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Chapter 4 Outline
Newton’s Laws of Motion
• Forces
• Contact and long range
• Superposition
• Free-body diagrams
• Newton’s first law
• Inertial frames of reference
• Newton’s second law
• Mass vs. weight
• Newton’s third law
Forces
• Forces are interactions between two
bodies or between a body and the
environment.
• Contact force
• Push, pull, friction…
• Long-range
• Gravitational, electric, magnetic…
• Vectors!
Superposition of Forces
• When more than one force is acting on a body, the net
force is the vector sum of the forces.
𝑭net =
𝑭𝑖 = 𝑭1 + 𝑭2 + 𝑭3 + ⋯
𝑖
• Sometimes the net force is called the resultant force, 𝑹.
Free-Body Diagram
• A free-body diagram helps us to understand what forces
are relevant and how to apply them to analyze a situation.
• Choose the body
• Only include forces acting on that body
Newton’s First Law
• Natural state of an object
• Aristotle, Galileo, Descartes…
• From Pricipia, the Latin followed by an English translation.
“Lex I: Corpus omne perseverare in statu suo quiescendi vel
movendi uniformiter in directum, nisi quatenus a viribus
impressis cogitur statum illum mutare.”
“Law I: Every body persists in its state of being at rest or of
moving uniformly straight forward, except insofar as it is
compelled to change its state by force impressed.”
• From our text: A body acted on by no net force moves with
constant velocity (which may be zero) and zero
acceleration.
Inertial Frame of Reference
• Is Newton’s first law always obeyed?
• An inertial frame of reference is a frame in which
Newton’s first law holds.
• The frame moves with constant velocity.
• Any inertial frame is equally valid, so we choose the one that is
easiest to work with.
Newton’s Second Law
• What happens when the net force is not zero?
• From Pricipia, the Latin followed by an English translation.
“Lex II: Mutationem motus proportionalem esse vi motrici
impressae, et fieri secundum lineam rectam qua vis illa
imprimitur.”
“Law II: The alteration of motion is ever proportional to the
motive force impress'd; and is made in the direction of the
right line in which that force is impress'd.”
• From our text: If a net external force acts on a body, the
body accelerates. The direction is the same as the direction
of the net force. The mass of the body times the
acceleration of the body equals the net force vector.
Newton’s Second Law
• More succinctly,
𝑭 = 𝑚𝒂
𝑭net = 𝑚𝒂
• Units:
• We measure mass in kg and acceleration in m/s 2 , so force must
have the unit of kg ∙ m/s2 .
• This is a newton, N.
1 N = 1 kg ∙ m/s2
• A pound (or pound-force) is about 4.4 N.
Newton’s Second Law Example
Mass vs. Weight
• Weight is the force due to gravity
acting on a body.
𝑤 = 𝑚𝑔
• Force, so measured in newtons, 𝑁.
• On the earth’s surface, 𝑔 = 9.8 m/s 2 ,
but the local gravity, and therefore
weight is different elsewhere.
• Mass is intrinsic to the body and
describes its inertial properties (as
well as gravitational attraction to
other masses).
• Measured in kilograms, 𝑘𝑔.
Mass vs. Weight Example
Newton’s Third Law
• Forces arise from interactions between bodies. Can one
body exert a force on another without being affected itself?
• From Pricipia, the Latin followed by an English translation.
“Lex III: Actioni contrariam semper et æqualem esse
reactionem: sive corporum duorum actiones in se mutuo
semper esse æquales et in partes contrarias dirigi.”
“Law III: To every action there is always opposed an equal
reaction: or the mutual actions of two bodies upon each other
are always equal, and directed to contrary parts.”
• From our text: If body 𝐴 exerts a force on body 𝐵 (an
“action”), then body 𝐵 exerts a force on body 𝐴 (a
“reaction”). These two forces have the same magnitude but
are opposite in direction. These two forces act on different
bodies.
Newton’s Third Law Example
Chapter 4 Summary
Newton’s Laws of Motion
• Forces
• Superposition: 𝑭net =
𝑖 𝑭𝑖
= 𝑭1 + 𝑭2 + 𝑭3 + ⋯
• Free-body diagrams
• Draw all forces acting on a body
• Newton’s first law:
• Inertial frames of reference
• Newton’s second law:
𝑭 = 𝑚𝒂
• Mass vs. weight: 𝑤 = 𝑚𝑔
• Newton’s third law: 𝑭𝐴 on 𝐵 = −𝑭𝐵 on 𝐴
Newton’s Second Law Example #2
Newton’s Third Law Example #2