Lesson 3.1 Homework Solutions
1.
Vector
A
= 2
i
– 3
j
and vector
B
= 4
i
+ 6
j
. Find
A
⋅
B
and the angle
between the two vectors.
A
= 2
i
– 3
j
,
B
= 4
i
+ 6
j
A
⋅
B
= 8 – 18 = 26
2
2
2
2
2
3
3.6
4
6
7.2
26
cos
1
3.6 7.2
A
B
A B
A
B
θ
=
+
=
=
+
=
⋅

=
=
= 
⋅
×
θ
= cos
1
= 180
o
2.
A force
F
= 3 N
i
– 5 N
j
produces a displacement on a particle given
by
s
= 5 m
i
– 2 m
j
. Find the work done by the force.
F
= 3 N
i
– 5 N
j
,
s
= 5 m
i
– 2 m
j
.
W = F
⋅
s = 15 + 10 =
25 J
3.
What is the work done to raise a 50kg box to a height of 3.0 m?
The force needed to raise the box is its weight = 50
×
9.8 = 490 N
W = F
⋅
y
= 490 N
×
3.0 m = 1470 J
4.
A tractor exerts a constant force of 4.5
×
10
4
N in moving a load
horizontally a distance of
150 m. (i) What is the work done? (ii) If the
tractor does this work in 45 s, what is the power developed by its
engine?
(i)
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 Fall '10
 George
 Physics, Work

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