System of Units – Dimensional Analysis – Resolution – EN
Commented Resolution
System of Units – Dimensional Analysis
01- Using a rule of three — 8s – 10 -2 km 2 — 32.10 6 s – n km 2 — n = 32.10 6 .10 -2 /8 — n = 4.10 4 km 2 = 40,000 km 2 .
R- And
02- The light year is a unit of length — it corresponds to the space traveled by a ray of light in 1 year, in a vacuum, at a speed of 3.10 8 m/s —
R- D — Note: This is too large a measurement for our common applications here on Earth.
This unit is used to measure distances in cosmic space, between stars in the same galaxy or between different galaxies. It is useful for astronomers.
03 – This is the Torricelli equation, V 2 = V o 2 + 2.ah — with V = 0 — whose deduction is made from V m = ΔS/Δt — where — V m = (V + V 0 )/2=h/t — h=(V + V o )t/2 — h=V m .t/2 — note in this equation that h is proportional to V m eat — R- E
04- Calories correspond to the unit of energy, which in SI is measured in joules (J) — R- D
05- 1 nanogram=10 -9 g — R- B — see table below
06- 1kW is equivalent to 10 3 W — 1h is equivalent to 3.6.10 3 s — relationship between Joule and ws — 1J = 1w.s —
1kWh = 10 3 W . 3.6.10 3 s = 3.6.10 6 W.s — 1kWh = 3.6.10 6 J — R- D
07- According to the text, the diameter of a strand of hair can measure approximately
100,000nm = 10 5 nm=10 5 .10 -9 m =10 4 m =10 2 .10 -6 m =100.10 -6 m=100mm — R- E
08 – 1. Correct — 6 m 2 = 6 (100 cm) 2 = 6.10 4 cm 2 = 60,000 cm 2 .
2. Correct — 216 km/h = 216/3.6 
m/s = 60 m/s.
3. Wrong — 3,000 m 3 = 3,000 (1,000 L) = 3,000,000 L.
4. Correct — 7,200 s = 7,200/3,600h = 2 h.
5. Correct — 2.5 10 5 g = 
2.5.10 2 kg = 250 g
R-B
09- Energy of a truck — E 1 = 10kWh = 10.10 3 Wh = 10 4 Wh — Total energy — E t = 200.000.MWh = 200.10 3 .10 6 Wh = 2.10 11 Wh — rule of three — 1 kg of coal – 10 4 Wh — M of coal – 2.10 11 Wh — M = 2.10 11 / 10 4 — M = 2.10 7 kg of coal — another rule of three — 1 truck – 1 ton = 10 4 kg — n trucks – 2.10 7 kg — n = 2.10 7 / 10 4 — n = 2.10 3 trucks — R – D
10- Carlos has 10 minutes out of every 30 to travel on BOMPASSEIO and 20 minutes out of every 30 to travel on ANDABEM.
Thus, considering that the expression “twice as large” means twice as much, the probability of Carlos traveling on a bus from the company ANDABEM is twice as large as the probability of him traveling on a bus from the company BOMPASSEIO.
R-D
11- Note that Pedro’s measurement has 4 significant digits while Gabriel’s has 3 — R- B
12- V total l = 1,000,000,000km 3 = 10 9 . 10 9 m 3 — V total l = 10 18 m 3 — V fish = 100 × 100,100 — V fish = 10 6 m 3 — V total / V fish = 10 18 m 3 / 10 6 m 3 — V total / V fish = 10 12 kisses — R- B
13- E=1354kWh=1,354.10 3 .10 3 W.3,6.10 3 s — E=4,9.10 9 Ws — OG=10.10 9 =10 10 J — R- A
14- Earth’s surface area — STEarth=π.r 2 =3.14.(6.4.10 3 ) 2 — S Earth =129.10 6 km 2 — year 2000 — S´=5% of 129.10 6 — S’= 0.05×129.10 6 — S’=6.45.10 6 — 6.45>3.16 — OG=10.10 6 — OG=10 7 km 2 — R- C
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