fisica1-youn-e-freedman-exercicios-resolvidos

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
−3
about 8.3× 10 %. c) If a handheld stopwatch (as opposed to electric timing devices) can
−2
measure to the nearest tenth of a second, the error will be about 2.8×
10 %.
1.16: The area is 9.69 ± 0.07 cm 2 , where the extreme values in the piece’s length and
width are used to find the uncertainty in the area. The fractional uncertainty in the
2
0 .07 cm
area is 2 = 0.72%, and the fractional uncertainties in the length and width are
9.69 cm
0 .01cm
0.01 cm
5.10 cm
= 0.20% and
1.9 cm
= 0.53%.
1.17: a) The average volume is
2
( 8.50 cm) ( )
3
π 0.050 cm = 2.8 cm
4
(two significant figures) and the uncertainty in the volume, found from the extreme
3
values of the diameter and thickness, is about 0 .3 cm , and so the volume of a
3
cookie is 2.8 ± 0.3 cm . (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.)
8 .50
b) = 170 ± 20.
.05
1.18: (Number of cars × miles/car . day)/mi/gal = gallons/day
(2 × 10 8 cars × 10000 mi/yr/car × 1 yr/365 days)/(20 mi/gal) = 2.75 × 10 8 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 cm 3 , a 2-L bottle will hold about 8000
kernels.