05prob_11

05prob_11 - Assigment #5, 4/29/11 Page 1 of 3 UC Davis F N...

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Unformatted text preview: Assigment #5, 4/29/11 Page 1 of 3 UC Davis F N F mg f oe = 30° F N mg f oe = Physics 9A-C Assignment #5 Cole [6.4]

Note
that
the
box
is
pushed
along
a
level
floor;
the
person
is
 pushing
down
on
the
box.

a)
Draw
a
free-body
diagram.

 Í F y 
=
F N 
-
F 
sin
oe
-
 mg 
=
0

õ F N 

=

F 
sin
oe
+
 mg.


ÍF x 

=

F 
cos
oe
-
μ k 
( F 
sin
oe
+
 mg )

=

0 
 because
 the
velocity
is
constant.

Solve
for
 F : F = μ k mg cos φ − μ k sin φ = 0.25 ( ) 30kg ( ) 9.8 m/s 2 ( ) cos 30¡- 0.25 ( ) sin30 ° 
=
99.2
N 
b) 
F Î x 
cos
oe
=
(99.2
N)(4.50
m)
cos
30°
=
386.5
J c)
The
normal
force
 is
 F N 

= 
 mg
+
F 
sinoe,
and
so
the
work
done
by
friction
is W f 

=

 
–(0.25)[(30
kg)(9.80
m/s 2 )
+
(99.2
N)
sin
30°](4.50
m)
=
-386.5
J. d)
Both
the
normal
force
and
gravity
act
perpendicular
to
the
direction
of
motion,
so
neither
 force
does
work.


e)
The
net
work
done
is
zero
(the
kinetic
energy
doesn’t
change.) [6.38]

 
 W = Fdx 3
m ∫ 

=
 area
under
the
curve.


a)

 W

=
 1 2 (2
m
ª
2
N)
+
(1
m
)(2
N)
=
4
J.

 Using
the
work
energy
theorem:

 W
=
ÎK


 1 2 mv 2 
-
 1 2 mvø 2 


õ

 v = 2 W m = 2 4 J ( ) 2 kg 
=
2.0
m/s b)

No
area
is
accumulated
so
the
speed
cannot
change.

 v
= 
2.0
m/s. c)

 W

=

4 
J

-

 1 2 (2
m)(1
N)

=
3
J.

 v

=

 v = 2 3 J ( ) 2 kg =
1.73
m/s. [6.47]

The
total
power
is
 
P
=
Fv
= (165
N)(9.00
m/s)
=
1.485
ª
10 3 
W,
so
the
power
per
rider
is
 742.5
W,
or
about
1.0
hp
(which
is
a
very
large
output,
and
cannot
be
sustained
for
long
periods). [6.68]

If
this
were
an
ideal
spring
the
applied
force
to
stretch
it
would
be
 F
=
kx. 

The
force
 varies,
so
we
must
integrate
it:

 W F = kx − bx 2 + cx 3 ( ) dx x ∫ 
=
 1 2 kx 2-
 1 3 bx 3
 +
 1 4 cx 
4 
=
 
 (50.0 N/m ) x 2 2 − (233 N/m 2 ) x 2 3 + (3000 N/m 3 ) x 2 4 . 
a)
When
 x 2 
=
0.050
m,
 W 
=
0.115
J,
or
0.12
J

 b)

When
x 2 
=
-
0.050
m,
 W 
=
0.173
J,
or
0.17
J.

c)
It’s
easier
to
stretch
the
spring;
the
quadratic

=
0....
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This note was uploaded on 09/28/2011 for the course PHY 9A taught by Professor Svoboda during the Spring '08 term at UC Davis.

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05prob_11 - Assigment #5, 4/29/11 Page 1 of 3 UC Davis F N...

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