time in minutes: tm+/_ 0.2 (minutes) 292.1 Imagine that you and a friend made a
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Question
time in minutes: tm+/_ 0.2 (minutes)
292.1
Imagine that you and a friend made a trip from Calgary to Edmonton. Since your friend was driving the car, you decided to make yourself busy by keeping a record of the distance travelled as a function of time. So, when you were waiting for the last trac light to turn green on the outskirts of Calgary, you reset the odometer to zero. When the green light turned on, you started timing the trip using a stopwatch. Every ten minutes you recorded the odometer reading. At the end of your trip, you had the two columns of data in Table 1.4.
Since the odometer gave the distance within 100 m, you estimated the uncertainty in d to be (d = ±0.1 km). Regarding the time, even though you did your best to take the meter reading at equal time intervals of 10 minutes, you still estimated a timing error of about 12 seconds (or tm = ±0.2 min).
Since you are using kilometre (km) as the unit of distance, then probably it is a good idea to use hour (h) as the unit of time. So, begin by transforming the elapsed time from minutes to hours and insert the results in the second column of Table 1.4. After completing the transformation, you need to calculate the uncertainty of the new quantity th. Remember that th = 1 60 ×tm and that thefactor 1 60 is an exact number with zero uncertainty.
time in minutes: tm+/_ 0.2 (minutes)
time in hours: th +/_ ? (hours) Distance: d +/_ 0.1 (km) 0 0 10.0 17.5 20.0 34.5 30.0 52.2 40.0 76.1 50.0 87.0 60.0 105.0 70.0 122.3 80.0 144.0 90.0 152.3 100.0 177.0 110.0 191.1 120.0 209.0 130.0 227.4 140.0 241.0 150.0 263.7 160.0 285.2 170.0292.1
Explanation / Answer
As you. This reduction units performing a measurement error remains constant and no factors that increase or decrease, so we need only reduce the error until the correct units
Error
12 s = 12 s 1 min /60 s = 0.2 min
0,2 min 1 h / 60 min = 0.003 h
This is the error in time for all measures
now we will reduce measurements
t (min) t (h)
10 10/60 = 0.166
20 20/60= 0.333
30 30/60= 0.500
40 40/60= 0.667
50 50/60= 0.833
60 60/60= 1.000
70 70/60= 1.166
80 80/60= 1.333
90 90/60= 1.500
100 1.666
110 1.833
120 2.000
130 2.167
140 2.333
150 2.500
160 2.667
170 2.833
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