Forces and the Laws of Motion

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Forces and the Laws of Motion
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What is a Force?

• Recall that acceleration describes a change in an
  objects velocity and velocity describes a change
  in an objects position.
• dr/dt v
• dv/dt a

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What is a Force?

• A force is a push or a pull on an object that
  causes a change in the objects acceleration.
• Forces can start motion, stop motion, or change
  the path of motion.
• The SI unit of force is the newton (N) named
  after Sir Isaac Newton.

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What is a Force?

• The newton is defined as the amount of force,
  that when acting on a 1 kg mass, produces an
  acceleration of 1 m/s2.
• N kg m/s2
• Forces are vectors
• The object experiencing the force is called the
  system, and the world around the object creating
  the force is called the environment.

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What is a Force?

• There are two main types of forces Contact and
  Field Forces
• A contact force is a force that arises from the
  physical contact of two objects.
• A field force, or long range force, is exerted
  without physical contact between objects.

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What is a Force?

• Examples of field forces include gravity and the
  attraction/repulsion between electrical charges.
• The theory of fields was developed by Michael
  Faraday to explain how objects could exert a
  force on each other without ever touching.
• At the atomic level, all forces can be classified
  as field forces.

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What is a Force?

• Currently, there are only four known forces.
• Strong Forces (subatomic particles)
• Electromagnetic (attraction/repulsion between
  electric charges)
• Weak Forces (radioactive decay processes)
• Gravity

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What is a Force?

• Each force has an immediate and identifiable
  cause known as an agent.
• The agent for gravity is the Earths mass.
• If you cannot identify the agent, the force does
  not exist.

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Force-Diagrams

• A force diagram, also known as a free-body
  diagram, is a pictorial representation of all the
  forces acting on an object or system.
• A free-body diagram shows only the object and any
  forces (contact and field) acting on it.

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Force-Diagrams

• Represent the object by a dot (particle model).
• Represent all forces acting on the object by
  using arrows.
• The tail of the arrow (force vector) is always on
  the object even if the force is a push.
• Label the force using F and a subscript to denote
  the type of force or agent. (Fg force due to
  gravity).

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Force-Diagrams
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Newtons 1st Law of Motion

• In the late 1600s, Sir Isaac Newton summarized
  the way in which force influence motion into
  three clear and concise laws.
• These laws apply only to objects with velocities
  ltlt the speed of light, and for inertial reference
  frames.

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Newtons 1st Law of Motion

• If an object has no force acting on it, is the
  object at rest or in motion?
• A common misconception is that an object with no
  force acting on it will always be at rest.
• Imagine rolling a ball on a variety of different
  surfaces carpet, a smooth floor, etc.
• What would happen to the motion of the ball if
  all friction were eliminated?

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Newtons 1st Law of Motion

• Galileo theorized that an object sliding on a
  smooth surface would slide forever in the absence
  of an applied force.
• In 1687, Newton further developed this idea, and
  it is now known as his first law of motion.

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Newtons 1st Law of Motion

• An object at rest remains at rest, and an object
  in motion will continue in motion with constant
  velocity (constant speed in a straight line)
  unless the object experiences a net external
  force.
• The tendency of an object not to accelerate is
  called inertia. (Mass is a measurement of an
  objects inertia.)

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Newtons 1st Law of Motion

• The first law of motion is also referred to as
  the Law of Inertia.
• Unless a force acts on an object and causes a
  change in velocity (acceleration), the object
  will preserve its current state of motion.

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Newtons 1st Law of Motion

• The acceleration an object experiences is the
  result of the net external force.
• The net external force is the vector sum of all
  forces acting on an object.
• The net external force is written as Fnet or SF.

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Newtons 1st Law of Motion

• When SF zero, then the object is in
  equilibrium.
• Note that being at rest is a special case of
  constant velocity.
• Newtons 1st Law identifies the net force as
  something that disturbs equilibrium.
• So, the net force changes the velocity of an
  object, and the change in velocity (acceleration)
  is the result of a net force on the object.

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Newtons 1st Law of Motion
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Newtons 2nd Law of Motion

• How does a known force affect the motion of an
  object?
• Imagine pushing a car on a flat level surface.
• Compare the speed of the car if only one person
  is pushing versus multiple people. Which case
  provides the greater increase in speed?

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Newtons 2nd Law of Motion

• The acceleration of an object is directly
  proportional to the net external force acting on
  it.
• Does mass affect acceleration?
• Objects with greater mass have greater inertia,
  or tendency to maintain its current state of
  motion.

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Newtons 2nd Law of Motion

• Newton summarized the relationship between mass,
  acceleration, and the net force acting on an
  object.
• SF ma
• Recall the acceleration and force are both vector
  quantities and the force in this equation is the
  vector sum of all forces acting on the object.

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Newtons 2nd Law of Motion

• Thus, the acceleration of an object is directly
  proportional to the net force and inversely
  proportional to the mass.
• This is known as Newtons 2nd Law of Motion.

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Newtons 2nd Law of Motion

• The direction of the acceleration is in the same
  direction as the net force acting on the object.

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Newtons 2nd Law of Motion

• Newtons 2nd Law of Motion identifies the cause
  of a change in velocity and the resulting
  displacement, and is sometimes called the law of
  nature.
• Newton believed that this law held true for all
  motions.
• However, scientists now know that Newtons 2nd
  Law does not hold true for objects that approach
  the speed of light or for atomic particles.
• But, this law does govern the motion of our
  everyday lives 300 years later.

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Newtons 2nd Law of Motion

• Problem Solving Skills
• Draw a free-body diagram and label all the forces
  acting on the object.
• Break the equation SFma into components.
• SFxmax
• SFymay

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Applications Newtons 2nd Law

• There are several types of forces that affect the
  motion of an object.
• Table 6-2 on page 123 lists some common forces
  and the standard notation for each force.
• Recall that forces are labeled using F and a
  subscript denoting the type of force.

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Applications Newtons 2nd Law

• Aristotle versus Galileo on falling objects
• While there is no evidence that Galileo dropped
  two balls from the Leaning Tower of Pisa, he did
  propose a theory on falling objects.
• Using Newtons 2nd Law and neglecting air
  resistance, there are no contact forces acting on
  falling objects.
• So what is the force causing the object to
  accelerate downward?

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Applications Newtons 2nd Law

• Recall that falling objects accelerate at a
  constant rate equal to 9.8 m/s2 (g).
• Using Newtons 2nd Law, the force causing the
  object to accelerate is the weight force. (Fg)
• Fg mg
• An objects weight is equal to its mass times the
  acceleration it would have if it were freely
  falling.

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Applications Newtons 2nd Law

• This is true on Earth and all planets, although
  the value of g is different for different
  planets.
• Mass does not change.
• What then is weight, and what do scales measure?

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Applications Newtons 2nd Law

• When you step on a bathroom scale, you exert a
  downward force on a spring, and the spring exerts
  an upward force on you.
• Because you are not accelerating, SF 0.
• Therefore, the magnitude of the force exerted by
  the spring on you is equal to your weight, not
  your mass.
• If you were on a different planet, the
  compression of the spring would be different, and
  your weight would be different.

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Applications Newtons 2nd Law

• What happens to weight though if you are
  accelerating?
• Imagine weighing yourself in an elevator that is
  accelerating downward.
• Would your weight on the scale increase or
  decrease?
• You would experience weightlessness.

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Applications Newtons 2nd Law

• The weight you read on the scale is the apparent
  weight.
• Weightlessness does not mean that your weight is
  zero, but that your apparent weight is zero.
• All objects have weight and experience a force
  directed downward caused by the acceleration due
  to gravity.

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Applications Newtons 2nd Law

• Friction is often minimized in problem solving,
  but in the real world friction is everywhere.
• Friction allows motion to start and stop.
• Imagine walking on an ice rink, riding a bike, or
  using a pencil.

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Applications Newtons 2nd Law

• Imagine pushing a car from rest on a level
  surface.
• Newtons 2nd Law states the car should move
  unless there is another force acting upon it.
• The resistive force that keeps the car from
  moving is the static friction force. (Fs)

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Applications Newtons 2nd Law

• As long as an object does not move, the force of
  static friction is always equal and opposite in
  direction to the component of the applied force
  in the horizontal direction.
• But, we know that if we keep pushing on the car,
  it will eventually move.
• So, the force of static friction has a maximum.

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Applications Newtons 2nd Law

• When the applied force is a great as it can be
  without causing the object to move, the force of
  static friction reaches its maximum value. (Fs,
  max)
• When the applied force exceeds Fs, max the object
  will begin to move.
• But, experience again tells us that once we
  remove the applied force, the car will eventually
  come to a stop.
• So, a retarding force is still acting upon the
  car.

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Applications Newtons 2nd Law

• The retarding force, or force opposing the
  direction of motion, is known as the kinetic
  friction force. (Fk)
• The kinetic friction force is the force exerted
  on one surface by the other when the surfaces are
  in relative motion.

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Applications Newtons 2nd Law

• Although frictional forces are complicated, a
  simplified model can be used to find solutions
  close to those found by experiments.
• Recall that friction depends on the type of
  surfaces in contact, the speed of their relative
  motion, and the surface area of contact.
• This model ignores surface area and speed, and
  deals only with the surfaces in contact.

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Applications Newtons 2nd Law

• The magnitude of the force of friction is
  proportional to the magnitude of the force
  pushing one surface against the other.
• This is the normal force. (FN)
• For objects on a flat level surface,
• FN Fg mg
• The normal force is always perpendicular to the
  area of contact but is not always opposite in
  direction to the force of gravity.

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Applications Newtons 2nd Law

• Fk µkFN
• Remember that the kinetic force of friction and
  the normal force are vectors.
• µk is the coefficient of kinetic friction and
  depends on the composition of the surfaces in
  contact.
• Table 6-3 on page 131 lists typical coefficients
  of frictions for various surfaces in contact.

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Applications Newtons 2nd Law

• Fs µsFN
• Thus, the force of static friction is greater
  than the force of kinetic friction.
• It is easier to keep an object in motion, than it
  is to begin its motion.

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Newtons 3rd Law

• Have you hear the phrase, For every action,
  there is an equal and opposite reaction?
• What exactly is an action, reaction, and why are
  they equal?
• If a car hits a brick wall, we know the car
  exerts a force on the wall. Does the wall exert a
  force on the car?

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Newtons 3rd Law

• Yes the wall exerts a force on the car as well.
• The force of the car on the wall (Fcar on wall)
  and the force of the wall on the car (F wall on
  car) are sometimes called action-reaction pairs.
• These forces are not a cause and effect pair.
• They either exist together or not at all.

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Newtons 3rd Law

• Newton theorized that forces always exist in
  pairs, and formulated his third law of motion.
• According to the third law of motion, an
  interaction pair is two forces that are in
  opposite directions and have equal magnitude.

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Newtons 3rd Law

• Action-Reaction pairs act on different objects.
• Recall the car hitting the wall.
• One force acts on the car, and the other force
  acts on the wall.
• Field forces also exist in pairs.

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References

• Physics. Holt, Rinehart, and Winston, 2002
• Physics Principles and Problems. Glencoe, 2002