Free Body
Digram
Free Body Diagram
Free-body diagrams are diagrams used to show the relative magnitude and
direction of all forces acting upon an object in a given situation.
The size of the arrow in a free-body diagram reflects the magnitude of the force.
The direction of the arrow shows the direction that 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
that the force is acting
Types of Forces
To construct free-body diagrams, it is extremely important to know the various types of forces:
A force is a push or pull acting upon an object as a result of its interaction with another object.
Practice
1. A book is at rest on a tabletop.
2. A gymnast holding onto a bar, is suspended motionless in mid-air.
The bar is supported by two ropes that attach to the ceiling. Diagram
the forces acting on the combination of gymnast and bar.
3. An egg is free-falling from a nest in a tree. Neglect air resistance.
Practice
4. A flying squirrel is gliding (no wing flaps) from a tree to the ground at
constant velocity. Consider air resistance.
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.
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.
Practice
7. A college student rests a backpack upon his shoulder. The pack is
suspended motionless by one strap from one shoulder.
8. A skydiver is descending with a constant velocity. Consider air
resistance.
9. A force is applied to the right to drag a sled across loosely packed
snow with a rightward acceleration. Neglect air resistance.
Practice
10. A football is moving upwards towards its peak after having
been booted by the punter. Neglect air resistance.
11. A car is coasting to the right and slowing down. Neglect air
resistance.
How to Identify Free-Body Diagrams for Objects on an
Inclined Plane
Inclined planes: Those are surfaces that are at an angle in relation to a horizontal line.
How to Identify Free-Body Diagrams for Objects on an
Inclined Plane
Normal force: It is a force exerted on an object that is supported by a
surface. The normal force is always perpendicular to the surface.
Weight: It is the force of attraction on an object due to gravity. This
force has always a downward vertical direction (pointing to the
center of the Earth). It is calculated by m*g, where m is the mass of
the object in kilograms, and g is the acceleration of gravity in m/s2.
FW=FN
Weight and normal force on horizontal
planes.
How to Identify Free-Body Diagrams for Objects on an
Inclined Plane
In inclined planes, there are usually 3 forces applied over the
object.
Normal force: perpendicular to the surface.
Weight: Vertical and downwards. It is usually decomposed into
two components. One of these components forces the object to
move down the plane and the other component balances the normal
force.
Friction (Ff): Resistance to the motion. Opposite to the component
of weight that pulls the object for moving down the plane.
Common forces on an inclined plane situation.
Examples of How to Identify Free-Body Diagrams for
Objects on an Inclined Plane
Example 1 Select the best diagram (among the three options in figure 5) that best describes an
object on an inclined plane with net force equals zero.
Diagram 'a' is INCORRECT. It represents a net force equals zero (vertical forces balance each other and horizontal forces
are not present). However, the object is over a horizontal line, not an inclined plane.
Diagram 'b' is INCORRECT. The object is on an inclined plane, however, the forces alongside the plane line do not
balance each other. There is clearly a net force different than zero pointing towards down the inclined plane.
Diagram 'c' is CORRECT. The object is on an inclined plane and all opposite forces seem to balance each other. Resulting
in a net force equal to zero.
Example 2 Among the two diagrams presented in figure 7, which one displays a weight component that is
compatible with an accelerated movement on an inclined plane?
The resultant force is the diagonal of a parallelogram
Resultant force (in right angle triangle)
4N
Fresultant =square root (42 + 42)