Soluções de Física

1

UNITS, PHYSICAL QUANTITIES AND VECTORS

1.1.

1.2.

IDENTIFY: Convert units from mi to km and from km to ft.
SET UP: 1 in. = 2.54 cm , 1 km = 1000 m , 12 in. = 1 ft , 1 mi = 5280 ft .
⎛ 5280 ft ⎞⎛ 12 in. ⎞⎛ 2.54 cm ⎞⎛ 1 m ⎞⎛ 1 km ⎞
EXECUTE: (a) 1.00 mi = (1.00 mi) ⎜
⎟⎜
⎟⎜
⎟⎜ 2
⎟⎜ 3 ⎟ = 1.61 km
⎝ 1 mi ⎠⎝ 1 ft ⎠⎝ 1 in. ⎠⎝ 10 cm ⎠⎝ 10 m ⎠

⎛ 103 m ⎞⎛ 102 cm ⎞ ⎛ 1 in. ⎞⎛ 1 ft ⎞
3
(b) 1.00 km = (1.00 km) ⎜
⎟⎜
⎟⎜
⎟⎜
⎟ = 3.28 × 10 ft
1
km
1
m
2.54
cm
12
in.
⎠⎝
⎠
⎝
⎠⎝
⎠⎝
EVALUATE: A mile is a greater distance than a kilometer. There are 5280 ft in a mile but only 3280 ft in a km.
IDENTIFY: Convert volume units from L to in.3 .
SET UP: 1 L = 1000 cm3 . 1 in. = 2.54 cm
3

⎛ 1000 cm3 ⎞ ⎛ 1 in. ⎞
3
0.473 L × ⎜
⎟×⎜
⎟ = 28.9 in. .
⎝ 1 L ⎠ ⎝ 2.54 cm ⎠
EVALUATE: 1 in.3 is greater than 1 cm3 , so the volume in in.3 is a smaller number than the volume in cm3 , which is 473 cm3 .
IDENTIFY: We know the speed of light in m/s. t = d / v . Convert 1.00 ft to m and t from s to ns.
SET UP: The speed of light is v = 3.00 × 108 m/s . 1 ft = 0.3048 m . 1 s = 109 ns .
0.3048 m
EXECUTE: t =
= 1.02 × 10−9 s = 1.02 ns
3.00 × 108 m/s
EVALUATE: In 1.00 s light travels 3.00 × 108 m = 3.00 × 105 km = 1.86 × 105 mi .
IDENTIFY: Convert the units from g to kg and from cm3 to m3 .
SET UP: 1 kg = 1000 g . 1 m = 1000 cm .
EXECUTE:

1.3.

1.4.

3

EXECUTE:

1.5.

EVALUATE: The ratio that converts cm to m is cubed, because we need to convert cm3 to m3 .
IDENTIFY: Convert volume units from in.3 to L.
SET UP: 1 L = 1000 cm3 . 1 in. = 2.54 cm .
EXECUTE:

1.6.

( 327 in. ) × ( 2.54 cm in.) × (1 L 1000 cm ) = 5.36 L
3

3

3

EVALUATE: The volume is 5360 cm3 . 1 cm3 is less than 1 in.3 , so the volume in cm3 is a larger number than the volume in in.3 .
IDENTIFY: Convert ft 2 to m 2 and then to hectares.
SET UP: 1.00 hectare = 1.00 × 104 m 2 . 1 ft = 0.3048 m .
EXECUTE:

1.7.

g ⎛ 1 kg ⎞ ⎛ 100 cm ⎞
4 kg
×
11.3
⎟×⎜