khounvivongsy (sk27799) – Homework 08b – Weathers – (17104)
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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
where
F
x
= 10 N,
F
y
=
−
4 N,
s
x
= 4 m, and
s
y
= 2 m.
Find the work done by the force on the
particle.
Correct answer: 32 J.
Explanation:
The work is given by
W
=
vector
F
·
vectors
=
F
x
s
x
+
F
y
s
y
= (10 N) (4 m) + (
−
4 N) (2 m)
=
32 J
.
002
(part 2 of 2) 10.0 points
Find the angle between
vector
F
and
vectors
.
Correct answer: 48
.
3665
◦
.
Explanation:
Since
W
=
vector
F
·
vectors
=
vextendsingle
vextendsingle
vextendsingle
vector
F
vextendsingle
vextendsingle
vextendsingle

vectors

cos
θ
θ
= cos
−
1
W
vextendsingle
vextendsingle
vextendsingle
vector
F
vextendsingle
vextendsingle
vextendsingle

vectors

.
vextendsingle
vextendsingle
vextendsingle
vector
F
vextendsingle
vextendsingle
vextendsingle
=
radicalBig
F
2
x
+
F
2
y
=
radicalBig
(10 N)
2
+ (
−
4 N)
2
= 10
.
7703 N
and

vectors

=
radicalBig
s
2
x
+
s
2
y
=
radicalbig
4 m
2
+ 2 m
2
= 4
.
47214 m
,
so
θ
= cos
−
1
bracketleftbigg
32 J
(10
.
7703 N) (4
.
47214 m)
bracketrightbigg
=
48
.
3665
◦
.
003
10.0 points
A shopper in a supermarket pushes a cart
with a force of 32
.
7 N directed at an angle of
23
.
9
◦
downward from the horizontal.
Find the work done by the shopper as she
moves down a 49
.
4 m length of aisle.
Correct answer: 1
.
47687 kJ.
Explanation:
Given :
F
shopper
= 32
.
7 N
,
θ
= 23
.
9
◦
,
and
d
= 49
.
4 m
.
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 Spring '09
 weathers
 Physics, Energy, Force, Correct Answer, θ

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