Measurement In-Class Practice (This is not homework!)
1. In each of the
given values circle the significant digits. To the side of each value
indicate the approximate uncertainty.
a. 576 m
b. 1.35 L
c. 1002 kg
d. 1.002 ´
103 kg
e. 4.56 ´
10-7 s
f. 0.000000456 s
g. 0.012 m
h. 0.22 g
i. 3.50 s
j. 81.0 L
k. 81.00 L
l. 3.070 g
m. 3.070 ´
105 L
n. 307000 m
o. 307000 m
p. 307000 m
q. 307000 m
r. 120 s
s. 12.0 s
t. 3 ´
104 kg
u. 30000 kg
v. 3 ´
10-4 kg
w. 0.0003 kg
2. Adjust the
answers to the correct number of significant digits using the rule for
multiplication and division:
a. 12 m ´ 5.2 m = 62.4 m2
b. 1.5 kg ¸
78.9 L = 0.0190114068441 kg/L
c. p ´ (125 cm)2
= 49087.3852123 cm2
d. 160.5 m ¸
6.42 s = 25 m/s
e. 3.00 ´ 108
m/s ´
1.75 ´ 10-7 s = 52.5 m
3. Adjust the
answers to the correct number of significant digits using the rule for addition
and subtraction:
a. 4.5 m + 7.6 m = 12.1 m
b. 1.2 m + 4.7 m = 5.9 m
c. 98.3 m + 5.2 m = 103.5 m
d. 8.24 s + 5.6 s = 13.84 s
e. 116 L -
27.4 L = 88.6 L
f. 1234 m - 1224.1 m = 9.9 m
g. 56.7 kg + 5.3 kg = 62 kg
4. The density of mercury is measured to be 14.01 g/cm3. The accepted value is 13.53 g/cm3. Find the absolute and relative error in the measured value.
5. Determine the relative and absolute error for an experiment that indicates the speed of light is 2.86 ´ 108 m/s.
6. The density of a
certain type of plastic is measured several times using different
samples. The resulting values of this experiment are: 6.710 g/cm3,
6.715 g/cm3, 6.703 g/cm3,
6.709 g/cm3, and 6.711 g/cm3. Determine the best
value, average absolute deviation, and average percent deviation for this set
of values.
7. Convert the
following values into base units:
a. 3.5 nm
b. 1.0 km
c. 25.3 GL
d. 894 ML
e. 36.4 ms
f. 247 mL
8. Write the
following values using the most appropriate metric prefix:
a. 2.9 ´ 10-2 m
b. 4.05 ´
109 L
c. 8.81 ´
10-7 s
d. 6.90 ´
108 m
e. 0.0286 g
f. 3.4 ´ 10-3 mm
9. The CRC handbook lists the maximum safe exposure for radon as 3 ´ 10-8 mCi/cm3, whereas a coworker states that it is 20 pCi/L. How similar are these two values?
10. Given that one mile is 5280 feet, convert 60.0 mph into fps.
11. Convert 2.5 g/cm2 into kg/m2.
12. Given that one inch is 2.54 cm, convert the 1.8 L into cubic inches (this is the displacement of the engine in Mr. M’s vintage VW bus).
13. Determine which of the following
calculations are incorrect by analyzing the units:
a. speed = (6.00 m) ´ (5.00 s)
b. area = (5.0 kg) ¸ (2.0 kg/m2)
c. distance = (70 km/h) ´ (4.0 s)
d. temperature = [(0.0821 L·atm/mol·K) ´ (0.50 mol)] ¸
[(3.0 L) ´ (1.2 atm)]
e. mass = (0.10 kg·m/s2) ´
(30 m)2 ¸ (6.67 ´ 10-11
m3/kg·s2)
Determine a probable solution for problems 14 through 19 based on a unit analysis:
14. Determine the speed of a car that travels 135 km in 1.8 hours.
15. Find the time for a car with speed 45 m/s to travel 10.0 m.
16. Given the density of water is 1.00 g/cm3, determine the mass of a 3.0 L sample.
17. The heat of fusion of water is 3.35 ´ 105 J/kg. How much heat will be needed to melt 0.40 kg of ice at 0 °C.
18. The specific heat of copper is 390 J/kg·C°. By how much will the temperature of a 2.00 kg sample of copper rise if 200 J of heat is added to it?
19. Find the Schwarzschild radius of a black hole with mass 1.5 ´ 1031 kg based on the speed of light, c = 3.0 ´ 108 m/s, and the gravitational constant, G = 6.67 ´ 10-11 m3/kg·s2. This is the distance from which nothing (not even light) can “escape” a black hole.
20. A car moves along a straight track and the distance from a fixed point is measured at various points in time as indicated in the table below. Graph the data and determine the best fit. What is the significance of the constants in the equation?
|
Time (s) |
Distance (m) |
|
1.00 |
17.1 |
|
2.00 |
24.2 |
|
3.00 |
33.1 |
|
4.00 |
40.6 |
|
5.00 |
50.5 |
|
6.00 |
61.2 |
21. An experiment is done in which a fixed quantity of nitrogen is subjected to various pressures and the resulting volume is measured. The experiment is conducted at a fixed temperature. The data are shown in the table below. Graph the data and determine the best fit. Supposing that the temperature was 300 K and there were 2.80 moles of nitrogen determine the value of the constant R in the ideal gas law: PV = nRT.
|
Pressure (kPa) |
Volume (m3) |
|
20.0 |
0.351 |
|
40.0 |
0.180 |
|
60.0 |
0.117 |
|
80.0 |
0.086 |
|
100.0 |
0.072 |
22. A small wall is placed in a wind tunnel and subjected to various speeds of winds to determine the resulting amount of force on the wall. The data from the experiment is shown in the table below. Graph the data and determine the best fit.
|
Speed (ft/s) |
Force (lb) |
|
1.00 |
5.8 |
|
2.00 |
22.8 |
|
3.00 |
51.7 |
|
4.00 |
91.9 |
|
5.00 |
143.0 |
23. Prepare curve straightening graphs for the previous two problems and find the best fit using the form of a line: y = mx + b.