System of Units – Dimensional Analysis – EN

ENEM

Contents with the highest incidence – 10; 12; 30;32;33;36

System of Units – Dimensional Analysis

01-(ENEM-MEC)

Data released by the National Institute for Space Research showed the devastation suffered by the Amazon region between August 1999 and August 2000. Analyzing satellite photos, experts concluded that, during this period, a total of 20,000 square kilometers of forest disappeared from the map. A media outlet reported the fact with the following:

text: The frightening rate of destruction is one football field every eight seconds. Considering that a year has approximately 32.10 ⁶ s (thirty-two million seconds) and that the official measurement of the area of a football field is approximately 10 ^-2 km ² (one hundredth of a square kilometer), the information presented in this news allows us to conclude that such a rate of deforestation, in one year, implies the destruction of an area of

a) 10000 km2 ^, and the comparison gives the idea that the devastation is not as serious as the numerical data indicates.

b) 10000 km2 ^, and the comparison gives the idea that the devastation is more serious than the numerical data indicates.

c) 20,000 km2 ^, and the comparison accurately portrays the pace of destruction.

d) 40,000 km2 ^, and the author of the news exaggerated the comparison, giving the false impression of gravity to a natural phenomenon.

e) 40,000 km2 ^and , when drawing attention to a really serious fact, the author of the news exaggerated the comparison.

02-(ENEM-MEC)

Gilberto Gil uses the compound word LIGHT-YEARS in the lyrics of the song. The practical meaning, in general, is not necessarily the same as in science.

In Physics, a light year is a measurement that relates the speed of light and the time of one year and which, therefore, refers to

a) time. b) acceleration. c) distance. d) speed. e) luminosity.

03-(ENEM-MEC)

Superman and the laws of motion

One reason to think about the physics of superheroes is, above all, that it is a fun way to explore many interesting physical phenomena, from everyday phenomena to events considered fantastic. The following figure shows Superman launching himself into space to reach the top of a building of height H. It would be possible to assume that with his superpowers he would be flying under his own power, but consider that he made a great leap.

In this case, his final velocity at the highest point of the jump must be zero, otherwise he would continue to rise. Since g is the acceleration of gravity, the relationship between Superman’s initial velocity and the height reached is given by: v ² = 2gh.

The height Superman reaches in his jump depends on the square of his initial velocity because

(A) the height of his jump is proportional to his average speed multiplied by the time he remains in the air squared.

(B) the time it remains in the air is directly proportional to the acceleration of gravity and this is directly proportional to the speed.

(C) the time it remains in the air is inversely proportional to the acceleration of gravity and this is inversely proportional to the average speed.

(D) the acceleration of the movement must be squared, as there are two accelerations involved: the acceleration of gravity and the acceleration of the jump.

(E) the height of the jump is proportional to its average speed multiplied by the time it remains in the air, and this time also depends on its initial speed.

Exercises with ENEM characteristics

04-(UCS-RS)

Currently, several companies have made less caloric foods available. To say that a

food has fewer calories meaning it has a lower amount of

a) watts.

b) newtons.

c) pascals.

d) joules.

e) amps.

05-(UECE-CE)

The nanogram is a submultiple of the gram equivalent to:

06-(FATEC-SP)

The kWh is the usual unit of measurement of electrical energy consumption, a multiple of the joule, which is

unit of the International System. The factor that relates these units is:

07-(FATEC)

“ To get an idea of the nanometric universe, in which the dimension of physics is represented by the prefix nano, 1 nm is approximately equivalent to the length of ten atoms lined up. A carbon nanotube has a diameter of around 10 nm. The size of a DNA molecule is around 100 nm and is slightly smaller than that of a virus. Red blood cells are around 10 micrometers (10 mm) or 10,000 nm. The diameter of a strand of hair can measure around 100,000 nm.”

(TOMA, Henrique E. The nanometric world: the dimension of the new century. São Paulo:
Oficina de Textos, 2004. p.13 adapted.)

According to the text and approximate measurements, it is correct to state that

a) a carbon nanotube is one hundred thousand times thinner than a strand of hair.

b) It takes one hundred thousand atoms lined up to make up the diameter of a strand of hair.

c) on the scale mentioned in the text, one micrometer (1 mm) is equivalent to 100 nanometers (100 nm).

d) red blood cells are approximately 10 times larger than viruses.

e) the diameter of a strand of hair is approximately 100 mm.

08-(UFPR-PR)

Regarding physical quantities, units of measurement and their conversions, consider the equalities represented below:

1. 6 m2 ⁼ 60,000 ^cm2 .

2. 216 km/h = 60 m/s.

3. 3000 m3 ⁼ 30 liters.

4. 7200 s = 2 h.

5. 2.5 x ¹⁰⁵ g = 250 kg.

Select the correct alternative.

a) Only the equalities represented in 1, 2 and 4 are true.

b) Only the equalities represented in 1, 2, 4 and 5 are true.

c) Only the equalities represented in 1, 2, 3 and 5 are true.

d) Only the equalities represented in 4 and 5 are true.

Scientific notation – order of magnitude – significant figures

10-(ENEM-MEC)

In a certain neighborhood there are two bus companies, ANDABEM and BOMPASSEIO, which take and bring passengers from the suburbs to the city center. A bus from each of these companies leaves the terminal every 30 minutes, at the times indicated in the table.

Carlos lives near the bus terminal and works in the city. Since he doesn’t have a set time to arrive at work and doesn’t have a preference for any of the companies, he always takes the first bus that leaves the terminal. In this situation, it can be said that the probability of Carlos traveling on a bus from the company ANDABEM is

a) a quarter of the probability of him traveling on a BOMPASSEIO bus.

b) one third of the probability of him traveling on a BOMPASSEIO bus.

c) half the probability of him traveling on a BOMPASSEIO bus.

d) twice as high as the probability of him traveling on a BOMPASSEIO bus.

e) three times greater than the probability of him traveling on a BOMPASSEIO bus.

11-(UNIMONTES-MG)