Transcript ICNS 132 : Work, Energy and Power

ICNS 132 : Work,
Energy and Power
Weerachai Siripunvaraporn
Department of Physics, Faculty of Science
Mahidol University
email&msn : [email protected]
What is in this chapter?
Work & Power
Energy : KE & PE
Conservation of Energy
Introduction to Energy
•A variety of problems can be solved with Newton’s Laws and
associated principles.
•Some problems that could theoretically be solved with
Newton’s Laws are very difficult in practice.
– These problems can be made easier with other techniques.
•The concept of energy is one of the most important topics in
science and engineering.
•Every physical process that occurs in the Universe involves
energy and energy transfers or transformations.
•Energy is not easily defined.
CH7
Introduction
System & Environments
Work
To understand what work means to the physicist, a force is applied
to a chalkboard eraser, and the eraser slides along the tray.
Which is showing the most effective way in moving the eraser?
If we want to know how effective the force is in moving the object, we
must consider not only the magnitude of the force but also its direction.
Work
So, work is the quantity to
measure how effective the
force is in moving the
object.
Negative
Positive
F and r are in the opposite
direction, i.e. cos  < 0
F and r are in the same
direction, i.e. cos  > 0
F
F
Zero
r
F=0
r
r = 0
F·r = 0,
i.e cos  = 0
F
or,  = 90˚
r
EXAMPLES:
F r
Positive
F and r are in the same
direction, i.e. cos  > 0
r
Negative
F and r are in the opposite
direction, i.e. cos  < 0
mg
F·r = 0,
i.e cos  = 0
or,  = 90˚
mg

r
--> Wmg = 0
n

r
--> Wn = 0
F1
F2
x1
W = F1x1 + F2x2 + F3x3
F3
x2
x3
i.e. Work done by varying force is
equal to the area under the curve
of F and x
Energy
F
Two external forces: applying force F and friction fk
Applying force F  positive work
Friction force f  negative work
 W = Fd - fkd
Potential energy is the energy associated with the configuration of a
system of objects that exert forces on each other.
It is present in the Universe in various forms, including gravitational,
electromagnetic, chemical, and nuclear.
Here, we consider two types of potential energy:
Gravitational potential energy and Elastic potential energy.
Reference level ---------------
H
h
Elastic Potential
Energy:
Hooke’s law
Hooke’s law
x is the position of the block relative
to its equilibrium (x=0) position
k is a positive constant called the
force constant or the spring constant
“the force required to stretch or
compress a spring is proportional to
the amount of stretch or compression
x”  Hooke’s law.
The value of k is a measure of the
stiffness of the spring. Stiff springs
have large k values, and soft springs
have small k values.
The units of k are N/m.
The negative sign signifies that the
force exerted by the spring is always
directed opposite to the displacement
from equilibrium.
Chemical energy is stored in your
body.
K.E. of runner -> P.E.
E  0
Closed system
No energy can get in nor get out.
Energy is therefore conserved.
Ei  Ef
Mechanical Energy = Kinetic Energy + Potential Energy.
Durian is dropped from the top of a building.
E  P.E.  mgh
P.E. K.E.
E  K.E.  P.E.
h
E  K.E.  P.E.
1 2
E  K.E.  mv
2
P.E. K.E.
P.E. K.E.
P.E. K.E.
reference
Example
A ball is dropped from a height of 2 m. Find its speed half way
down.
A
v0
U  2mg
v0
U  1mg
v0
U 0
B
vv
U  1mg
vv
U 0
vv
U   mg
C
U 0
A  2mg  0
1 2
B  1mg  mv
2
1 2
2mg  1mg  mv
2
U  1mg
A  1mg  0
1
B  0  mv 2
2
1
1mg  mv 2
2
U  2mg
A00
1
B  1mg  mv2
2
1
0  1mg  mv2
2
Conservation of Energy :
Conservative and Non-conservative forces
Huuu-raayy !!!
Friction
(non-conservative)
Example
A stone is thrown with an initial velocity of u at an angle . Using
the conservation of energy, show that the maximum height
reached is
(u sin  )
H
2g
v  u cos
u
H

2