Transcript Part I

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.
• Up to now, we’ve expressed Newton’s Laws of Motion using the
concepts of position, displacement, velocity, acceleration & force.
• Newton’s Laws with Forces are quite general & work well
for describing the dynamics of 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 which are often easier to apply.
• One of these is an approach that uses ENERGY instead
of Force as the most basic physical quantity.
• The discussion of Work & Energy in Chs. 7 & 8 is actually
just a statement of
Newton’s Laws in Energy Language.
• Before we discuss this, we need to learn some Energy
Language vocabulary.
• Energy: A 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.
• In our discussions of Newton’s Laws of Motion
in terms of Forces we’ve considered the
dynamical properties of a particle by talking
about various Particle Properties.
• Now, we’ll take a different approach & talk about
Systems & System Properties
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 is precisely defined in physics. It describes
what is accomplished by a force in moving an
object through a distance.
• For an object moving under a Constant Force, the work
done (W) is defined as the product of magnitude of the
displacement (Δr) & the component of the force parallel
to the displacement (F||):
W  F||Δr  FΔrcosθ
Work Done by a Constant Force
Work: W  F||Δr  FΔr cosθ
Δr 
Δr
NOTE: This form is valid for a constant force ONLY!
W = F||Δr = FΔr cosθ
• Consider a simple special case when F & d
are parallel:  θ = 0, cosθ = 1
 W = FΔr
• Example: Δr = 50 m, F = 30 N
W = (30N)(50m) = 1500 N m
SI Work Units:
Newton - meter  Joule
1 N m = 1 Joule = 1 J
Work: W  F||Δr  FΔr cosθ
• Its possible to exert a
force & do no work!
• Could have Δr = 0
W=0
• Could have F  Δr
 θ = 90º, cosθ = 0
W=0
• Example, walking at
constant v with a
grocery bag:
W  F||Δr  FΔr cosθ
An object is displaced by a force F on a frictionless,
horizontal surface. The free body diagram is show here
The normal force n & the weight mg do no work in the
process, since both are perpendicular to the displacement.
For the Normal Force, n,
θ = 90°, cosθ = 0
For the Weight mg,
θ = 270 (or - 90°), cosθ = 0
W = F||Δr = FΔr cosθ
Note
• W is a scalar (in 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