Physics 112 HW #1 Solutions Spring 06
110
[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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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 +xaxis
(b)
A

B
=
28.5 m at 22° downward from the xaxis
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 Fall '07
 LECLAIR,A
 Physics, mechanics, Orders of magnitude, measurement uncertainty, mi/h

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