exerted on you (m).
where R is the distance
between you and Earth’s center
• The weight of an object of mass m “near” Earth’s
surface is:
where
(g is called the gravitational field strength)
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Weight on Other Planets
• The weight of an object of mass m “near” a
planet’s surface is:
• For example, gMoon = 1.62 N/kg ≈ 1/6 gEarth.
– Let’s say there is a man whose mass is 100 kg.
• At the surface of Earth, his mass and weight are 100 kg and
980 N (=m×gEarth), respectively.
• At the surface of Moon, his mass and weight are 100 kg and
162 N (=m×gMoon), respectively.
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ILQ 2
A parachutist drifts slowly downwards towards the earth with
constant speed. Only two forces, P and W, act on the
parachutist. Force P is the upwards pull from the parachute
and W is the downwards pull from the Earth.
A) P and W are equal in size and opposite in direction
B) W is larger than P
C) P is larger than W
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Free Body Diagrams
• A simple recipe:
– Simple picture of just object of interest
– Choose coordinate system (x,y)
– Identify all forces acting on object and draw arrow
showing direction
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Free Body Diagrams
• “Free-body” means your diagram is free of other objects
• “The zeroth law”: An object responds only to forces acting on
it!
• Draw force vectors only for forces exerted by other objects
on the object of interest
• Put the tail of the vector on the dot that represents the object
of interest
• Use a symbol for the force that indicates the kind of force.
• Use subscripts to indicate the object on which the force is
acting (first subscript) and the object that exerted the force
(second subscript)
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Labeling Forces
• Which force are important when you do FBD?
• Draw force vectors only for forces exerted by
other objects on the object of interest. First index
must always be the one representing the object
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Labeling Forces
F21= Force on 2 by 1
F12= Force on 1 by 2
Fgc
Fmf Ffm
Fcg
Fae
Fea
Fsh Fhs
Using indices you can recognize easily force linked by third law
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Book Pushed Across Table
• Book sliding across table
y
– Choose Object (book)
– Label coordinate axis
– Identify All Forces
•
•
•
•
Hand (to right)
Gravity (down)
Normal (table, up)
Friction (table, left)
x
Normal
friction
hand
Gravity
Physics
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Summary
•
•
•
•
Force
4 fundamental forces
Newton’s first law
Inertia: mass vs. weight
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