Chapter 7: Energy of a System
THE COURSE THEME is
NEWTON’S LAWS OF MOTION!
• Chs. 5 & 6: Motion analysis with forces.
• NOW (Chs. 7 & 8): An alternative analysis
using the concepts of Work & Energy.
– Easier? My opinion is yes!
• Conservation of Energy: NOT a new law!
– We’ll see that this is just Newton’s Laws of
Motion re-formulated or re-expressed
(translated) from Force Language to Energy
Language.
• We’ve expressed Newton’s Laws of Motion using concepts of
position, displacement, velocity, acceleration, force.
• Newton’s Laws with Forces: Quite general (macroscopic objects). In
principle, could be used to solve any dynamics problem, But, often, they
are very difficult to apply, especially to very complicated systems. So,
alternate formulations have been developed. Often easier to apply.
• One of these is an approach that uses Energy instead of Force as the
most basic physical quantity.
• Newton’s Laws in a different language (Energy). Before we
discuss these, we need to learn vocabulary in Energy Language .
• Energy: Very common term in everyday usage. Everyday
meanings might not coincide with the PHYSICS meaning!
• Every physical process involves energy or energy transfer or
transformations. Energy in physics can be somewhat
abstract.
Sect. 7.1: Systems & Environments
• So far, we’ve expressed Newton’s Laws of Motion in terms
of forces & we’ve considered the dynamics properties of a
particle by talking about various particle properties.
• Now, we take a different approach & talk about Systems &
System Properties.
• System: A small portion of the universe which we focus on in a
given problem. What the system is depends on the problem.
• A System may be, for example:
•
•
•
•
Single particle.
Collection of particles.
A region of space.
May vary in size & shape, depending on the problem
• In addition to a System, we also talk about the system environment.
System interacts with environment at it’s boundaries.
Sect. 7.2: Work Done by a Constant Force
• Work: Precisely defined in physics. Describes what is
accomplished by a force in moving an object through
a distance.
• For an object moving under a Constant Force, Work
done (W) = product of magnitude of displacement (d)
 component of force parallel to displacement (F||):
W = F||Δr = FΔr cosθ
Work by a Constant Force
Work:
W = F||Δr = FΔr cosθ
Δr
NOTE: Valid for a constant force ONLY!
W = F||Δr = FΔr cosθ
• Simple special case: F & Δr are parallel:
θ = 0, cosθ = 1

W = Δr d
• Example: Δr = 50 m, F = 30 N
W = (30N)(50m) = 1500 N m
• Work units: Newton - meter = Joule
1 N m = 1 Joule = 1 J
W = F||d = Fd cosθ
• Can exert a force & do no work!
Could have d = 0  W = 0
Could have F  d
 θ = 90º, cosθ = 0
W=0
Example, walking at
constant v with
grocery bag:
W = F||Δr = FΔr cosθ
Typical Problem:
An object displaced by force F
on a frictionless, horizontal surface.
Free body diagram is shown 
Normal force n & weight mg do no
work in the process, since both
are perpendicular to the displacement.
Normal force, θ = 90°, cosθ = 0
Weight: θ = 270 (or - 90°), cosθ = 0
W = F||Δr = FΔr cosθ
Note:
• W is a scalar (contrast to forces, which are vectors).
• However, W can have either a positive or a
negative sign, since cosθ can be positive or
negative.
• IMPORTANT: Work (as we’ll see) is a
Transfer of Energy: The System either gains
energy (if W > 0) or loses energy (W < 0).
Example 7.1
Example
W = F||Δr =FΔr cosθ
m = 50 kg, FP = 100 N, Ffr = 50 N, θ = 37º
Δr
n