1ºEM - Practice with Significant Figures

 1-) Determine the perimeter and area of ​​an A4 sulfite sheet using a millimeter ruler for the length and the ruler indicated by the teacher for the width.

2-) Determine the grammage (G) of a sheet of paper defined as

 G = m / A 

where m is the mass of the sheet and A is the area calculated in exercise 1. Response in       g / m² (grams per square meter).

3-) Determine the density of the water,           

 d = m / V,

by measuring its mass m on a accuracy balance and its volume V in a  graduated cylinder in ml. Reminder: measure the mass of the empty graduated cylinder and after this, the mass of graduated cylinder  with water and subtract to obtain the water mass

4-) Determine the acceleration of local gravity by measuring the mass of a wooden block on an accuracy balance and its weight on a dynamometer. 

Reminder: weight = P = m. g, where m is the mass of the body and g is the acceleration of gravity. Logo g = P / m (P in N, m in kg and g in m / s²) 

2º EM - Atividade Impulso e Quantidade de movimento

 ATIVIDADE DE IMPULSO E QUANTIDADE DE MOVIMENTO

1-) Uma força constante atua durante 5,0 s sobre uma partícula de massa 2,0 kg, na direção e no sentido de seu movimento, fazendo com que sua velocidade varie de 5,0 m/s para 9,0 m/s. Determine:

a-) o módulo da variação da quantidade de movimento da partícula;

b-) a intensidade do impulso da força atuante;

c-) a intensidade da força.

2-) um corpo de massa m = 10 kg possui velocidade v1 de direção horizontal e intensidade 3 m/s. Recebe um impulso I de uma força F que altera sua velocidade inicial v1 para v2 perpendicular a v1 e de intensidade igual a 4 m/s. Determine o impulso I dessa força F.

3-) Um projétil de massa 20 g incide horizontalmente sobre uma tábua com velocidade de 500 m/s e a abandona com velocidade horizontal e de mesmo ssentido de valor 300 m/s. Qual a intensidade do impulso aplicado ao projétil pela tábua?

4-) Um corpo é lançado verticalmente para cima com velocidade inicial de 20 m/s. Sendo 5,0 kg a massa do corpo, determine a intensidade do impulso da força-peso entre o instante inicial e o instante em que o corpo atinge o ponto mais alto da trajetória

5-) Sobre um corpo de massa 3,0 kg, movendo-se a 5,0 m/s, age uma força de maneira que, após 10 s, sua velocidade tem o valor de 2,0 m/s em sentido oposto ao inicial. Qual o valor da intensidade da força que atuou sobre esse corpo?

6-) Um carrinho de massa 100 g encontra-se em repouso quando nele passa a atuar uma força resultante F de direção constante e cuja intensidade varia com o tempo conforme o gráfico. Determine:

a-) a intensidade do impulso da fora F no intervalo de tempo de 0 a 1,0 s;

b-) a velocidade do carrinho no instante 2,0 s.

2º EM - Laboratory: Horizontal Launch

 One of the great branches of Physics, studied since the beginning of human history, is the movement of projectiles called Ballistics. They involve projectile launch in 3 situations: when the launch is made in the vertical direction (the velocity only has a vertical component), when the initial velocity has only a horizontal component and when the initial velocity has both vertical and horizontal components (called oblique launch). In today's class we will work with horizontal releases. To do this, go to the link below:

https://phet.colorado.edu/sims/html/projectile-motion/latest/projectile-motion_pt_BR.html

1. After accessing the link, enter the second icon: vectors. Click on the " + " sign at the base of the cannon and raise it until it reaches 15 m and place the cannon horizontally (0° inclination). Select a 0.2 m diameter, 2 kg mass cannonball, turn off air resistance, select a velocity of 10 ms-1 and fire the cannon (red icon at the bottom). Measure horizontal range and movement time. Repeat the procedure for speeds of 15 m/s and 18 m/s.

Questions:

Has the horizontal range changed?

Has the movement time changed?

Has the vertical component of velocity changed?

CONCLUSIONS:

2. Change the height to 12 m, launch with speeds of 10 m/s, 15 m/s and 18 m/s. Measure horizontal range and movement time. Compare with previous results and draw conclusions.

3. a Return the cannon to a height of 15 m, quadruple the bullet diameter and repeat the procedure for a velocity of 18 m/s. Comparing the two situations, was there any change in movement time? And in the horizontal range?

3. b Return the diameter to 0.2 m and quadruple the bullet's mass. Repeat the procedure for the speed of 18 m/s. Comparing the results for this situation and the initial one, was there a change in the movement time? And in the horizontal range?

CONCLUSIONS:

4. Go back to the starting bullet (0.2 m and 2 kg) but now add air resistance.

a. Make throws at 5 m/s, 10 m/s and 15 m/s, noting movement time and horizontal reach.

b. Triple the bullet diameter and repeat this procedure.

c. Return to 0.2 m in diameter and triple the bullet's mass, repeating the procedure used in the two previous situations.

QUESTIONS:

Does fall time depend on launch speed?

Does the fall time depend on the diameter of the bullet?

Does the fall time depend on the bullet's mass?

CONCLUSIONS:

1º EM - Exercises: Operations with significant figures

 1-) Write the following measurements with only 3 significant figures:

a-) 624.45 cm 

b-) 7.546 g 

c-) 76.58 s 

d-) 65.445 m

2-) A train travels by recording the time intervals below between stations:

from A to B: 4.83 h

from B to C: 6.50 h

from C to D: 0.982 h

from D to E: 4 h

Correctly express the time the train takes:

a-) to go from A to C 

b-) to go from B to D 

c-) on the total route

d-) write the result of item a-) in non-decimal form (in h min s).

3-) Perform the indicated operations:

a-) 57.68 cm + 6.672 cm - 8.7 cm =

b-) 627.50 m²: 1.20 m =

c-) 0.48 m x 825.3 m =

d-) 321.785 m + 254.7 cm - 0.270 km =

e-) (2.045x103) m .(2.35x102) m  =

4-) The mass of the Sun is about 1.99x1030 kg. The mass of the hydrogen atom, the main constituent of the Sun, is 1.67x10-27 kg. How many hydrogen atoms are there in the Sun? What is the order of magnitude of this result?

5-) A prism-shaped solid has volume V = 18.60 m³ and base area S = 2.25 m². Remembering that V = S.h, determine your height h in meters.

6-) A triangle has a base of 192.81 cm and a height of 8.9 cm. Calculate your area and represent the result with the correct number of S. F..

7-) The value of the electrical force between two charges, Q1 and Q2, is given by the expression:

F =(k. Q1 . Q2) : d2

If Q1 = 8.20x10-6 C, Q2 = 3.87x10-6 C, d = 1.45x10-2 m and k = 9.0x109 N.m2 /C² , calculate the magnitude of the electric force and express the result using significant figures .

8-) The measurement of the length of a pencil was performed by a student using a ruler graduated in mm. Of the alternatives presented, the one that correctly expresses the measure obtained is: (justify your choice)

a-) 15 cm 

b-) 150 mm 

c-) 15.00 cm 

d-) 15.0 cm 

e-) 150.00 mm

1º EM - Physical Measures

 PHYSICAL MEASURES

A - SCIENTIFIC NOTATION 

In Physics, you will have to cope with very small and very large numbers. Numbers are written using powers of ten to make them less awkward. This is known as SCIENTIFIC NOTATION. This type of representation, in addition to being more compact, allows us a quick comparison with other known values, facilitating its understanding. Any number can be written as the product of a number between 1 and 10 by an integer power of 10.

B - Significant Figures

Significant Figures of a measure: We call significant figures all the correct figures (read on the measuring device) and one more doubtful figure (evaluated by the operator).

PRACTICE: Measure the 3 straight segments using devices with different accuracy. Express these measurements using significant figures.

Straight segment	Scale 1	Scale 2	Scale 3
AB
CD
EF

NOTE: The number of significant figures depends on the device used in the measurement. As the last digit is ALWAYS doubtful (evaluated by the operator), the previous digit shows the smallest scale division of the device. If we have a measurement like 2.4 m, this indicates that the “ruler” used was divided every 1 meter. If it were 2.40 m, the doubtful number is in the cm and therefore the smallest division is dm. Therefore, in the case of measurements, 2.4 m is different from 2.40 m.

C - OPERATIONS WITH SIGNIFICANT FIGURES

Calculations involving measurements should only contain significant figures in the results. For that, it is necessary to follow some rules that, if not followed, may generate figures that are not significant.

1.  ADDITION AND SUBTRACTION: suppose you want to add the following portions:

2807.5 + 0.0648 + 83.645 + 523.35

In order for the result of the addition to contain only significant figures, you should initially observe which or which of the plots has the least number of decimal places. In our example it is the portion that has only one decimal place. This portion will be kept as is. The remaining plots must be modified in order to keep the same number of decimal places as the first chosen installment, leaving as many digits in them as necessary.

Thus, in the 0.0648 portion we must abandon the digits 6, 4 and 8. When we abandon digits in a number, the last digit maintained must be added by one unit if the first digit abandoned is greater than or equal to 5 or remains as it is. if the first digit left is less than 5 (rounding rule). Let's see how the example portions look like:

2807.5 remains unchanged 2807.5

0.0648 is replaced by 0.1

83.645 is now written 83.6

535.35 is replaced by 525.3

The correct result is 3416.5

In SUBTRACTION, the same procedure must be followed.

2. MULTIPLICATION AND DIVISION: Suppose we want, for example, to multiply 6.85 by 3.2. Normally performing the operation, we find

6.85. 3.2 = 21.92

However, proceeding in this way, figures appear that are not significant. To avoid this, we must observe the following rule: check which factor has the lowest number of significant figures and, in the result, keep only a number of figures equal to this factor. Thus, in the previous example, since the factor with the fewest significant figures is 3.2, we must maintain, in the result, only two figures, that is, the result must be written as follows:

6.85. 3.2 = 22

In the application of this rule, when abandoning figures in the product, we must follow the same rounding criterion clarified in the addition. A similar procedure must be followed when making a DIVISION.

COMMENTS:

- when counting the significant figures of a measurement, we must note that the figure zero is only significant if it is located to the right of a significant figure. So,

0.00035 has only two significant digits (3 and 5) because the zeros are not significant

35000 has five significant digits, because zeros here are significant

0.00305 has three significant figures, since the zeros to the left of the figure 3 are not significant.

- when making a change of units, we must be careful not to write zeros that are not significant. For example, suppose that we want to express, in grams, a measure of 8.5 kg. Note that this measure has two significant figures,  and the figure 5 is doubtful. If we were to write

8.5 kg = 8500 g

we would be giving the erroneous idea that 5 is a correct number, the last zero being added to the doubtful number. To avoid this misinterpretation, we use scientific notation and write

8.5 kg = 8.5x10³ g

In this way, the change of units was made and we continue to indicate that the number 5 is doubtful.

(text adapted from COURSE OF PHYSICS volume 1 by Beatriz Alvarenga and Antônio Máximo Ed. Harbra SP / 1985).

Other sources for operations with significant figures:

https://chem.libretexts.org/Courses/Eastern_Mennonite_University/EMU%3A_CHEM_155_-_Matter_and_Energy_(Yoder)/Unit_1/A%3A_Preliminary/2.5%3A_Significant_Figures_in_Calculations (access on 03/15/21) 

https://www.khanacademy.org/math/arithmetic-home/arith-review-decimals/arithmetic-significant-figures-tutorial/v/significant-figures (access on 03/15/2021)