Unit IV: Balanced Forces

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Unit IV Balanced Forces
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What is a force?

• A force is an interaction between two objects
  that results in a push or a pull.

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Types of Forces

• Forces can be classified into two types
• Contact The two objects that interact are in
  direct contact (they touch)
• Long-Range The two objects interact at a
  distance (they do not touch)

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Examples of Contact Forces

• Tension (FT) pulling force along strings,
  ropes, cables, etc.
• Friction (Ff) contact force between an object
  and a surface. Always parallel to the surface and
  opposing motion
• Normal Force (FN) Contact force between an
  object and a surface, always perpendicular to the
  surface.

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Examples of Long-Range Forces

• Gravity (Fg) force between any two objects with
  mass.
• Electric Force (FElec)
• Magnetic Force (FMag)
• We will not be looking at electric or magnetic
  forces at this point in the year. So the only
  long-range force we will deal with right now is
  gravity!

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Newtons First Law of Motion

• Objects in motion
• will remain in motion
• (with constant velocity)
• unless acted upon
• by unbalanced forces.

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Newtons First Law

• In other words, Newtons First Law means
• If forces are balanced, then the object has
  constant velocity.
• If an object has constant velocity, then the
  forces are balanced.

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Balanced Forces?

• Balanced Forces means that all UP forces added
  together equal all DOWN forces added together,
  and all LEFT forces added together equal all
  RIGHT forces added together.
• UP DOWN LEFT RIGHT

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Components of Forces

• In determining the UP, DOWN, LEFT, RIGHT
  forces, we really need to look only at the part
  of a force that is in each of those directions.
• These parts are called components.

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Components of Forces

• For example, the force illustrated below could be
  described as a force that is to the RIGHT and UP.
  

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Components of Forces

• For example, the force illustrated below could be
  described as a force that is to the RIGHT and UP.
  
• Notice the red arrow shows how much of the force
  is to the right, and the blue arrow shows how
  much is up.

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Finding Components

• To find x and y components of a force, first
  DRAW A TRIANGLE, with legs of the triangle being
  horizontal and vertical.
• This forms a right triangle.
• Label the sides of the triangle.

F
Fy
Fx
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Right Triangles

• There are special properties of right triangles
  that we can use to find the x and y components.
• The longest side is called the hypotenuse.
• The side opposite a known angle (?) is called the
  
• opposite side.
• The side adjacent to a known angle (?) is called
  the
• adjacent side.

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Three Useful Ratios

• Taking the ratio (fraction) of any two sides of a
  right triangle gives us a number.
• Mathematicians have found that for a right
  triangle with a given angle, the ratio of any two
  sides will be the same, no matter how big or
  small the right triangle is.
• They came up with fancy names for three of these
  side length ratios.

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Three Useful Ratios
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Example

• A 30 Newton force acts at a 27 angle. Find the
  x and y components of this force.

F 30 N
27
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Example

• Draw the triangle. (legs go in x and y
  directions)
• Label the sides and the known angle.
• Use sin, cos, or tan to find missing side.

F 30 N
Fy
27
Fx
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F 30 N
Fy
13.6 N
27
Fx
26.7 N
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Solving Balanced Force Problems

• Four Steps
• Draw a force diagram.
• Write UD and LR. (leave room for work)
• Identify the Up, Down, Left, Right components
  of forces.
• Plug in known values, draw triangle to find
  missing force components, solve.

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Example

• Find how much the object weighs

70º
FT1
FT2 45 N
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Example

• Find how much the object weighs
• Draw the force diagram

70º
FT1
FT2 45 N
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Example

• Find how much the object weighs
• Draw the force diagram
• U D L R
• FT1Y Fg FT1X FT2
• FT1X 45 N
• Now, draw the triangle,
• and Solve it.

70º
FT1
FT2 45 N
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• Remember, we want to
• Find Fg, and Fg FT1Y
• We know FT1X (Adjacent),
• We want FT1Y (Opposite),
• So we use the Tangent

So, Fg 124 N
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How Big Is FT1?

• We know FT1X (Adjacent),
• We want FT1 (Hypotenuse),
• So we use the Cosine

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• Thats All Folks!!!
• Good Luck!