Download Chapter 4 - Department Of Computer Science

Phys141 Principles of Physical Science
Chapter 4
Work and Energy
Instructor: Li Ma
Office: NBC 126
Phone: (713) 313-7028
Email: [email protected]
Webpage: http://itscience.tsu.edu/ma
Department of Computer Science & Physics
Texas Southern University, Houston
Sept. 20, 2004
Topics To Be Discussed
Work
 Kinetic Energy and Potential Energy
 Conservation of Energy
 Power

About Work & Energy

Common meaning of Work
– Work is done to accomplish some task or
job
– When work is done, energy is expended
Mechanically, Work involves force &
motion
 Energy is a concept, is abstract, is
stored work

Work

The work done by a constant force F
acting on an object is the product of the
magnitude of the force (or component of
force) and the parallel distance d
through which the object moves while
the force is applied
W = F·d
Work (cont)

If only apply force but no motion, then there is
technically no work
 Only the component of force in the direction
of motion has contribution to work
 Example:
Fh
W = F ·d
h
Fv
d
F
Work (cont)

Unit of Work
– In Metric system: N·m, or joule (J)
– In British system: pound·foot (ft·lb)

Newton’s third law force pair
– When the force is applied, work is done
against this force pair
– Moving box forward: do work against
friction
– Lifting the box: do work against gravity
Energy

Common sense:
– when work is done, some physical quantity
changes: work against gravity, height is
changed; work against friction, heat is
produced; etc.

With concept of energy:
– When work is done, there is a change in
energy, and the amount of work done is
equal to the change in energy
Energy (cont)
Energy is described as a property
possessed by an object or system
 Energy is ability to do work:

– An object or system that possess energy
has the ability or capability to do work

Unit of Energy
– Same as work
Work and Energy

Doing work is the process by which
energy is transferred from one object to
another:
– When work is done by a system, the
amount of energy of the system decreases
– When work is done on a system, the
system gains energy

Both work and energy are scalar
quantities
Work and Energy (cont)

One scenario: when work is done on an
object (at rest initially), the object’s
velocity changes
d = ½a·t2, v = a·t, F = m·a, W = F·d
W = m·a·d = m·a·(½a·t2)
= ½ m·(a·t)2 = ½ m·v2
W = ½ mv2
 This amount of work is now energy of
motion, or kinetic energy
So
Work and Energy (cont)
Another scenario: when work is done on
an object, the object’s position changes
 There is also a change in energy, since
the object has potential ability to leave
that position and do work
 This amount of work is energy of
position, or potential energy
 Kinetic & Potential energy: two forms of
Mechanical energy

Kinetic Energy

Kinetic energy is the energy an object
possesses because of its motion, or
simply stated, it is energy of motion:
kinetic energy = ½ x mass x (velocity)2
Ek = ½ mv2
Kinetic Energy (cont)

If the work done goes into changing the
kinetic energy, then
work = change in kinetic energy
W = ΔEk = Ek2 – Ek1
So W = ½ mv22 - ½ mv21
Potential Energy
An object does not have to be in motion
to have energy
 Potential energy is the energy an object
has because of its position or location,
or simply, it is energy of position
 Examples: lifted weight, compressed or
stretched spring, drawn bowstring

Potential Energy (cont)
One scenario: Lift an object at a (slow)
constant velocity up to a height h from
the ground (or saying sea level)
 Work is done against gravity

Work = weight x height
W = m·g·h
(W = F·d)
Gravitational Potential Energy
The object has potential ability to do
work, it has energy
 Gravitational potential energy is equal to
the work done against gravity

gravitational potential energy = weight x height
Ep = m·g·h
More generally, Ep = m·g·Δh
Conservation of Energy

Understanding of conservation
– Energy can be neither created nor
destroyed
– Energy can change from one form to
another, but the amount remains constant
– Energy is always conserved

The total energy of an isolated system
remains constant
Conservation of Mechanical
Energy

Ideal systems
– Energy is only in two forms: kinetic and
potential

Conservation of mechanical energy
– The mechanical energy of the ideal system
remains constant
Initial Energy = Final Energy
(Ek + Ep)1 = (Ek + Ep)2
(½ mv2 + mgh)1 = (½ mv2 + mgh)2
Conservation of Mechanical
Energy (cont)

Want the velocity of a freely falling
object when fallen a height of Δh:
– velocity and acceleration:
Vt = gt, Δh = ½ gt2 (Δh = d)
=> Vt = (2gΔh) ½
– Conservation of mechanical energy:
(½ mv2 + mgh)i = (½ mv2 + mgh)t
½ m(v2t - v2i ) = mg(hi - ht)
=> Vt = (2gΔh) ½
Power
Do same thing in different amount of
time: the rate at which the work is done
is different
 Power is the time rate of doing work
power = work / time
P = W/t = F·d/t
 Unit: watt in the SI, 1 W = 1 J/s

Power (cont)
The greater the power of an engine or
motor, the faster it can do work
 Power may be thought of as energy
produced or consumed divided by the
time taken
P = E/t
=> E = p·t
