homework 07 – – Due: Mar 7 2007, 4:00 am
1
Question 1, chap 7, sect 1.
part 1 of 1
6 points
Stan does 151 J of work lifting himself
0
.
1 m.
The acceleration of gravity is 9
.
8 m
/
s
2
.
What is Stan’s mass?
Correct answer:
154
.
082
kg (tolerance
±
1
%).
Explanation:
Let :
w
= 151 J
,
h
= 0
.
1 m
,
and
g
= 9
.
8 m
/
s
2
.
The work done is
W
=
m g h
m
=
W
g h
=
151 J
(9
.
8 m
/
s
2
) (0
.
1 m)
=
154
.
082 kg
.
Question 2, chap 8, sect 2.
part 1 of 1
8 points
A bullet with a mass of 2
.
66 g and a speed
of 673 m
/
s penetrates a tree horizontally to
a depth of 4
.
08 cm. Assume that a constant
frictional force stops the bullet.
Hint:
Try energy considerations.
Calculate the magnitude of this frictional
force.
Correct answer:
14764
.
6
N (tolerance
±
1
%).
Explanation:
Let :
m
= 2
.
66 g
,
v
= 673 m
/
s
,
and
d
= 4
.
08 cm
.
We can use conservation of energy to relate
the initial kinetic energy of the bullet to the
work done by the frictional force.
1
2
m v
2
=
f
·
s
Solving for the frictional force,
f
,
f
=
m v
2
2
d
=
(0
.
00266 kg) (673 m
/
s)
2
2 (0
.
0408 m)
= 14764
.
6 N
.
Question 3, chap 7, sect 3.
part 1 of 1
8 points
A 1240 kg pile driver is used to drive a
steel Ibeam into the ground. The pile driver
falls 5
.
93 m before contacting the beam, and
it drives the beam 6
.
38 cm into the ground
before coming to rest.
The acceleration of gravity is 9
.
8 m
/
s
2
.
Using the workenergy theorem, calculate
the magnitude of the average force the beam
exerts on the pile driver while the pile driver
is brought to rest.
Correct answer: 1
.
14164
×
10
6
N (tolerance
±
1 %).
Explanation:
The work energy theorem tells us that the
change in potential energy of the falling pile
driver equals the work done on the I beam.
We can express this relation as
m g h
=
F
·
s ,
where h is the distance the pile driver falls,
i.e.
,
h
= (5
.
93 m) + (0
.
0638 m).
Solving for
the average force,
F
, we obtain
F
=
m g h
s
=
(1240 kg)(9
.
8 m
/
s
2
)(5
.
93 m + 0
.
0638 m)
0
.
0638 m
=
1
.
14164
×
10
6
N
.
Question 4, chap 3, sect 4.
part 1 of 1
8 points
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homework 07 – – Due: Mar 7 2007, 4:00 am
2
Vector
vector
A
has components
A
x
=
−
2
.
93
,
A
y
= 6
.
32
,
A
z
= 1
.
06
while vector
vector
B
has components
B
x
= 3
.
84
,
B
y
=
−
6
.
8
,
B
z
= 6
.
66
.
What is the angle
θ
AB
between these vectors?
(Answer between 0
◦
and 180
◦
.)
Correct answer: 130
.
708
◦
(tolerance
±
1 %).
Explanation:
Consider two formulæ for the scalar prod
uct
vector
A
·
vector
B
of two vectors:
vector
A
·
vector
B
=
A
x
B
x
+
A
y
B
y
+
A
z
B
z
(1)
in terms of the two vectors’ components, and
also
vector
A
·
vector
B
=

vector
A
 
vector
B

cos
θ
AB
(2)
in term of their magnitudes and the angle be
tween them. Given the data, we immediately
calculate

vector
A

=
radicalBig
A
2
x
+
A
2
y
+
A
2
z
= 7
.
04634
,
(3)

vector
B

=
radicalBig
B
2
x
+
B
2
y
+
B
2
z
= 10
.
2636
,
(4)
and using eq. (1),
vector
A
·
vector
B
=
−
47
.
1676
.
(5)
Hence, according to eq. (2),
cos
θ
AB
=
vector
A
·
vector
B

vector
A
 
vector
B

=
−
0
.
6522
(6)
and therefore
θ
AB
= arccos(
−
0
.
6522) = 130
.
708
◦
.
(7)
Question 5, chap 7, sect 1.
part 1 of 2
6 points
To move a refrigerator of mass
m
= 210 kg
into a house, the mover puts it on a dolly and
covers the steps leading into the house with a
wooden plank acting as a ramp. The plank is
3
.
4 m long and rises 1
.
3 m. The mover pulls
the dolly with constant velocity and with a
steady force 1100 N up the ramp.
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 Spring '08
 Turner
 Acceleration, Force, Friction, Gravity, Kinetic Energy, Mass, Potential Energy, Work, Correct Answer

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