Problemas resueltos física universitaria

1.1: 1 mi × (5280 ft mi ) × (12 in. ft ) × (2.54 cm in .) × 1 km 105 cm = 1.61 km Although rounded to three figures, this conversion is exact because the given conversion from inches to centimeters defines the inch.

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1.2:

⎛ 1000 cm 3 ⎞ ⎛ 1in ⎞ 3 0.473 L × ⎜ ⎟ ⎟ ⎜ ⎜ 1 L ⎟ × ⎜ 2.54 cm ⎟ = 28.9 in . ⎠ ⎠ ⎝ ⎝

3

1.3: The time required for light to travel any distance in a vacuum isthe distance divided by the speed of light; 103 m = 3.33 × 10− 6 s = 3.33 × 103 ns. 8 3.00 × 10 m s

1.4:

g ⎛ 1 kg ⎞ ⎛ 100 cm ⎞ 4 kg ×⎜ 11.3 3 ⎜ 1000 g ⎟ × ⎜ 1 m ⎟ =1.13 × 10 m 3 . ⎟ ⎜ ⎟ cm ⎝ ⎠ ⎝ ⎠

3

1.5:

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

1.6:

⎛ 1000 L ⎞ ⎛ 1 gal ⎞ ⎛ 128 oz. ⎞ ⎛ 1 bottle ⎞ 1 m3 × ⎜ ⎜ 1 m 3 ⎟ × ⎜ 3.788 L ⎟ × ⎜ 1 gal ⎟ × ⎜ 16 oz. ⎟. ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ = 2111.9 bottles ≈ 2112 bottles

The daily consumption must then be bottles ⎛ 1 yr ⎞ bottles 2.11 × 10 3 ×⎜ ⎜ 365.24 da ⎟ = 5.78 da . ⎟ yr ⎝ ⎠
1.7:

(1450 mi hr ) × (1.61 km mi) = 2330 km hr . 2330 km hr × (103 m km )× (1 hr 3600 s ) = 648 m s.
180,000 furlongs ⎛ 1 mile ⎞ ⎛ 1 fortnight ⎞ ⎛ 1 day ⎞ mi ×⎜ ⎟ ⎟ ⎜ ⎜ 8 furlongs ⎟ × ⎜ 14 day ⎟ × ⎜ 24 h ⎟ = 67 h . ⎟ ⎜fortnight ⎝ ⎠ ⎠ ⎝ ⎠ ⎝

1.8:

1.9:

15.0

km ⎛ 1 mi ⎞ ⎛ 3.788 L ⎞ mi ×⎜ ⎟×⎜ ⎜ 1 gal ⎟ = 35.3 gal . ⎟ L ⎝ 1.609 km ⎠ ⎝ ⎠

⎛ mi ⎞ 1.10: a) ⎜ 60 ⎟ ⎝ hr ⎠

⎛ 1h ⎞ ⎜ ⎜ 3600 s ⎟ ⎟ ⎝ ⎠

⎛ 5280 ft ⎞ ft ⎜ ⎜ 1 mi ⎟ = 88 s ⎟ ⎝ ⎠

m ⎛ ft ⎞ ⎛ 30.48 cm ⎞ ⎛ 1 m ⎞ b) ⎜ 32 2 ⎟ ⎜ ⎜ 1 ft ⎟ ⎜ 100 cm ⎟ = 9.8 s 2 ⎟ ⎝ s ⎠⎝ ⎠ ⎠⎝

g ⎞ ⎛ 100 cm ⎞ ⎛ c) ⎜1.0 ⎟⎜ ⎟ cm 3 ⎠ ⎝ 1 m ⎠ ⎝

3

⎛ 1 kg ⎞ 3 kg ⎜ ⎜ 1000 g⎟ = 10 m 3 ⎟ ⎝ ⎠

1.11: The density is mass per unit volume, so the volume is mass divided by density. V = (60 × 103 g ) (19.5 g cm3 ) = 3077 cm3 4 Use the formula for the volume of a sphere, V = πr 3 , 3 1/ 3 to calculate r : r = (3V 4π ) = 9.0 cm

1.12:

(3.16 × 10 7 s − π × 10 7 s) (3.16 × 10 7 s) × 100 = 0.58%

1.13: a)

10 m = 1.1× 10 −3 %. 3 890 × 10 m

b) Since the distance wasgiven as 890 km, the total distance should be 890,000 meters. To report the total distance as 890,010 meters, the distance should be given as 890.01 km.
1.14: a) (12 mm ) × (5.98 mm ) = 72 mm 2 (two significant figures). .98 mm b) 512 mm = 0.50 (also two significant figures). c) 36 mm (to the nearest millimeter). d) 6 mm. e) 2.0.

1.15: a) If a meter stick can measure to the nearest millimeter,the error will be about 0.13%. b) If the chemical balance can measure to the nearest milligram, the error will be about 8.3 × 10−3%. c) If a handheld stopwatch (as opposed to electric timing devices) can measure to the nearest tenth of a second, the error will be about 2.8 × 10 −2 %.

1.16: The area is 9.69 ± 0.07 cm2, where the extreme values in the piece’s length and width are used to find theuncertainty in the area. The fractional uncertainty in the cm 2 area is 0..07 cm 2 = 0.72%, and the fractional uncertainties in the length and width are 9 69
0.01 cm 5.10 cm

= 0.20% and

0.01 cm 1.9 cm

= 0.53%.

1.17: a) The average volume is (8.50 cm )2 (0.050 cm ) = 2.8 cm 3 π 4 (two significant figures) and the uncertainty in the volume, found from the extreme values of the diameterand thickness, is about 0.3 cm3 , and so the volume of a cookie is 2.8 ± 0.3 cm3 . (This method does not use the usual form for progation of errors, which is not addressed in the text. The fractional uncertainty in the thickness is so much greater than the fractional uncertainty in the diameter that the fractional uncertainty in the volume is 10% , reflected in the above answer.) b)
8.50 .05= 170 ± 20.

1.18: (Number of cars × miles/car.day)/mi/gal = gallons/day (2 × 108 cars × 10000 mi/yr/car × 1 yr/365 days)/(20 mi/gal) = 2.75 × 108 gal/day 1.19: Ten thousand; if it were to contain ten million, each sheet would be on the order of a millionth of an inch thick. 1.20: If it takes about four kernels to fill 1 cm3, a 2-L bottle will hold about 8000 kernels.

1.21: Assuming the...