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171
Chapter 5
1. We are only concerned with horizontal forces in this problem (gravity plays no direct
role). We take East as the +
x
direction and North as +
y
. This calculation is efficiently
implemented on a vectorcapable calculator, using magnitudeangle notation (with SI
units understood).
a
F
m
9 0
0
8 0
118
30
2 9
53
.
.
.
.
b
g b
g
b
g
Therefore, the acceleration has a magnitude of 2.9 m/s
2
.
2. We apply Newton’s second law (Eq. 51 or, equivalently, Eq. 52). The net force
applied on the chopping block is
F
F
F
net
1
2
, where the vector addition is done using
unitvector notation. The acceleration of the block is given by
a
F
F
m
1
2
d
i
/
.
(a) In the first case
1
2
?
?
3.0N i
4.0N j
3.0N i
4.0N j
0
F
F
so
a
0.
(b) In the second case, the acceleration
a
equals
2
?
[(3 3) i
(4 4) j] N
ˆ
3.2 m/s j
2.5 kg
a
(c) In this final situation,
a
is
2
?
[(3 3) i
(4 4) j] N
ˆ
2.4 m/s i
2.5 kg
a
3. We apply Newton’s second law (specifically, Eq. 52).
(a) We find the
x
component of the force is
2
cos 20.0
1.00kg
2.00m/s
cos 20.0
1.88N.
x
x
F
ma
ma
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172
(b) The
y
component of the force is
2
sin 20.0
1.0kg
2.00m/s
sin 20.0
0.684N.
y
y
F
ma
ma
(c) In unitvector notation, the force vector is
?
?
i
j
(1.88 N)i
(0.684 N)j .
x
y
F
F
F
4. Since
v
= constant, we have
a
= 0, which implies
F
F
F
ma
net
1
2
0 .
Thus, the other force must be
2
1
?
( 2 N) i
(6 N) j.
F
F
5. The net force applied on the chopping block is
F
F
F
F
net
1
2
3
, where the vector
addition is done using unitvector notation. The acceleration of the block is given by
a
F
F
F
m
1
2
3
d
i
/
.
(a) The forces exerted by the three astronauts can be expressed in unitvector notation as
follows:
1
2
3
?
?
ˆ
(32 N) cos 30 i
sin 30
(27.7 N)i
(16 N)j
j
?
ˆ
(55 N) cos 0 i
sin 0
(55 N)i
j
?
?
ˆ
(41 N) cos
60
i
sin
60
(20.5 N)i
(35.5 N)j.
j
F
F
F
The resultant acceleration of the asteroid of mass
m
= 120 kg is therefore
2
2
?
?
?
27.7i
16 j N
55i N
20.5i
35.5j N
?
(0.86m/s )i
(0.16m/s )j .
120 kg
a
(b) The magnitude of the acceleration vector is
2
2
2
2 2
2
2
(0.86 m/s )
0.16 m/s
0.88 m/s .
x
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 Spring '11
 Force, Gravity

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