Force and Its Representation
Drawing Free-Body Diagrams
Free-body
diagrams are diagrams used to show the relative magnitude
and direction of all forces acting upon an object in a given
situation. A free-body diagram is a special example of the
vector diagrams which were discussed in
an earlier unit. These diagrams will be used throughout
our study of physics. The size of the arrow in a free-body
diagram is reflects the magnitude of the force. The
direction of the arrow shows the direction which the force
is acting. Each force arrow in the diagram is labeled to
indicate the exact type of force. It is generally customary
in a free-body diagram to represent the object by a box and
to draw the force arrow from the center of the box outward
in the direction which the force is acting. An example of a
free-body diagram is shown at the right.
The free-body diagram above depicts four forces acting upon the object. Objects do not necessarily always have four forces acting upon them. There will be cases in which the number of forces depicted by a free-body diagram will be one, two, or three. There is no hard and fast rule about the number of forces which must be drawn in a free-body diagram. The only rule for drawing free-body diagrams is to depict all the forces which exist for that object in the given situation. Thus, to construct free-body diagrams, it is extremely important to know the various types of forces. If given a description of a physical situation, begin by using your understanding of the force types to identify which forces are present. Then determine the direction in which each force is acting. Finally, draw a box and add arrows for each existing force in the appropriate direction; label each force arrow according to its type. If necessary, refer to the list of forces and their description in order to understand the various force types and their appropriate symbols.
Practice
Apply the method described in the paragraph above to construct free-body diagrams for the various situations described below. Answers are shown and explained at the bottom of this page.
- A book is at rest on a table top. Diagram the forces
acting on the book. See answer.
- A girl is suspended motionless from the ceiling by
two ropes. Diagram the forces acting on the combination
of girl and bar. See answer.
- An egg is free-falling from a nest in a tree. Neglect
air resistance. Diagram the forces acting on the egg as
it is falling. See answer.
- A flying squirrel is gliding (no wing
flaps) from a tree to the ground at constant
velocity. Consider air resistance. Diagram the forces
acting on the squirrel. See answer.
- A rightward force is applied to a book in order to
move it across a desk with a rightward acceleration.
Consider frictional forces. Neglect air resistance.
Diagram the forces acting on the book. See
answer.
- A rightward force is applied to a book in order to
move it across a desk at constant velocity. Consider
frictional forces. Neglect air resistance. Diagram the
forces acting on the book. See
answer.
- A college student rests a backpack upon his shoulder.
The pack is suspended motionless by one strap from one
shoulder. Diagram the vertical forces acting on the
backpack. See answer.
- A skydiver is descending with a constant velocity.
Consider air resistance. Diagram the forces acting upon
the skydiver. See answer.
- A force is applied to the right to drag a sled across
loosely-packed snow with a rightward acceleration.
Diagram the forces acting upon the sled. See
answer.
- A football is moving upwards towards its peak after
having been booted by the punter. Diagram the
forces acting upon the football as it rises upward
towards its peak. See answer.
- A car is coasting to the right and slowing down.
Diagram the forces acting upon the car. See
answer.
Answers
Answers to the above exercise are shown here. If you have difficulty drawing free-body diagrams, then you ought to be concerned. Continue to review the the list of forces and their description and this page in order to gain a comfort with constructing free-body diagrams.
1. A book is at rest on a
table top. A free-body diagram for this situation looks like
this:
2. A girl is suspended motionless from the
ceiling by two ropes. A free-body diagram for this situation
looks like this:
3. An egg is free-falling from a nest in a tree. Neglect air resistance. A free-body diagram for this situation looks like this:
4. A flying squirrel is gliding (no
wing flaps) from a tree to the ground at
constant velocity. Consider air resistance. A free-body
diagram for this situation looks like this:
5. A rightward force is applied to a book
in order to move it across a desk with a rightward
acceleration. Consider frictional forces. Neglect air
resistance. A free-body diagram for this situation looks
like this:
6. A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance. A free-body diagram for this situation looks like this:
7. A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. A free-body diagram for this situation looks like this:
8. A skydiver is descending with a constant velocity. Consider air resistance. A free-body diagram for this situation looks like this:
9. A force is applied to the right to drag a sled across loosely-packed snow with a rightward acceleration. A free-body diagram for this situation looks like this:
10. A football is moving upwards towards its peak after having been booted by the punter. A free-body diagram for this situation looks like this:
Return to Info on Free-body diagrams
Return to on-line Force Description List
11. A car is coasting to the right and slowing down. A free-body diagram for this situation looks like this:
