P207  Fall 2008
Solutions Assignment 4
1 Chapter 5, Problem 13
(a) The
net
force
on
the
salami
is
F
net
=
F
gravity
+
T
cord

to

scale
where
F
gravity
is the force of gravity and
T
cord

to

scale
is
the
force
of
the
scale.
Since
F
net
=
ma
and
a
=
0,
then
F
net
=
0
=
F
gravity
+
T
cord

to

scale
and therefore
T
cord

to

scale
=

F
gravity
=
mg
=
(11 kg)(10 m
/
s
2
) =
110 N
.
salami
scale
F
gravity
T
cord

to

scale
T
cord

to

ceiling
T
cord

to

salami
?
6
?
6
b
b
(b) The tension
T
in the string is equal
to the force of gravity on the salami
so that the net force on the salami
is zero. The tension in the string is
equivalent to the reading on scale.
T
=
mg
=
110 N
.
salami
scale
F
gravity
T
cord

to

scale
T
cord

to

wall
T
cord

to

salami
?
6

b
b
(c) Again, the tension in the string bal
ances the force of gravity. The ten
sion in the string is the same as the
reading on the scale.
T
=
mg
=
110 N
.
left
salami
right
salami
scale
F
gravity
T
F
gravity
T
T
T
?
6
?
6

b
b
b
1
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2. Chapter 5, Problem 20
(a) The net force on the box is
F
net
=
ma
=
F
1
+
F
unknown
. All of the forces,
and the motion of the box are in the
ˆ
i
direction. We solve for the unknown
force
F
unknown
=
ma

F
1
= (2
.
0 kg)(10
m/s
2
)

20 N =
0
(b)
F
unknown
=
ma

F
1
= (2
.
0 kg)(20
m/s
2
)

20 N =
20 N
(c)
F
unknown
=
ma

F
1
= (2
.
0 kg)(0
m/s
2
)

20 N =
20 N
(d)
F
unknown
=
ma

F
1
= (2
.
0 kg)(

10
m/s
2
)

20 N =
40 N
(e)
F
unknown
=
ma

F
1
= (2
.
0 kg)(

20
m/s
2
)

20 N =
60 N
3. Chapter 5, Problem 32
(a) In addition to the applied force
~
F
, there is also the force of gravity acting
on the crate, and the normal force of the ramp on the crate. Since the
acceleration of the crate is zero, so is the net force on the crate, namely
~
F
net
=
~
F
+
~
F
g
+
~
F
N
.
We solve for
~
F
and get
~
F
=

~
F
g

~
F
N
.
The
applied force is purely in the x direction. (
F
x
=

~
F

, F
y
= 0). The force
of gravity is purely in the y direction. (
~
F
g
=

mg
ˆ
j
). The normal force
has x component

F
N

sin
θ
and y component

F
N

cos
θ
, where
θ
= 30
◦
.
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