karna (pk4534) – HW 6 – coker – (58245)
1
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printout
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17
questions.
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001
(part 1 of 2) 10.0 points
A force
vector
F
=
F
x
ˆ
ı
+
F
y
ˆ
acts on a particle that
undergoes a displacement of
vectors
=
s
x
ˆ
ı
+
s
y
ˆ
.
Let:
F
x
= 6 N,
F
y
=

5 N,
s
x
= 5 m, and
s
y
= 2 m.
Find the work done by the force on the
particle.
Correct answer: 20 J.
Explanation:
The work is given by
W
=
vector
F
·
vectors
=
F
x
s
x
+
F
y
s
y
= (6 N) (5 m) + (

5 N) (2 m)
= 20 J
.
002
(part 2 of 2) 10.0 points
Find the angle between
vector
F
and
vectors
.
Correct answer: 61
.
607
◦
.
Explanation:
Since
W
=
vector
F
·
vectors
=
vextendsingle
vextendsingle
vextendsingle
vector
F
vextendsingle
vextendsingle
vextendsingle

vectors

cos
θ .
The first and the third sides can be solved for
θ
to give
θ
= cos
−
1
W
vextendsingle
vextendsingle
vextendsingle
vector
F
vextendsingle
vextendsingle
vextendsingle

vectors

.
First of all
vextendsingle
vextendsingle
vextendsingle
vector
F
vextendsingle
vextendsingle
vextendsingle
=
radicalBig
F
2
x
+
F
2
y
=
radicalBig
(6 N)
2
+ (

5 N)
2
= 7
.
81025 N
and

vectors

=
radicalBig
s
2
x
+
s
2
y
=
radicalbig
5 m
2
+ 2 m
2
= 5
.
38516 m
.
Thus
θ
= cos
−
1
bracketleftbigg
20 J
(7
.
81025 N) (5
.
38516 m)
bracketrightbigg
= 61
.
607
◦
.
003
(part 1 of 3) 10.0 points
Sally applies a horizontal force of 605 N with
a rope to drag a wooden crate across a floor
with a constant speed.
The rope tied to the
crate is pulled at an angle of 46
◦
relative to
the floor.
The acceleration of gravity is 9
.
8 m
/
s
2
.
m
F
605 N
46
◦
How much force is exerted by the rope on
the crate?
Correct answer: 870
.
932 N.
Explanation:
Given :
F
h
= 605 N
,
and
θ
= 46
◦
.
The horizontal component of the force exerted
by the rope is defined by
cos
θ
=
F
h
F
so that
F
=
F
h
cos
θ
=
605 N
cos 46
◦
=
870
.
932 N
.
004
(part 2 of 3) 10.0 points
What work is done by Sally if the crate is
moved 29 m?
Correct answer: 17545 J.
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karna (pk4534) – HW 6 – coker – (58245)
2
Explanation:
The motion is in the direction of the hori
zontal component, so the work Sally does is
W
=
F
h
d
= (605 N) (29 m)
=
17545 J
.
005
(part 3 of 3) 10.0 points
What work is done by the floor through force
of friction between the floor and the crate?
Correct answer:

17545 J.
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 Spring '08
 Turner
 Physics, Force, Potential Energy, Correct Answer, Karna

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