HW_Solns_1_F05[1]

HW_Solns_1_F05[1] - Physics 112 - HW #1 Solutions 1-10 (a)...

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Physics 112 — HW #1 Solutions Fall 2005 1-10 [Unit Conversions] (a) 60 mph = 60 mi 1 hr 5280 ft 1 mi 3600 s = 88 ft/s (b) 32 ft/s 2 = 32 ft 1 s 2 30.48 cm 1 ft 1 m 100 cm = 9.75 m/s 2 (c) 1.0 g/m 3 = 1.0 g (1 cm ) 3 (100 cm ) 3 (1 m) 3 1 kg 1000 g = 1000 kg/m 3 1-12 [Precision & Significant Digits] 1 yr = 1 yr 365.24 days yr 24 hr day 3600 s hr = 3.1557 × 10 7 s and π = 3.1416 fractional error = 3.1557 × 10 7 s - 3.1416 × 10 7 s 3.1557 × 10 7 s = 0.00447 = 0.447% 3 significant digits! [NOTE: Our calculation starts with 5 significant digits since that’s the number of significant digits given in 1 yr = 365.24 days. The conversion factors, 1 day = 24 hr and 1 hr = 3600 s, are regarded as exact , i.e., definitions without uncertainty.] 1.15 [Measurement Uncertainty] (a) The precision depends somewhat on the quantity being measured. Does it have rough or smooth edges? The smallest subdivision on a meter stick is 1 mm = 0.1 cm. If we take this as an estimate of our measurement uncertainty, then: % uncertainty = 0.1 cm 75 cm × 100% = 0.13% or ~ 0.1% (b )A chemical balance can probably measure to the nearest milligram = 0.001 gram. % uncertainty = 0.001 gm 12 gm × 100% = 8.3 × 10 -3 % or ~ 0.01 % (c ) A stopwatch can measure to the nearest 0.01 s. However, typical human reaction time from when a stimulus or event happens until we react to it is of the order of 0.1 s, which probably defines the measurement uncertainty here. 6 min = (6 min) 60 s 1 min = 360 s % uncertainty = 0.1 s 360 s × 100% = 0.028% or ~ 0.03%
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1-32 The required results are found by measuring these figures with a ruler and protractor: (a) A + B = 11.1 m at 78° upward from the +x-axis (b) A - B = 28.5 m at 22° downward from the -x-axis (c) - A - B has the same length as A + B but points in the opposite direction, so… - A - B = 11.1 m at 78° downward from the -x-axis (d) B - A has the same length as A - B but points in the opposite direction, so… B - A = 28.5 m at 22° upward from the +x-axis
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This homework help was uploaded on 04/21/2008 for the course PHYS 1112 taught by Professor Leclair,a during the Fall '07 term at Cornell.

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HW_Solns_1_F05[1] - Physics 112 - HW #1 Solutions 1-10 (a)...

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