Transcript The Work Energy Theorem - Mr. Cheng

The Work Energy Theorem
Textbook: 4.1 - 4.3
Homework:
pg. 183 # 2, 5, 6, 7
pg. 188 # 2, 5, 6, 7, 8
pg. 194 # 1 – 7
Work
• Work is the energy transferred to an object by
a force F, through a displacement d
• W=Fdcos
– W = [J], F = [N], d = [m]
James Prescott Joule (1818 – 1889):
- English physicist
- Discovered relationship btw. heat & mechanical work (energy)
- Conservation of Energy Theorem
Mechanical Energy
is a combination of two fundamental types of
energy:
• Kinetic energy (the energy of motion)
• Potential energy (energy that is stored)
- Gravitational Potential Energy
- Elastic Potential Energy
Kinetic Energy
• Work done by the net force causes a change in
speed
• The kinetic energy of an object of mass m, in
kg, and speed v, in m/s:
Gravitational Potential Energy
• “stored energy” in an object at a
particular height w.r.t. a reference point.
W.E.T. (Work-Energy Theorem)
• The total work done on an object equals the change in the
object’s kinetic energy and/or gravitational potential energy.
Wtotal  EK
Wtotal  EK 2  EK 1
1 2 1 2
F  d  mv2  mv1
2
2
Wtotal  Eg
Wtotal  Eg 2  Eg1
F  d  mgh2  mgh1
Ek = -Eg
Ex 1: By what factor does a cyclist’s kinetic
energy increase if the cyclist’s speed:
(a) doubles
(b) triples
(c) increases by 37%
Ex 2. A 45-g golf ball leaves the tee with a speed of 43 m/s after
a golf club strikes it.
(a) Determine the work done by the club on the ball.
(b) Determine the magnitude of the average force applied by the
club to the ball, assuming that the force is parallel to the motion
of the ball and acts over a distance of 2.0 cm.

A 27g arrow is shot horizontally. The bowstring exerts an average force of 75 N
on the arrow over a distance of 78 cm. Determine, using the workenergy
theorem, the maximum speed reached by the arrow as it leaves the bow
Elastic Potential Energy
& Conservation of Energy
Textbook: 4.5
Homework: WS – Spring problems
What is Hooke’s LAW
A Hookean System (i.e. spring,
wire, rod etc) is one that returns
to its original configuration after
being distorted and then released.
Hooke’s Law …cont
Fapplied on spring
Slope = k = spring constant
x, (i.e distance from equilibrium)
Potential Elastic Energy
Fapplied on spring
Work
done
x, (i.e distance from equilibrium)
Elastic Potential Energy
• The energy stored in a spring of spring
constant k [N/m] compressed or extended
from equilibrium a distance x [m] is:
The Law of Conservation of Energy
• Energy cannot be created or destroyed, but only
transferred from one form to another without any
loss.
• The total energy of a closed system is constant.
ET 1  ET 2
Elastic Potential Energy
& Simple Harmonic Motion (SHM)
Textbook: 4.5
Homework: pg 214-215 # 16 – 21
pg 217-218 # 23 – 28
Simple Harmonics Motion (SHM)
- Motion that obeys Hooke’s law
- Periodic and follows sinusoidal function
Period of SHM
4 2 r
ac 
T2
4 2 r
2
T 
ac
T 
4 2 r
ac
T  2
r
ac
a x  ac , x  r
T  2
T  2
x
ax
x
Fs
m
T  2
x
kx
m
T  2
m
k
SHM & Damping:
The effect of friction on SHM is called damping.
• Three Types of Damping:
1) Overdamping: Oscillation ceases and the
mass slowly returns to equilibrium position
2) Critical damping: Oscillation ceases and
the mass moves back to equilibrium position
as fast as theoretically possible without
incurring further oscillations. This special
point is never perfectly reached in nature
3) Underdamping: Oscillation is continually
reduced in amplitude
Decreasing amplitude
“Envelope” of the
damping motion
Pg 214 # 18.