1
Chap.5
HW1
Questions
4
.
At time
t
= 0, a single force
F
of constant magnitude begins to act on a rock moving through deep
space in the positive direction of an
x
axis.
The rock continues to move along that axis.
(a) For time
t
> 0, which are possible functions
x(t)
for the rock's position: (1)
x
= 4
t
– 3, (2)
x
= –4
t
2
+ 6
t
– 3, (3)
x
= 4
t
2
+ 6
t
– 3?
Using
dt
dx
v
/
=
,
v
is positive for
t
> 0 for cases (1) and (3)
(b) For which function is
ur
F
directed opposite the rock's initial direction of motion?
Using
dt
dx
v
/
=
and
dt
dv
a
/
=
(and taking
t
> 0)
For (1) initial
v
is positive.
Also
a
(and therefore
F
) is zero
For (2) initial
v
is positive.
Also
a
(and therefore
F
) is negative
For (3) initial
v
is positive.
Also
a
(and therefore
F
) is positive
So there is no case where the initial (at
t
= 0)
v
is opposite
F
.
Problems
4.
Three astronauts, propelled by jet backpacks, push and
guide a 120 kg asteroid toward a processing dock, exerting the
forces shown, with
F
1
= 32 N,
F
2
= 55 N,
F
3
= 41 N,
1
θ
= 30°,
and
3
= 60°. What is the asteroid's acceleration
(a) in unitvector notation
Forces exerted by the three astronauts are:
()
1
2
3
ˆˆ
ˆ
ˆ
32 cos 30 i
sin 30
27.7i+16 j
j
ˆ
55 cos 0 i
sin 0
55i
j
ˆ
ˆ
41 cos
60
i
sin
60
20.5i
35.5 j.
j
F
F
F
=°
+
°
=
+
°
=
=−
°
+
−
°
=
−
r
r
r
(unit: N)
The acceleration of the asteroid is :
m
F
a
/
v
v
=
(
)
(
)
22
ˆ
ˆ
ˆ
27.7i
16 j
35.5j
(0.86m/s )i
(0.16m/s )j .
120
a
++
+
−
==
−
r
(b) a magnitude and
(c) a direction relative to the positive direction of the
x
axis?
Magnitude of
r
a
is
2
2
2
2
2
m/s
88
.
0
16
.
0
86
.
0
=
+
=
+
=
y
x
a
a
a
v
The angle
r
a
makes with the +
x
axis
o
x
y
a
a
5
.
10
186
.
0
/
tan
−
=
⇒
=
=
5.
There are two forces on the 2.00 kg box in the overhead view of
Figure 532, but only one is shown. For
F
1
= 20.0 N,
a
= 12.0 m/s
2
, and
= 30.0°, find the second force (a) in unitvector notation and as (b) a
magnitude and (c) an angle relative to the positive direction of the
x
axis.
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 Spring '08
 oshea
 Force

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