Unit 1 Homework A...pdf - Troy High School

Algebra in Physics Homework Answers:
1. a) m = DV b) V = m D
4. a) m 1
= Fr2
Gm 2
b) r = Gm 1m 2
F
7. B =
!"P •V
"V
11. V ball
= 2V cube
D = m V ! V = m D
2
2. v o
= 2v rms
! v 2 3. n = PV
RT
5. v = 2gh 6. a) L = !r4 (P 1
" P 2
)
8nQ
8. v = c 1! m 2
o
m 2 9. r = 3m
3 10. h = m
4
3 "r3 = 2 m D
4!D
r =
3
3m
2"D
Dlw
12. Rt = W W 1
+ W 2
= W T
16t + 32t = 16 48t = 16 t = 1 3 h = 20min
b) P 2
= P 1
! 8nQL
"r 4
13. let C = cost motor
and N = # motors (C + 1)(N ! 20) = 350 C •N = 300
N = 300
C
(C + 1)( 300
C
! 20) = 350 300 ! 20C +
300
C
! 20 = 350
!20C + 300
C = 70 ! 20C2 + 300 = 70 C ! 20C 2 ! 70 C + 300 = 0 "quadratic"
C = 70 ± !702 ! (4 •!20 • 300)
2(!20)
= $2.50 N = 300
C = 300 = 120 motors
2.50
14. solve for x: 4.9t 2 + 12.4t - 115 = 0
x = !12.4 ± 12.42 ! (4 • 4.9 •!115)
quadratic yields: 3.7 & -6.3
2(4.9)
-------- HOMEWORK ANSWERS: SIG FIGS & EXPONENTIAL NOTATION ------------
1. How many significant figures are there in each value?
(a) 112.00 cm 5 (b) 0.00075 kg 2 (c) 120,000,000 g 2 to 9 (d) 12.1 dm 3
(e) 306 L 3 (f) 8.050 hr 4 (g) 2.5 x 10 7 m/s 2 (h) 6.0 nm 2
(i) 1.11 x 10 -4 V 3 (j) 1,050 m 3 3,4 (k) 1.5 x 10 6 kV 2 (l) 2.0000 x 10 -3 mg 5
2. Add the following and then express the final answer with correct sig figs.
(a) 803 + 7 + 0.66 = 811 (b) 16.425 + 7.21 + 5.0 = 28.6
(c) 0.0035 + 0.067 + 0.255 = 0.326 (d) 4.0 + 0.732 + 0.748 = 5.5
3. Subtract the following and then express the final answer with correct sig figs.
(a) 6.26 - 0.2 = 6.1 (b) 352.4 - 16.8 = 335.6 (c) 44 - 0.2 = 44 (d) 125.7 - 4 = 122
4. Multiply the following and then express the final answer with correct sig figs.
(a) 2.81 x 0.3 = 0.8 (b) 92.4 x 0.074 = 6.8 (c) 2.02 x 3.117 = 6.30
(d) 157.86 x 0.610 = 96.3 (c) 19.4 x 89 = 1.7 x 10 3 (d) 82.4 x 9.6 = 7.9 x 10 2
5. Divide the following and then express the final answer with correct sig figs.
(a) 91.52/7.54 = 12.1 (b) 19.28/0.614 = 31.4 (c) 0.032/0.004 = 8 (d) 9.8/2.3 = 4.3
6. Convert to exponential notation: (a) 1,550,000,000 1.555 x 10 9
(b) 0.00000750 7.50 x 10 -6 (c) 133,000 1.33 x 10 5 (d) 0.008000 8.000 x 10 -3
7. Give the answer in correct exponential notation using correct significant figures:
1.28 x 10 12
(a)
8.85 x 10 = (b) (4.4 x 108 ) x (5.7 x 10 9 )
= 15 (6.76 x 10 !31 ) 3 (a) 1.45 x 10 -4 (b) 7.6 x 10 -25
8. Give the answer in correct exponential notation using correct significant figures:
(a) (1850) 4 1.17 x 10 13 (b) (1.5 x 10 -5 ) 5 7.6 x 10 -25
9. Give the answer in correct exponential notation using correct significant figures:
5 4
(a) 1,990,000,000,000 (b) 6.02 x 10 23 (a) 182 (b) 8.81 x 10 5
10. (a) (6.12 x 10!6 ) 4 5.55 x 1044
= (b)
(2.15 x 10 4 3
) 6.66 x 10 = 32 (a) 1.41 x 10-34 (b) 8.33 x 10 11

11. (3.33 x 10 5 ) 4 x (3.75 x 10 6 ) 3 = 6.48 x 10 41
12. 5.55 x 10 !18
3
x (4.44 x 10 14 ) 4 x (3.95 x 10 !22 ) 2 1.07 x 10 10
13. (a) (1.28 x 1012 ) 5
(8.85 x 10 15 ) = (b) (4.98 x 1012 ) 2 x (5.55 x 10 5 ) 4
= 3 (6.76 x 10 !11 ) 3 (a) 4.96 x 10 12 (b) 7.62 x 10 28
========= METRIC HOMEWORK ANSWERS =================
1. Give the symbol and multiplier for each of the following metric prefixes:
(a) kilo = k 1000 (b) centi = c 10 -2 (c) hecto = h 10 2 (d) deka = da 10 1
(e) Mega = M 10 6 (f) nano = n 10 -9 (g) milli = m 10 -3 (h) Giga = G 10 9
(i) micro = µ 10 -6 (j) Tera = M 10 6 (k) deci = d 10 -1 (l) pico = p 10 -12
2. Give the name of each of these units, and show how many of the base unit it is:
(a) cm= centimeter 0.01m (b) Mg = Megagram (c) ns= nanosecond 10 -9 s (d) dg= decigram 10 -1 g
(e) kg = kilogram 1000 m (f) ps=picosecond 10 -12 s (g) hm=hectometer 100 m (h) Gm=Gigameter 10 9 m
(i) µg= microgram 10 -6 g (j) µL = microliter 10 -6 L (k) dam = dekameter 10 m (l) nL= nanoliter 10 -9 s
3. Circle the larger unit: (a) pound - kilogram (b) liter - gallon
(c) quart - liter (d) meter - yard (e) mile - kilometer
(f) nanometer - Angstrom (g) micron = micrometer (h) English ton-Metric ton
4. What word and symbol prefixes indicate the following multipliers?
(a) 10 -6 = µ micro (b) 10 3 = k kilo (c) 10 -9 = n nano (d) 10 12 = T Tera
(e) 10 -1 = d deci (f) 10 9 = G Giga (g) 10 -3 = m milli (h) 10 2 = h hecto
(i) 10 6 = M Mega (j) 10 -2 = c centi (k) 10 1 = da deka (l) 10 -12 = c pico
5. (a) 1m = 1000 mm 1mm = 0.001 m 1nm = 10 -9 m 1 m = 10 9 nm
(b) 1 cm = 0.01 m 100 cm = 1.00 m 1,000 g = 1 kg 10 -6 g = 1 µg
(c) 1 hm = 100 m 10 m = 1 dam 1,000 L = 1 kL 1 dm = 0.1 m
(d) 1 km = 1000 m 1 mW = 0.001 W 1 ns = 10 9 s 10 6 g = 1 Mg
(e) 1 µL = 10 -6 L 1 L = 10 6 µL 1 dam = 10 m 1m = 0.1 dam
6. Fill in the blank with the missing unit:
(a) 3.2 x 10 -6 g = 3.2 µg (b) 8.8 s = 8.8 x 10 9 ns (c)125 cm = 1.25 m
(d) 5.7 x 10 -3 L = 5.7 mL (e) 1.23 x 10 -12 m =1.23 A (e) 16 m = .16 hm
(f) 5.3 x 10 -3 m = 5.3 mm (g) 0.0055 kg = 5.5 g (h) 55 nm = 550 µm
7. Convert: (a) 4.94 kg = 4.94 x 10 3 g (b) 178 mL = 0.178 L (c) 6.50 m = 6.50 x 10 2 cm
(d) 82 ms = 8.2 x 10 4 µs (e) 27.5 pm = 0.0275 nm (f) 0.000055 km = 55 mm
8. Convert: (a) 125 dm = 1.25 x 10 3 cm (b) 0.055 kg = 5.5 x 10 4 mg
(c) 125,000 L = 0.125 ML
(d) 0.01733 L = 17.33 mL
(e) 45 mL = 45 cm 3 (f) 12.5 hm = 1.25 x 10 12 nm
(g) 3.4 x 10 6 µg = 3.4 x 10 -3 kg (h) 0.0033 kL = 0.33 daL
(j) 56.5 ns = 5.65 x 10 -5 ms (k) 2.2 x 10 -4 Mg = 2.2 x 10 8 µg
9. Circle the smallest? Underline the largest: (a) 0.000055 m (b) 0.000567 cm
all converted to meters: (a) 5.5 x 10 -5 (b) 5.67 x 10 -6
(c) 6.5 nm (d) 123,255 pm (e) 4.7 x 10 -8 km (f) 0.005 mm (g) .48 µm
(c) 6.5 x 10 -9 (d) 1.23255 x 10 -7 (e) 4.7 x 10 -5 (f) 5 x 10 -6 (g) 4.8 x 10 -7
=== Dimensional Analysis Homework Answers ===
Answers: 1 . 8.95 m 2. 1.04 x 10 7 m 2 3. 24.6 m/s 4. 5.36 L 5. 7.27 g/cm 3
6. 3.60 x 10 12 ns 7. $59.14 8. (a) 99.1 L (b) 218 lb 9. 2.22 x 10 4 furlongs/fortnight
10. 3.96 x 10 25 atoms 11. 121 mm 12. 0.175 km
13. $6,904 (Wow! No wonder Hummer rhymes with dumber)