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Graphing the Four Forces
| Background: |
The concept of force can be effectively represented on a graph
using the Cartesian coordinate system. By representing four of the
aeronautical forces (lift, drag, thrust, weight) on a graph, students
can visualize both parts of the definition of force: magnitude and
direction.
In the lesson, Computing the Net Force, students learned how to
calculate the magnitude and direction of the net force, given two
parallel forces. In this lesson, students will use information about
four forces to make a decision about whether or not an airplane
is (theoretically!) able to fly.
This lesson concentrates on the actual representation of the forces
on a graph. If, after combining the four forces, the net force is
plotted in the upper right quadrant of the graph, then we will draw
the conclusion that the airplane is able to fly.
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| Directions: |
Have students examine the graph on the following page. Point out
that lift is "up toward the top of the paper", weight is "down toward
the bottom of the paper", thrust is "forward toward the right of
the paper" and drag is "back toward the left of the paper".
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Using the magnitudes below, follow the steps and plot your points
on the graph on the previous page.
| Weight |
3 units |
| Lift |
7 units |
| Drag |
2 units |
| Thrust |
5 units |
The forces can be plotted in any order. For example: |
| Step 1: |
Start at the origin and count down three squares (for Weight).
Plot a small dot. |
| Step 2: |
From that small dot (do not start again from the origin!) count
up seven squares (for Lift). Plot another small dot. |
| Step 3: |
From that small dot (do not start again from the origin!) count
to the left two squares (for Drag). Plot another dot. |
| Step 4: |
From that small dot (do not start again from the origin!) count
to the right 5 squares (for Thrust). Plot a large dot. This is the
representation of the net force. |
See the graphs on the following page for guidance, then continue.
| Step 5: |
Determine whether or not the airplane is flyable. If the net force
is plotted in the upper right quadrant, the airplane is flyable.
If the net force is plotted in the upper left quadrant, the airplane
is not flyable - it has too much drag.
If the net force is plotted in the lower left quadrant, the airplane
is not flyable - it has too much drag and weight.
If the net force is plotted in the lower right quadrant, the airplane
is not flyable - it has too much weight.
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Exercise 1
| Directions: |
Use the steps from the previous example to plot the following
magnitudes. After you plot the net force, make a decision about
whether or not the airplane is flyable.
| Weight |
4 units |
| Lift |
10 units |
| Drag |
2 units |
| Thrust |
10 units |
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| Question 1: |
This plane is / is not flyable. |
| Question 2: |
If it is not, tell what force or forces are too great for the airplane
to fly. |
Exercise 2
| Directions: |
Use the steps from the previous example to plot the following
magnitudes. After you plot the net force, make a decision about
whether or not the airplane is flyable.
| Weight |
8 units |
| Lift |
4 units |
| Drag |
6 units |
| Thrust |
4 units |
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| Question 1: |
This plane is / is not flyable. |
| Question 2: |
If it is not, tell what force or forces are too great for the airplane
to fly. |
Graphing the Four Forces
Exercise 1 - Key
Starting at the origin:
the end of the weight arrow will be at (0,-4)
the end of the lift arrow will be at (0,6)
the end of the drag arrow will be at (-2,6)
the end of the thrust arrow will be at (8,6)
since (8,6) is in the upper right quadrant, the airplane is flyable
Note: the arrows may be drawn in any order, you will always end up
at the same place!
Exercise 2 - Key
Starting at the origin:
the end of the weight arrow will be at (0,-8)
the end of the lift arrow will be at (0,-4)
the end of the drag arrow will be at (-6,-4)
the end of the thrust arrow will be at (-2,-4)
since (-2,-4) is in the lower left quadrant, the airplane is not flyable
both weight and drag are too great
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