7. Strategy
Graph the vectors and their sum. Use the scale of the graph to find the magnitude of the
vector sum.
Solution
The length of the vector sum is
approximately equal to seven sides of a grid square, so
the magnitude is 14 N. The vector points east, so the
vector sum of the forces is 14 N to the east. (Note that
F
r
and the vector sum overlap.)
D
E
F
D
+
E
+
F
N
26. Strategy
Use Newton’s second law.
Solution
Compute the acceleration of the automobile.
3
2
3
3.36
10
N forward
2.40 m s
forward
1.40
10 kg
m
Σ
×
=
=
=
×
F
a
r
r
42. Strategy
The gravitational field strength is given by
2
.
g
GM
R
=
Use the mass of the Earth and
the gravitational field strength of the Moon and solve for
R
, which, in this case, is the distance from
the center of the Earth. Then, subtract the radius of the Earth to find the height above the surface.
Solution
Solving for
R
, we have
11
2
2
24
4
2
(6.674
10
N
m
kg
)(5.974
10
kg)
1.57
10
km.
1.62 m s
GM
R
g
−
×
⋅
×
=
=
=
×
So, the height above the surface is
4
3
3
1.57
10
km
6.371
10
km
9.3
10
km .
×
−
×
=
×
54. (a)
Strategy
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 Winter '08
 REHSE
 Physics, Force, Mass, kg, ΔT

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