Adding Force Vectors

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Adding Force Vectors

• In Class Demo
• PWYR
• Example Problem

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Adding Force Vectors

• When more than one force is acting on an object,
  we have to add the vectors
• The resulting force will be a combination of the
  individual forces
• Before adding two non-parallel vectors, we first
  must break each vector into its horizontal and
  vertical components

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PWYR Adding Multiple Vectors

• Just for fun, Juliana and Margulies are trying to
  drag a large wooden railroad tie across their
  back yard. In order to get the railroad tie to
  travel in a straight line, the girls discovered
  that Margulies needed to pull at an angle of
  78.8 with a force of 95.2 N and Juliana needed
  to pull at an angle of 23.6 because she could
  only pull with a force of 20.2 N. What force did
  the girls apply to the railroad tie?

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PWYR Adding Multiple Vectors

• First of all, we know that the railroad tie
  travels in the y-direction only. This must mean
  that the forces in the x-direction must be
  balanced. Therefore
• The force applied to the railroad tie would then
  come from the component in the y-direction of
  each of the girls forces.

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PWYR Adding Multiple Vectors

• First we need to label the diagram.

FM
FJ
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PWYR Adding Multiple Vectors

• Now we can find the combined force the girls
  apply to the railroad tie. Remember that the
  forces in the x-direction cancel each other out.

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PWYR Adding Multiple Vectors

• Margulies force in the y-direction is

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PWYR Adding Multiple Vectors

• To find the total force that the railroad tie
  feels, add the y-components of each of the girls
  force.
• The railroad tie feels 101.5N pulling it in the
  y-direction.

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PWYR Adding Multiple Vectors

• The only way the railroad tie can move in the
  y-direction is if the x direction is balanced.

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PWYR Adding Multiple Vectors

• The forces in the x-direction have the same
  magnitude but opposite direction, therefore the
  forces are balanced, and the object should not
  accelerate in the x-direction.
• The angle at which the girls apply their forces
  determines how much of their force is applied in
  each direction. Since Juliana cannot pull as
  hard as Margulies she needs to pull at a smaller
  angle to match Margulies x-direction force.

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PWYR Adding Multiple Vectors

• If Juliana were to match the Margulies angle,
  more of Julianas force would be in the
  y-direction which would accelerate the railroad
  tie. At the same time less of her force would be
  in the x-direction, so the tie would drift to the
  right, toward Margulies.

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Adding Vectors Example 1

• Jackie and Michelle are working together to push
  a box. Jackie applies a force of 843 N and
  Michelle applies a force of 247N. What is the
  magnitude of the resulting force? Does the box
  travel directly to the right?

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Adding Vectors Example 1

• First break the two force vectors into their
  horizontal and vertical directions
• Now find the value of each component

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Adding Vectors Example 1
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Adding Vectors Example 1
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Adding Vectors Example 1

• Add parallel components
• FT is the total force
• The box feels a force of 974N in the x direction
  and 99 N in the y direction.
• At this point we can say that the box will move
  to the right and up a little, since the forces in
  the y-direction do not completely cancel.

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Adding Vectors Example 1

• Use can use the Pythagorean Theorem to find the
  Magnitude of the resultant vector