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Drawing and Using
Free-Body Diagrams
Adapted from Minds on Physics Activity #51:
Recognizing and Interpreting Free-Body Diagrams
Goal:
After completing this activity, you should be able to draw valid free-body
diagrams. Also, you should be able to use free-body diagrams to write
expressions for the components of the net force.
Explanation of Activity and Examples:
You will draw valid free-body diagrams for blocks in a variety of situations.
PART A: Drawing Free-Body Diagrams
For each block in each situation, draw and label a valid free-body diagram to describe
the forces acting on it. (Note: You should ignore the forces of air resistance and
buoyancy in this activity.)
E1. A block of mass m is support from the ceiling by two ropes as shown.
Answer:
Explanation:
Notes:
There are two ropes, so
this object: The sketch of
the block there are two
tension forces, labeled
FT1 and/or the
coordinate system may
and FT2. The force of
gravitation points
straight down.
There are many ways
to draw the free-body
diagram for this
object: The sketch of
the block and/or
coordinate system may
be missing, or the
coordinate system may
be moved to one side.
Al.
A block of mass m is suspended from the
ceiling by a light string.
Answer:
Explanation:
A2.
A block having mass m is pulled by a
horizontal force Fa in the positive xdirection along a rough, horizontal
surface.
Answer:
Explanation:
A3.
A block of mass ml is suspended from
the ceiling by a rope. Attached to the
bottom of m1 is a second rope, from
which a second mass, m2, hangs.
Answer:
Explanation:
A4. 100kg block is pushed up a smooth
(frictionless) ramp by a horizontal force,
Fa = 2000N. The ramp makes an angle
of 30° relative to the horizontal.
Answer:
Explanation:
A5. Two blocks, having masses m1 =
5kg and m2 = 10kg, are in contact and sit
side-by-side on a smooth, horizontal
surface. A force Fa directed to the right
is applied to ml and both blocks
accelerate with a = 2m/s2
Answer:
Explanation:
A6. A 5kg block is at rest on a smooth
ramp that makes an angle of 30° with the
horizontal. The block is supported by a
spring placed at the bottom of the ramp.
Answer:
Explanation:
A7. A block of mass m is attached to a
string and released from rest when the
string is horizontal. (Draw the free-body
diagram for the block at the instant
shown.)
Answer:
Explanation:
Summary
How are the forces in a free-body diagram related to the net force exerted on an object?
The net force is the vector sum of all the external forces exerted on the object, and
therefore, it should never appear in a free-body diagram. After all, it is in essence already
there!
How can I make my free-body diagrams as useful as possible?
First of all, you should make sure that the directions of all your forces are accurately
drawn. This will help you find the components of the forces, which will help you find the
net force, and ultimately, the acceleration of the object.
Then, if the sizes of the force vectors are also drawn accurately, often we can identify the
direction of the net force Fnet. By Newton's second law, an object will always accelerate
in the same direction as Fnet. Therefore, the net force implied by your free-body diagram
should always be consistent with the magnitude and/or the direction of the object's
acceleration (if either is known). For example, an object at rest or traveling with constant
velocity has zero acceleration. In this instance, the vectors in your free-body diagram
should add to zero, as closely as possible.
What if the acceleration of the object is non-zero?
Sometimes, we do not know the magnitude of the acceleration, particularly before
we have solved the problem! Often we want to solve for the acceleration of an
object. Even if we do not yet know the magnitude of the acceleration, sometimes we
know its direction. For instance, if an object is sliding along a flat surface, we know
that the velocity always points parallel to the surface. Therefore, all changes in
velocity (as well as accelerations) also point parallel to the surface. Thus, the
direction of the net force is known. Your free-body diagrams should be consistent
with this fact. Fnet should point parallel to the surface; there should be no component
of Fnet perpendicular to the surface.