This document outlines a lecture on engineering dynamics that covers: 1) The difference between treating an object as a particle versus a rigid body in dynamics problems. 2) Reviewing Newton's second law and how to relate real-world forces to theoretical free body diagrams. 3) The various forces that must be considered in dynamics problems, including gravity, normal forces, friction, spring stiffness, and damping. 4) How to draw free body diagrams to isolate the forces on individual objects in order to apply Newton's second law.

1. Faculty of Engineering
ENG1040
Engineering Dynamics
Particle vs Rigid Bodies
Free body diagrams
Dr Lau Ee Von – Sunway
Lecture 5
ENG1040 – Engineering Dynamics

2. Lecture Outline
Lecture Outline
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
•
•
•
•
•
Particle vs Rigid bodies
Review of Newton’s second law
Free body diagrams
Forces to consider
An Example
Forces to
consider
Free Body
Diagrams
Example
2

3. Particles vs Rigid Bodies
Lecture Outline
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
When we apply Newton’s Laws of Motion we need
to be clear on a number of matters.
• What is a particle?
We can treat a body as a particle if:
Relating reality
to theory
• Its geometry is irrelevant to its motion
Forces to
consider
• Motion is through its mass centre
Free Body
Diagrams
Example
• Rotation is neglected / irrelevant
A particle is a body of negligible
dimensions
For particle dynamics coverage, see Hibbeler Ch. 12-14
3

4. Particles vs Rigid Bodies
Lecture Outline
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
When we apply Newton’s Laws of Motion we need
to be clear on a number of matters.
• What is a rigid body?
We can treat a body as a rigid body if:
• Geometry is relevant to its motion, but it
experiences negligible changes in shape
• Motion can be in rotation or translation
• Motion depends on where forces are applied
Example
For rigid body dynamics coverage, see Hibbeler Ch. 16-18
4

5. Particles vs Rigid Bodies
Lecture Outline
In this example which is a rigid body and which is
a particle?
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
Example
5

6. Kinetics
Lecture Outline
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
Example
In this unit, we will use Newton’s Laws as a
model governing the motion of mechanical
devices.
He deduced three laws of motion.
The Second Law

7. Relating reality to theory
Lecture Outline
How do we transfer what we see in reality to our
mathematical model?
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
F2
Free Body
Diagrams
F1
Example
Answer: using a free
body diagram (FBD)!
mg
7

8. Distributed Loading
Lecture Outline
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
• Equivalent Point Forces:
• Often we have a distributed load. Usually, we can
approximate a distributed load with an equivalent
point force.
• For example, if someone sits on a see-saw, their
mass is distributed across the chair they are sitting
on. However we could approximate them as a
point mass.
Free Body
Diagrams
Example
m1 g
m2 g
8

9. Distributed Loading
Lecture Outline
• Sometimes, we cannot
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
Example
A yacht mast is subject to distributed
loading.
It may not be appropriate to replace the
distributed force with a point force
(depending on what results we need)
9

10. Forces to consider: Gravity
• Gravity affects all masses (and is
referred to as a body force)
• In FBD, the body force (i.e. weight)
always act downwards
Lecture Outline
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
At sea level, the force due to gravity is
defined as:
F
Forces to
consider
Free Body
Diagrams
Example
m g
Typically (in SI units) the acceleration
due to gravity is defined at sea-level as:
g
9.81 m s
2
10

11. Forces to consider: Gravity
Lecture Outline
In FBD, the body force (i.e. weight) always
act downwards
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
Example
11

12. Forces to consider: Normal Force
When a mass is placed
on a surface, the surface
exerts a force normal to
the surface, pushing the
mass outward from the
surface.
Lecture Outline
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
Fn
This models the fact that the
mass does not fall through the
surface.
Example
Newton’s 3rd law shows why it
is needed.
12

13. Forces to consider: Normal
Force
Lecture Outline
Particles vs
Rigid Bodies
In FBD, the normal force, Fn exists whenever
there is contact between two surfaces.
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
Example
When a mass is no longer in contact, Fn = 0
13

14. Forces to consider: Friction
Lecture Outline
• The effect of friction is
modeled as:
Particles vs
Rigid Bodies
F fr
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
•
FN
is the coefficient of friction
(material dependent)
• Fn is the normal force
Free Body
Diagrams
Example
• Kinetic friction
always acts against
the motion of the
object.
14

15. Forces to consider: Friction
Static vs kinetic friction:
Lecture Outline
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
Example
• Typically, there are two friction coefficients:
• A static friction coefficient (µs) which must be overcome for
an object to start slipping,
• A kinetic friction coefficient (µk) which must be overcome for
an object to continue slipping.
• Typically, µs > µk
•
We need bigger force
to overcome a still
object than to
overcome a moving
object
15

16. Forces to consider: Friction
Lecture Outline
A note on static friction:
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
Example
The equation:
F fr , static
static
FN
Provides the maximum static friction force. This has to be
overcomed in order to move an object.
A lower force acting on the object will not cause it to move
16

17. Forces to consider: Friction
Lecture Outline
Particles vs
Rigid Bodies
Determine what happens to the block when an
external force, F of 25 N is applied. (µs = 0.74)
W = mg
Review :
Newton’s 2nd
Law
m = 10kg
Relating reality
to theory
Ffr
Forces to
consider
Free Body
Diagrams
Example
F = 25 N
Fy
ma y
0,
(external force)
FN
FN
mg
98 .1N
Maximum static friction needed to move the block,
F fr , static ,max
F fr , static ,max
static
F
FN
72 .6 N
i.e. Block does not move
17

18. Forces to consider: Friction
Lecture Outline
Particles vs
Rigid Bodies
Determine what happens to the block when an
external force, F of 100 N is applied. (µk = 0.57)
W = mg
Review :
Newton’s 2nd
Law
m = 10kg
Relating reality
to theory
Fr
Forces to
consider
Free Body
Diagrams
Example
F = 100 N
Fy
ma y
0,
(external force)
FN
FN
mg
98 .1N
Maximum static friction needed to move the block,
F fr , static ,max
F fr , static ,max
static
F
FN
72 .6 N
i.e. Block moves (slides) to
the left
18

19. Forces to consider: Friction
Lecture Outline
Particles vs
Rigid Bodies
Determine what happens to the block when an
external force, F of 100 N is applied. (µk = 0.57)
W = mg
Review :
Newton’s 2nd
Law
m = 10kg
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
Example
Fr
+
Fx
Fr
(external force)
FN
ma x
100
F = 100 N
ma x
100
ax
k
FN
4.4m / s 2
10 a x
i.e. Block moves to the
left with an acceleration
of 4.4m/s2
19

20. Forces to consider: Friction
Lecture Outline
Static friction vs kinetic friction for wheels
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
Remember:
Example
We only use kinetic friction when two surfaces are sliding past
each other.
For rolling tyres (without slip), we use the static friction
coefficient.
20

21. Forces to consider: Spring stiffness
Lecture Outline
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
Example
• Linear springs are
modelled with Hooke’s
Law (1660):
F
k x
• k is the spring coefficient.
• x is the displacement.
• Direction of
displacement is
important!
25

22. Forces to consider: Spring stiffness
Lecture Outline
Extended spring
Compressed spring
Particles vs
Rigid Bodies
Mass
Review :
Newton’s 2nd
Law
Relating reality
to theory
Mass
Forces to
consider
Free Body
Diagrams
FBD:
FBD:
Example
26

23. Forces to consider: Damping
Lecture Outline
• Linear damping is modelled with the following equation:
Particles vs
Rigid Bodies
F
c v
Review :
Newton’s 2nd
Law
•
c is the damping
coefficient
Forces to
consider
•
v is the velocity
Free Body
Diagrams
•
All fluids provide
some damping
•
Damping always acts
against the direction
of motion.
Relating reality
to theory
Example
27

24. Forces to consider
•
•
•
•
•
Lecture Outline
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
•
Forces to
consider
In reality, all these forces (and possibly even more) have to be
taken into account, and summed together form the LHS of
Newton’s 2nd law:
F
Free Body
Diagrams
Example
Gravity
Normal Force
Friction
Spring stiffness
Damping forces
m a
•
In this unit, you will be told if you need to include a force. For
example, you may be given a friction coefficient.
•
Usually gravity is always acting, and must always be included.
28

25. A single mass example
Lecture Outline
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
• Commence by defining the coordinate system.
• It is usually better to define +ve in the direction of
motion
• Next draw a representation for the mass.
• Finally draw all the forces acting on the mass.
Relating reality
to theory
y
m g
Forces to
consider
Free Body
Diagrams
FFr
x
Example
Fn
x
y
29

26. A single mass example
y
• Finally, using our FBD,
rewrite Newton’s 2nd law for
the problem in each
dimension:
Lecture Outline
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
x
FFr
Fn
y
y
y
x
mg
x
+
+
x
Fx
m ax
Fx
m ax
Fy
m ay
Fy
m ay
Free Body
Diagrams
Example
30

27. Dealing with multiple masses
Lecture Outline
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
• Where there are multiple, independently moving
masses, ISOLATE the body and draw one FBD for
each mass.
• Apply Newton’s 2nd law for each mass in isolation.
• How many equations would you have for this system?
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
Example
31

28. Free Body Diagrams
Lecture Outline
What are the forces acting on this body?
Particles vs
Rigid Bodies
Draw simple diagrams (FBD) for each component
(each isolated body)
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
Example
T′
T′

29. Dealing with elastic objects
Lecture Outline
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
• In reality, all masses have some elastic
properties.
• We can assume there are no elastic properties if
the body is rigid.
• In order to model this, we separate out the forces
acting on the mass:
m g
Forces to
consider
Free Body
Diagrams
Example
y
k x
Fn
33

30. Rotation
Lecture Outline
• Rotation of a mass adds further complexity to a
problem. This will be considered from lecture 7.
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
Example
34

31. Free Body Diagrams
Lecture Outline
Particles vs
Rigid Bodies
Review :
Newton’s 2nd
Law
Relating reality
to theory
Forces to
consider
Free Body
Diagrams
Example
• Example
• An elevator E has a mass of 500 kg and the
counterweight at A as a mass of 150 kg.
• If the elevator attains a
speed of 10 m/s after it
rises 40 m, determine the
constant force developed
in the cable at B.
• Neglect the mass of the
pulleys and cable.

32. Conclusions
• Free Body Diagrams (FBD) allow us to separate
a difficult problem into a series of simpler
problems
• They also remind us of all the forces acting on all
the components of a mechanical device.
• They are essential to solving dynamics problems
successfully
44