Free-BodyDiagrams
PHYSICSSEMESTER ONE
NANSLO Physics Core Units and Laboratory Experimentsby the North American Network of Science Labs Online,a collaboration between WICHE, CCCS, and BCcampus
is licensed under a Creative Commons Attribution 3.0 Unported License;
based on a work at rwsl.nic.bc.ca.Funded by a grant from EDUCAUSE through the Next
Generation Learning Challenges.
Introduction• Physical objects can be subjected to
several different forces at one time
• Force magnitudes and directions vary
• Forces can be related to each other
• Finding unknown forces may be complicated
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Free-Body Diagrams
• Free-body diagrams (FBDs) are sketches showing the relative magnitude and direction of all forces acting on an object
• They help us see the relationships between the forces
• They assist in organizing our solutions.
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Creating a FBD
Case:Find the net force on a 1.0 kg object (rock, animal, crate, computer …) on a horizontal surface with an applied force of 5.0 N to the right, and a coefficient of kinetic friction of 0.20.
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Creating a FBD
1. Represent the object with a square.
2. Add and label an arrow with the approximate magnitude and direction of one force acting on the object.
3. Repeat step 2 for all forces. 4. Choose a convenient set of
axes.
Fg
nFFk
FBD showing the forces on the object.
y
x
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Other Notes on FBDs
• It is usually easiest to set one axis in the expected direction of motion.
• FBDs only show all forces on a single object. If you need to consider forces on two objects, draw two FBDs.
• Assume that all forces apply to the same point. Otherwise, the question is a torque and rotational equilibrium problem.
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Back to Case: Define Terms
m = 1.0 kg, F = 5.0 N i, μk = 0.20, ΣF =?• We can assume that the acceleration
due to gravity is g = 9.8 m/s2 (this doesn’t need to be stated).
• You can often define most variables within the FBD itself.
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Net Force• We are looking the net force
ΣF = FN + Fg + F + Ff
• Express the forces in components
ΣFxi + ΣFy j= FN j – Fg j + F i – Ff i
ΣFx= F – Ff
ΣFy = FN – Fg
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Using the FBD• There is no motion in the y-direction so,
according to Newton’s First Law, the normal force must balance force of gravity.
ΣFy = FN – Fg = 0
21.0 9.8
9.8
N g
ms
F F
mg
kg
N
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Unported License
Using the FBD
The magnitudes of the normal force and friction are related by the equation
Evaluating,
f k NF F
N
NFf
0.2
8.920.0
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Using the FBD
Using the definitions of the directions, we can write the forces as vectors.
Fg = -9.8 N j, FN = 9.8 N j, F = 5.0 N i
and Ff = -2.0 N i
The net force on the object is then
Fnet = n + Fg + F + Ff = 3.0 N i
The net force is 3.0 N to the right.
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Sample FBDs
• A book at rest on a table top.
• A satellite orbiting earth.
Fg
FN
Fg
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More Sample FBDs
• An apple suspended from a branch.
• A crate being pushed up a ramp. Fg
T
FAFf
FN
Fg coordinates x
y
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Summary• Free-Body Diagrams are useful tools in
organizing the relationships between the forces on a single object. – The object in a FBD is represented by a box.– The forces are represented by arrows with
appropriate directions and relative magnitudes.
• A suitable coordinate system can be selected to simplify calculations.
• Unknown forces can be found using Newton’s Laws of Motion and other physics relationships.
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