1) A free-body diagram (FBD) represents all the unknown forces acting on a body when it is isolated from its surroundings. 2) Common connections shown in FBDs include springs and cables/pulleys. Springs exert a force proportional to their elongation/compression. Tension in cables acts in the direction of the cable and has a constant magnitude. 3) Drawing an FBD involves outlining the body, showing all active and reactive forces, and labeling known and unknown forces.

1. 3.2 The Free-Body Diagram
Best representation of all the unknown
forces (∑F) which acts on a body
A sketch showing the particle “free” from
the surroundings with all the forces acting
on it
Consider two common connections in this
subject – Spring
– Cables and Pulleys

2. 3.2 The Free-Body Diagram
Spring
- Linear elastic spring: change in length is
directly proportional to the force acting on it
- spring constant or stiffness k:
defines the elasticity of
the spring
- Magnitude of force when spring
is elongated or compressed
F = ks

3. 3.2 The Free-Body Diagram
Spring
where s is determined from the difference in
spring’s deformed length l and its
undeformed length lo
s = l - lo
- If s is positive, F “pull”
onto the spring
- If s is negative, F “push”
onto the spring

4. 3.2 The Free-Body Diagram
Example
Given lo = 0.4m and k = 500N/m
To stretch it until l = 0.6m, A force, F = ks
=(500N/m)(0.6m – 0.4m) = 100N is needed
To compress it until l = 0.2m,
A force, F = ks
=(500N/m)(0.2m – 0.4m)
= -100N is needed

5. 3.2 The Free-Body Diagram
Cables and Pulley
- Cables (or cords) are assumed to have
negligible weight and they cannot stretch
- A cable only support tension or pulling force
- Tension always acts in the
direction of the cable
- Tension force in a continuous
cable must have a constant
magnitude for equilibrium

6. 3.2 The Free-Body Diagram
Cables and Pulley
- For any angle θ, the cable is
subjected to
a constant tension T
throughout its length

7. 3.2 The Free-Body Diagram
Procedure for Drawing a FBD
1. Draw outlined shape
- Isolate particle from its surroundings
2. Show all the forces
- Indicate all the forces
- Active forces: set the particle in motion
- Reactive forces: result of constraints and
supports that tend to prevent motion

8. 3.2 The Free-Body Diagram
Procedure for Drawing a FBD
3. Identify each forces
- Known forces should be labeled with
proper magnitude and direction
- Letters are used to represent
magnitude and directions of unknown
forces

9. 3.2 The Free-Body Diagram
A spool is having a weight
W which is suspended
from the crane bottom
Consider FBD at A since
these forces act on the
ring
Cables AD exert a resultant
force of W on the ring
Condition of equilibrium is
used to obtained TB and TC

10. 3.2 The Free-Body Diagram
The bucket is held in
equilibrium by the cable
Force in the cable =
weight of the bucket
Isolate the bucket for
FBD
Two forces acting on
the bucket, weight W
and force T of the cable
Resultant of forces = 0
W=T

11. 3.2 The Free-Body Diagram
Example 3.1
The sphere has a mass of 6kg and is
supported. Draw a free-body diagram of
the
sphere, the cord
CE and the knot at C.

12. 3.2 The Free-Body Diagram
Solution
FBD at Sphere
Two forces acting,
weight and the
force on cord CE.
Weight of 6kg
(9.81m/s2) = 58.9N

13. 3.2 The Free-Body Diagram
Solution
Cord CE
Two forces acting, force
of the sphere and force
of the knot
Newton’s Third Law: FCE
is equal but opposite
FCE and FEC pull the cord
in tension
For equilibrium, FCE =
FEC

14. 3.2 The Free-Body Diagram
Solution
FBD at Knot
Three forces acting, force by cord CBA, cord CE
and spring CD
Important to know that
the weight of the sphere
does not act directly on
the knot but subjected to
by the cord CE