Newton's Laws and Force. 1 October 31, 2017 Oct 218:32 AM Introduction to Newton‛s Laws Newton‛s First Law. Oct 218:32 AM Isaac Newton • Arguably the greatest scientific genius ever. • Came up with 3 Laws of Motion to explain the observations and analyses of Galileo and Johannes Kepler. • Discovered that white light was composed of many colors all mixed together. • Invented new mathematical techniques such as calculus and binomial expansion theorem in his study of physics. • Published his Laws in 1687 in the book Mathematical Principles of Natural Philosophy.
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Newton's Laws and Force.
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October 31, 2017
Oct 218:32 AM
Introduction to Newton‛s LawsNewton‛s First Law.
Oct 218:32 AM
Isaac Newton• Arguably the greatest scientific genius ever.• Came up with 3 Laws of Motion to explain the observations
and analyses of Galileo and Johannes Kepler.• Discovered that white light was composed of many colors all
mixed together.• Invented new mathematical techniques such as calculus and
binomial expansion theorem in his study of physics.• Published his Laws in 1687 in the book Mathematical
Principles of Natural Philosophy.
Newton's Laws and Force.
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What is Force?• A force is a push or pull on an object.• Forces cause an object to accelerate…
> To speed up> To slow down> To change direction
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Newton‛s First Law• A body in motion stays in motion at constant
velocity and a body at rest stays at rest unless acted upon by a net external force.
• This law is commonly referred to as the Law of Inertia.
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The First Law is Counterintuitive
Aristotle firmly believed this.But Physics 1 students know better!
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Implications of Newton‛s 1st Law
• If there is zero net force on a body, it cannot accelerate, and therefore must move at constant velocity, which means> it cannot turn,> it cannot speed up,> it cannot slow down.
Newton's Laws and Force.
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Oct 3011:22 AM
Free Body Diagram of a book at rest on a table
Free Body Diagram a picture that shows all the forces acting on an object where all forces originate a single point at the center of the object (the center of mass).
Misconception Alert: This type of diagram applies only to translational motion and not rotational motion (we will examine rotation in another unit)
Free Body Diagram of a book sliding at a constant velocity on a table
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Sample Problem• A monkey hangs by its tail from a tree
branch. Draw a free body diagram representing all forces on the monkey
FT
FG
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Sample Problem• Now the monkey hangs by both hands from two
vines. Each of the monkey‛s arms are at a 45o from the vertical. Draw a force diagram representing all forces on the monkey.
FG
Fa1 Fa2
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Newton‛s Second Law
Newton's Laws and Force.
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Newton‛s Second Law• A body accelerates when acted upon by a net
external force.• The acceleration is proportional to the net
force and is in the direction which the net force acts.
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Newton‛s Second Law
Σ F = ma
where Σ F is the net force measured in Newtons (N)
m is mass (kg) this is inertial mass.
a is acceleration (m/s2)
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Units of force• Newton (SI system)
> 1 N = 1 kg m /s2 • 1 N is the force required to accelerate a 1 kg
mass at a rate of 1 m/s2. It is approximately the force required to lift an apple or two.
• Pound (British system)> 1 lb = 1 slug ft /s2
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Working 2nd Law Problems• Draw a free body diagram.• Set up X & Y chart to find 2nd Law equations
in each dimension. (F = ma)• Add the columns to get the
Net Force in the x & y directionsΣFx = max and/or ΣFy = may
• Use Pyth. Theorem to solve for the Overall Net Force (Fnet) and the tan-1 (Fnet y / Fnet x) to get θ.
x yForces
F net
ΣFx = max ΣFy = may
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Oct 3011:34 AM
3 Forces act on a 20 kg object: F1 = 200 N at 35 degrees above the x, F2 = 50 N in +y, F3 = 150 N at 20 degrees below the +x. a) Determine the magnitude and direction of the net force for the situation. b) Find the acceleration of tjhe object (magnitude and direction).
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Newton‛s Third Law
Newton's Laws and Force.
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Newton‛s Third Law• For every action there exists an equal and
opposite reaction.• If A exerts a force F on B, then B exerts a
force of -F on A.• The pair of forces are known as an action-
reaction pair.
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Examples of Newton‛s 3rd Law
Copyright James Walker, “Physics”, 1st edition
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Treating multiple objects as a SystemSample Problem
A force of magnitude 7.50 N pushes three boxes with masses m1 = 1.30 kg, m2 = 3.20 kg, and m3 = 4.90 kg as shown. Find the contact force between (a) boxes 1 and 2 and (b) between boxes 2 and 3.
Copyright James Walker, “Physics”, 1st edition
Oct 218:32 AM
Sample ProblemAn object acted on by three forces moves with constant velocity. One force acting on the object is in the positive x direction and has a magnitude of 6.5 N; a second force has a magnitude of 4.4 N and points in the negative y direction. Find the direction and magnitude of the third force acting on the object.
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Specific Forces
1. Weight or Gravity G
2. Normal N
3. Friction f
4. Tension T
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Mass and Weight
Misconception Alert
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Mass and Inertia• Chemists like to define mass as the amount
of “stuff” or “matter” a substance has.• Physicists define mass as inertia, which is the
ability of a body to resist acceleration by a net force.
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Mass and Weight• Many people think mass and weight are the
same thing. They are not.• Mass is inertia, or resistance to acceleration.• Weight can be defined as the force due to
gravitation attraction.• G = mg - gives you gravitational force
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Normal Force
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Normal force• The normal force is a force that keeps one
object from penetrating into another object.• The normal force is always perpendicular to a
surface.• The normal force exactly cancels out the
components of all applied forces that are perpendicular to a surface.
• There is No formal equation for normal force, you have to determine it from the other forces acting on the object.
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Ex: Normal force • If the box has a mass of 5 kg, what is its weight (G)?• What normal force is acting on the box?• If I push downward on the box with 11 N of force, what
is the normal force?• If I pull up on the box with 11 N of force what is the
normal force?
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Normal force not associated with weight.
• A normal force can exist that is totally unrelated to the weight of an object.
applied force Wall
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Normal force on ramp• The normal force is perpendicular to angled
ramps as well.
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Sample problem• Find the normal force exerted on a 2.5kg book resting on a
surface inclined at 280 above the horizontal. • If the angle of the incline is reduced, do you expect the normal
force to increase, decrease, or stay the same?
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Sample problemA gardener mows a lawn with an oldfashioned push mower. The handle of the mower makes an angle of 32 degrees with the surface of the lawn. If a 249 N force is applied along the handle of the 21kg mower, what is the normal force exerted by the lawn on the mower? What is the acceleration of the lawnmower?
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FrictionFriction (f) – force that attempts to counteract sliding
2 types: kinetic friction, fk, (object moving/sliding) & static friction, fs, (object at rest)
For the same surfaces in contact: Static friction is always larger than kinetic friction.
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Friction (cont.)Both utilize the same equation: f = μ N
where μ is the coefficient of friction and is dependent upon the surfaces in contact. For most materials, μ < 1.
Static friction is also a “lazy” force and does only as much as it has to, but it has a limit. Once a force is applied that is greater than static friction the object will move and kinetic friction will act on the object.
Oct 218:32 AM
TensionTension (T) – pulling force with in a cord, string or rope. It acts in both directions within the cord because of Newton’s 3rd law.
Ex: Think about dragging a box by a rope. You pull on the rope (Action) & the rope pulls on you (Reaction). Those forces are equal and opposite.
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Nov 31:00 PM
Atwood Problems mass attached by idealized strings with a pulley.
Idealized = no friction, no mass, no stretching
Nov 31:04 PM
Solve for acceleration of blocks and tension in rope.
How does the acceleration of each block compare?
What values will the acceleration be between?
How does the tension in the cord compare to the force of gravity acting on each block?
What values will the tension be between?
mb= 3 kg mc= 5 kg
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Dec 152:48 PM
Dec 108:20 AM
Solve for the acceleration and tension
mb= 0.21 kg mc= 0.20 kg
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Oct 218:44 AM
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