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# HW_solution__1 - Physics 112 HW#1 Solutions Spring 06...

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Physics 112- HW #1 Solutions Spring 06 1-10 [Unit Conversions] (a) 60 mph = 60 mi 1 hr 5280 ft 1 mi 1 hr 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 1.15 [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: 22° (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
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HW_solution__1 - Physics 112 HW#1 Solutions Spring 06...

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