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UNITS, PHYSICAL QUANTITIES AND VECTORS 1

1.1. 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.

EXECUTE: (a) 1.00 mi = (1.00 mi) ⎛ 5280 ft ⎞ ⎛ 12 in.⎞ ⎛ 2.54 cm⎞ ⎛ 1m ⎞ ⎛ 1 km ⎞ = 1.61 km

⎝⎜ 1 mi ⎠⎟ ⎝⎜ 1 ft ⎟⎠ ⎝⎜ 1 in. ⎟⎠ ⎝⎜ 102 cm⎟⎠ ⎜⎝ 103 m⎟⎠

(b) 1.00 km = (1.00 km) ⎛ 103 m ⎞⎛ 102 cm ⎞ ⎛ 1 in. ⎞⎛ 1 ft ⎞ = 3.28 ×103 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.

1.2. IDENTIFY: Convert volume units from L to in.3.

SET UP: 1 L = 1000 cm3. 1 in. = 2.54 cm

EXECUTE: 0.473 L × ⎛ 1000 cm3 ⎞ × ⎛ 1 in. ⎞3 = 28.9 in.3.

⎜⎜⎝ 1L ⎟⎟⎠ ⎜⎝ 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.

1.3. 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.

EXECUTE: t = 0.3048 m = 1.02 ×1029 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.

1.4. IDENTIFY: Convert the units from g to kg and from cm3 to m3.

SET UP: 1 kg = 1000 g. 1 m = 1000 cm.

EXECUTE: 19.3 g × ⎛ 1 kg ⎞ ⎛ 100 cm ⎞3 = 1.93×104 kg

cm3 ⎜ ⎟ × ⎜ ⎟ m3

⎝ 1000 g ⎠ ⎝ 1m ⎠

EVALUATE: The ratio that converts cm to m is cubed, because we need to convert cm3 to m3.

1.5. IDENTIFY: Convert volume units from in.3 to L.

SET UP: 1 L = 1000 cm3. 1 in. = 2.54 cm.

EXECUTE: (327 in.3) × (2.54 cm/in.)3 × (1 L/1000 cm3) = 5.36 L

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.

1.6. IDENTIFY: Convert ft2 to m2 and then to hectares.

SET UP: 1.00 hectare = 1.00 ×104 m2. 1 ft = 0.3048 m.

© Copyright 2012 Pearson Education, Inc. All rights reserved. This material is protected under all copyright laws as they currently exist.

No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

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1.1. 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.

EXECUTE: (a) 1.00 mi = (1.00 mi) ⎛ 5280 ft ⎞ ⎛ 12 in.⎞ ⎛ 2.54 cm⎞ ⎛ 1m ⎞ ⎛ 1 km ⎞ = 1.61 km

⎝⎜ 1 mi ⎠⎟ ⎝⎜ 1 ft ⎟⎠ ⎝⎜ 1 in. ⎟⎠ ⎝⎜ 102 cm⎟⎠ ⎜⎝ 103 m⎟⎠

(b) 1.00 km = (1.00 km) ⎛ 103 m ⎞⎛ 102 cm ⎞ ⎛ 1 in. ⎞⎛ 1 ft ⎞ = 3.28 ×103 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.

1.2. IDENTIFY: Convert volume units from L to in.3.

SET UP: 1 L = 1000 cm3. 1 in. = 2.54 cm

EXECUTE: 0.473 L × ⎛ 1000 cm3 ⎞ × ⎛ 1 in. ⎞3 = 28.9 in.3.

⎜⎜⎝ 1L ⎟⎟⎠ ⎜⎝ 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.

1.3. 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.

EXECUTE: t = 0.3048 m = 1.02 ×1029 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.

1.4. IDENTIFY: Convert the units from g to kg and from cm3 to m3.

SET UP: 1 kg = 1000 g. 1 m = 1000 cm.

EXECUTE: 19.3 g × ⎛ 1 kg ⎞ ⎛ 100 cm ⎞3 = 1.93×104 kg

cm3 ⎜ ⎟ × ⎜ ⎟ m3

⎝ 1000 g ⎠ ⎝ 1m ⎠

EVALUATE: The ratio that converts cm to m is cubed, because we need to convert cm3 to m3.

1.5. IDENTIFY: Convert volume units from in.3 to L.

SET UP: 1 L = 1000 cm3. 1 in. = 2.54 cm.

EXECUTE: (327 in.3) × (2.54 cm/in.)3 × (1 L/1000 cm3) = 5.36 L

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.

1.6. IDENTIFY: Convert ft2 to m2 and then to hectares.

SET UP: 1.00 hectare = 1.00 ×104 m2. 1 ft = 0.3048 m.

© Copyright 2012 Pearson Education, Inc. All rights reserved. This material is protected under all copyright laws as they currently exist.

No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

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