Newton

1
Newtons Laws

• Forces and Motion

2
Laws of Motion

• formulated by Issac Newton in the late 17th
  century
• written as a way to relate force and motion
• Newton used them to describe his observations of
  planetary motion.

3
History

• Aristotle was an ancient Greek philosopher
• Based on his observations the common belief was
  that in order for an object to continue moving, a
  force must be exerted in the direction of the
  motion
• This lasted until Issac Newton proposed his Laws
  of Motion based on observations made of bodies
  free from earths atmosphere.

4
Newtons 1st LawInertia

• An object at rest will stay at rest, and an
  object in motion will stay in motion at constant
  velocity unless acted on by an unbalanced force.

This statement contradicted Aristotles teaching
and was considered a radical idea at the time.
However, Newton proposed that there was, in fact,
an unrecognized force of resistance between
objects that was causing them to stop in the
absence of an applied force to keep them moving.
This new unseen resistance force became known as
friction.
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Newtons 2nd LawFnet ma

• If an unbalanced force acts on a mass, that mass
  will accelerate in the direction of the force.

Since 8N is greater than 2N, the unbalanced force
(6N) is to the right so the acceleration is to
the right.
2 N
8 N
a
Newtons 1st Law says that without an unbalanced
force objects will remain at constant velocity
(a0)so it seems logical to say that if we apply
a force we will see an acceleration.
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Newtons 3rd LawAction - Reaction

• For every action force there is an equal and
  opposite reaction force.

Example If you punch a wall with your fist in
anger, the wall hits your fist with the
same force. Thats why it hurts!
Action-reaction forces cannot balance each other
out because they are acting on different objects.
The forces acting on an object determine their
motion.
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or

• Acceleration and net force are directly related.
  If Fnet doubles, acceleration doubles.
• Acceleration and mass are indirectly related. If
  m doubles, acceleration is half as much.

8
A Force is

• Measured in Newtons (N) in the metric (SI) system
  and pounds (lbs) in the English system
• A vector quantity requiring magnitude and
  direction to describe it
• Represented by drawing arrows on a diagram

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Types of Forces(that we will study now there
are many more)

• Weight - force of gravity
• Normal force surface pushing back
• Friction - resistance force that opposes motion
• Applied force - force you exert, push or pull
• Tension - applied through a rope or chain
• Net force total vector sum of all forces
• Balanced forces equal and opposite forces
• Unbalanced forces not equal and opposite

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Weight

• The force of gravity acting on a mass.
• Weight always acts down!

Weight mass (kg) acceleration due to gravity
Weight is a forceso this is a special case of
Fma and the unit is a Newton.
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Mass is

• The amount of matter in an object.
• Measured in kilograms.
• NOT a force.
• The same at any location, even on another planet.
  Not influenced by gravity.

12
Normal Force (FN)

• Defined as the force of a surface pushing back on
  an object.
• Always directed perpendicular to the surface.
• This is a contact force. No contactno normal
  force.
• NOT always equal to weight.

FN
Examples
FN
Wa l l
Table
13
Friction

• A resistance force usually caused by two surfaces
  moving past each other.
• Always in a direction that opposes the motion.
• Measured in Newtons.
• Depends on surface texture and how hard the
  surfaces are pressed together.
• Surface texture determines the coefficient of
  friction (µ) which has no units.
• Normal force measures how hard the surfaces are
  pressed together.

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Types of friction

• Static friction is the force an object must
  overcome to start moving.
• Kinetic friction is the force an object must
  overcome to keep moving.

Static friction is always greater than kinetic
friction!
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Calculating the Force of Friction
Where f is the force of friction, µ is the
coefficient of friction, and FN is the normal
force. µ has no units!
For kinetic friction
For static friction
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May the Net Force be with you

• Total force acting on an object
• Vector sum of all the forces
• The unbalanced force referred to in Newtons Law
  of Motion
• Net force is equal to the mass of an object times
  the acceleration of that object.

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Net force can be found by finding the sum of the
force vectors or by mass times acceleration.
Example using mass times acceleration Find the
net force for a 20 kg object that is being
accelerated at 3 m/s2 .
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If acceleration is not given, use the kinematics
equations to find a first
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Or conversely you may have to use the Fnet
formula to get acceleration and then the
kinematics equations to find t, d, vi, or vf.
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Finding net force using sum of the force vectors
Example 2
Example 1
30 N
10 N
Fnet 20 N
Example 3
Must draw vectors tip to tail first before
solving
Fnet

14 N
?
7 N
Fnet 2 14 2 7 2 ? tan-1 (14 / 7)
Fnet 15.7 N ? 63.4º
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Force Diagrams

• Force diagrams must include the object and all
  forces acting on it.
• The forces must be attached to the object.
• No other vectors may be attached to the object.
• Components of forces, axis systems, motion
  vectors and other objects or surfaces may be
  included in force diagrams.
• Put the mass in the object box.

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Force Diagram
Problem A 10 kg crate with an applied force of
100 N slides across a warehouse floor where the
coefficient of static friction is 0.3 between
the crate and the floor. What is the
acceleration of the crate?
Weight Fg (10 kg)(9.81m/s2)
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To Solve the ProblemNow that you have the force
diagram!
Problem A 10 kg crate with an applied force of
100 N slides across a warehouse floor where the
coefficient of static friction is 0.3 between
the crate and the floor. What is the
acceleration of the crate.
FN
Fapplied 100 N
f µFN
a
10 kg
Weight Fg (10 kg)(9.81m/s2)
Write the Newtons 2nd Law equation for the x-
and y- directions. This time we will use both sum
of forces and ma as Fnet.
Now plug in what you know and solve for what you
dont.
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Solving the Problem
Problem A 10 kg crate with an applied force of
100 N slides across a warehouse floor where the
coefficient of static friction is 0.3 between
the crate and the floor. What is the
acceleration of the crate.
FN
Fapplied 100 N
f µFN
a
10 kg
Weight Fg (10 kg)(9.8m/s2)