Download Ch 7--Energy Transfer #1

Chris
McWilliams
Lab:
AP
Review
Sheet
Chapter
07:
Energy
of
a
System
Summary
So
far
we
have
been
using
kinematics
equations
and
force
analysis
to
solve
problems.
Though
these
techniques
are
appropriate
for
many
scenarios,
they
fall
short
in
others
and
it
is
for
these
that
we
will
use
an
energy
approach.
By
examining
the
work
done
on
a
system,
we
can
determine
the
amount
of
energy
transferred
from
one
object
to
another.
We
will
also
review
potential
and
kinetic
energy
and
use
these
principles
to
calculate
the
total
energy
in
a
system.
Equations
Energy
Terms
Work:
a
transfer
of
energy
that
occurs
when
a
force
is
applied
to
an
object
over
a
certain
distance.
⋅
SI
unit
for
work
is
newton meter(N
⋅
Work
W = FΔr cosθ
M)
xf
W =
Dot
product
 
Kinetic
energy:
Energy
associated
with
the
motion
of
a
particle.
€
A • B ≡ ABcos θ
Force
of
a
spring
€
Potential
energy:
Energy
that
represents
the
amount
of
kinetic
energy
that
a
particle
has
the
potential
to
possess.
x
xi
Spring
constant:
the
spring
constant
k
is
a
value
that
is
unique
to
each
individual
spring.
€
∫ F dx
€
Work­kinetic
energy
theorem:
When
work
is
done
on
a
system
and
the
only
change
in
the
system
is
in
its
speed,
the
net
work
done
on
the
system
equals
the
change
in
kinetic
energy
of
the
system.
€
€
Potential
energy
of
a
spring
1
U s = kx 2 2
SI
unit
for
energy
is
joules
(J)
Conservative
force:
a
force
which
satisfies
the
conservative
force
properties,
the
most
prominent
being
gravitational
force
and
€
spring
force.
Fs = −kx
External
Work
1
1
2
2
W ext = ΔK = mv f − mv i 2
2
Chris
McWilliams
Conservative
force
properties:
1.
The
work
done
by
a
conservative
force
on
a
particle
moving
between
any
two
points
is
independent
of
the
path
taken
by
the
particle.
2.
The
work
done
by
a
conservative
force
on
a
particle
moving
through
any
path
for
which
the
beginning
and
endpoint
are
the
same
is
zero.
Practice
Problems
€
€
Equations
Kinetic
energy
K=
1
mv 2 2
Potential
energy
U g = mgh Force­energy
relationship
Fx = −
€
dU
dx Problem
1:
A
man
pulls
box
across
the
floor
with
a
force
of
50.0
N
at
an
angle
of
30°
with
the
horizontal.
Calculate
the
work
done
by
the
force
on
the
box
as
the
box
is
displaced
3.00
m
to
the
right.
€
30°
€
Solution:
W = FΔr cosθ
€
W = (50.0N)(3.00m)(cos(30°)) W = 130J
Chris
McWilliams
Problem
2:
A
spring
is
hung
vertically,
and
an
object
of
mass
m
is
attached
to
its
lower
end.
Under
the
action
of
the
load,
the
spring
stretches
a
distance
d
from
its
equilibrium
position.
A)
If
a
spring
is
stretched
2.0
cm
by
a
suspended
object
having
a
mass
of
0.55
kg,
what
is
the
force
constant
of
the
spring?
B)
How
much
work
is
done
by
the
spring
on
the
object
as
it
stretches
through
this
distance?
Solution:
A)
Fs − mg = 0
Fs = mg
kx = mg
mg (0.55kg)(9.80m /s2 ) k=
=
d
2.0 ×10−2 m
k = 2.7 ×10 2 N /m
B)
€
€
1
W s = 0 − kd 2
2
1
W s = − (2.7 ×10 2 N /m)(2.0 ×10−2 m) 2
2
W s = −5.4 ×10−2 J
Chris
McWilliams
Problem
3:
A
6.0
kg
block
initially
at
rest
is
pulled
to
the
right
along
a
frictionless,
horizontal
surface
by
a
constant
horizontal
force
of
12
N.
Find
the
block’s
speed
after
it
has
moved
3.0
m.
Solution:
1
2
W ext = K f − K i = mv f
2
2W ext
2FΔx
vf =
=
m
m
vf =
€
2 ⋅ (12N)(3.0m) 6.0kg
v f = 3.5m /s