06prob_11

06prob_11 - Assigment#6 Page 1 of 3 UC Davis Physics 9A-C...

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Unformatted text preview: Assigment #6, 5/6/11 Page 1 of 3 UC Davis Physics 9A-C Assignment #6 Cole [7.9]

a)

The
normal
force
is
perpendicular
to
the
displacement,
so
it
does
no
work.

The
work
 done
by
gravity
is
 mgh 
=
 mgR 
=
0.
98
J.

b)

When
nonconservative
forces
do
work,
they
change
 the
energy
of
the
system:

 W f 
=
E
-
Eø

 
 õ

W f 
=
 1 2 mv 2-
mgh

õ

 v = 2 gh + W f m ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 

=

 v = 2 9.8m/s 2 ( ) 0.5 m ( ) + − 0.22 J 0.2 kg ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 
=
2.8
m/s. [7.30]

The
magnitude
of
the
friction
force
on
the
book
is 

 f

=

 μ k mg 
=
(0.25)(1.5
kg)(9.80
/s 2 )
=
3.68
N.

a)
The
work
done
during
each
part
of
the
motion
 is
the
same,
and
the
total
work
done
is
 W 
=
-2(3.68
N)(8.0
m)
=
-59
J
(round
to
two
places). b)
The
magnitude
of
the
displacement
is
Î r 
=

 2 (8
m)
so
the
work
done
by
friction
is
. W f = − 2 8.0 m ( ) 3.68 N ( ) 
=
-42
J

c)
The
work
is
the
same
both
coming
and
going,
and
the
total
 work
done
is
the
same
as
in
part
(a),
-59
J.

d)
The
work
required
to
go
from
one
point
to
another
 is
path
dependent,
and
the
work
required
for
a
round
trip
is
not
zero,
so
friction
is
not
a
 conservative
force. [7.32]

The
force
is
 F x = − dU dx = C 6 d dx 1 x 6 = − 6 C 6 x 7 .

One
hydrogen
atom
particle
is
at
the
origin
 and
the
other
at
 x.

 This
force
is
on
the
particle
at
 x 
and
because
it
is
negative,
it
acts
toward
the
 atom
at
the
origin,
so
it
is
an
attractive
force. [7.37]


a)

 F r = − ∂ U dr = 12 a r 13 − 6 b r 7 
b)
Setting
 F r 
=
0
and
solving
for
 r 
gives
 r min 
=
(2 a/b ) 1/6 .
This
is
 the
minimum
of
potential
energy,
so
the
equilibrium
is
stable. c) U ( r min ) = a r min 12 − b r min 6 = a ((2 a / b ) 1/6 ) 12 − b ((2 a / b ) 1/6 ) 6 = ab 2 4 a 2 − b 2 2 a = − b 2 4 a . 
 To
separate
the
particles
means
to
give
enough
energy
to
get
them
to
zero
energy,
and
requires
 ÎE binding =
0
-
 E o 
=
b 2 /4a . d)
The
expressions
for
 Eø 
and
 r min 
in
terms
of
 a 
and
 b 
are

 E = b 2 4 a r min 6 = 2 a b Multiplying
the
first
by
the
second
and
solving
for
 b 
gives
 b = 2 E r min 6 ,
and
substituting
this
into
 the
first
and
solving
for
 a 
gives
 a = E r min 12 .

Using
the
given
numbers,....
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06prob_11 - Assigment#6 Page 1 of 3 UC Davis Physics 9A-C...

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