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8
Chapter 3. Technical Measurement and Vectors
Unit Conversions
3-1. A soccer field is 100 m long and 60 m across. What are the length and width of the field in
feet?
100 cm
1 in.
1 ft
(100 m)
3
2
8
ft
1 m
2.54 cm
12 in.
L = 328 ft
100 cm
1 in.
1 ft
(60 m)
1
9
7
ft
1 m
2.54 cm
12 in.
W = 197 ft
3-2. A wrenchhas a handle 8 in. long. What is the length of the handle in centimeters?
2.54 cm
(8 in.)
2
0
.
3
cm
1 in.
L = 20.3 cm
3-3. A 19-in. computer monitor has a viewable area that measures 18 in. diagonally. Express this
distance in meters.
.
2.54 cm
1 m
(18 in.)
0
.
4
5
7
m
1 in.
100 cm
L = 0.457 m
3-4. The length of a notebook is 234.5 mm and thewidth is 158.4 mm. Express the surface area
in square meters.
1 m
1 m
Area = (234.5 mm)(158.4 mm)
0
.
0
3
7
1000 mm
1000 mm
A = 0.0371 m
2
3-5. A cube has 5 in. on a side. What is the volume of the cube in SI units and in fundamental
USCS units?
.
3
3
3
3
3
2.54 cm
1 m
(5 in.)
1
2
5
in.
0
.
0
0
2
0
5
m
1 in.
100 cm
V
V =0.00205 m
3
3
3
3
1 ft
(125 in. )
0
.
0
7
2
3
ft
12 in.
V
V = 0.0723 ft
3

Chapter 3 Technical Measurement and Vectors
Physics, 6
th
Edition
9
3-6. The speed limit on an interstate highway is posted at 75 mi/h. (a) What is this speed in
kilometers per hour? (b) In feet per second?
(a)
mi 1.609 km
75
h
1 mi
121 km/h (b)mi
1
h
5
2
8
0
ft
75
h
3
6
0
0
s
1
mi
= 110 ft/s
3-7. A Nissan engine has a piston displacement (volume) of 1600 cm and a bore diameter of 84
3
mm. Express these measurements in cubic inches and inches. Ans. 97.6 in. , 3.31 in.
3
(a)
3
3
1 in.
1600 cm
2.54 cm
= 97.6 in.
3
(b) 84 mm =
1 in.
25.4 mm
= 3.31 in.
3-8. Anelectrician must install an underground cable from the highway to a home located 1.20
mi into the woods. How many feet of cable will be needed?
5280 ft
1
.
2
mi
6
3
4
0
ft
1 mi
L = 6340 ft
3-9. One U.S. gallon is a volume equivalent to 231 in. . How many gallons are needed to fill a
3
tank that is 18 in. long, 16 in. wide, and 12 in. high?
Ans. 15.0 gal.
V = (18 in.)(16in.)(12 in.) = 3456 in.
3
3
3
1 gal
(3456 in. )
1
5
.
0
gal
231 in.
V
V = 15.0 gal
3-10. The density of brass is 8.89 g/cm . What is the density in kg/m ?
3
3
3
3
3
g
1
kg
1
0
0
cm
kg
8.89
8890
cm
1
0
0
0
g
1
m
m
= 8890 kg/m
3
Addition of Vectors by Graphical Methods
3-11. A woman walks 4 km east and then 8 km north. (a)Use the polygon method to find her
resultant displacement. (b) Verify the result by the parallelogram method.
Let 1 cm = 1 km; Then: R = 8.94 km,
= 63.4
0
4 km
8 km
R

Chapter 3 Technical Measurement and Vectors
Physics, 6
th
Edition
10
3-12. A land-rover, on the surface of Mars, moves a distance of 38 m at an angle of 180 . It then
0
turns andmoves a distance of 66 m at an angle of 270 . What is the displacement from
0
the starting position?
Choose a scale, e.g., 1 cm = 10 m
Draw each vector to scale as shown.
Measure R = 7.62 cm or R = 76.2 m
Measure angle
= 60.1 S of W
0
= 180 + 60.1 = 240.1
0
0
0
R = 76.2 m, 240.1
0
3-13. A surveyor starts at the southeast corner of a lot and charts the following displacements:A = 600 m, N; B = 400 m, W; C = 200 m, S; and D = 100 m, E. What is the net
displacement from the starting point?
.
Choose a scale, 1 cm = 100 m
Draw each vector tail to tip until all are drawn.
Construct resultant from origin to finish.
R = 500 m,
= 53.1 N of E or
0
= 126.9 .
0
3-14. A downward force of 200 N acts simultaneously with a 500-N force directed to the left.
Use the...