Nature of Science EXPRESSING NUMBERS FROM STANDARD FORMAT TO SCIENTIFIC NOTATION
Science – systematized body of knowledge (“Scientia” – knowledge) STEP 1. Locate the decimal point
STEP 2. Move the decimal point so as to follow the format M x10n
Branches of Science: STEP 3. Count the number of times you move the decimal point (AND THAT WILL BE THE
• Mathematics and Logic – analysis of numerical data and reasoning EXPONENT) RULEs: If you move the decimal point to the LEFT, the exponent will be POSITIVE.
• Natural Science – study of nature and universe If you move the decimal point to the RIGHT, the exponent will be NEGATIVE.
a. Physical Science – physical entities
b. Biological Science – study of living tings EXPRESSING NUMBERS FROM SCIENTIFIC NOTATION TO STANDARD FORMAT
• Social Science – concerned with society and human interactions STEP 1. Locate the decimal point
STEP 2. Move the decimal point depending on the given exponent.
Physics - study of matter and energy and their interaction to each other and in space and time (EXPONENT = the number of times you will move the decimal point)
RULEs: If the exponent is POSITIVE, move the decimal point to the RIGHT.
Branches of Physics If the exponent is NEGATIVE, move the decimal point to the LEFT.
• Classical Physics – study of motion and energy
a. Mechanics – motion and forces ADDITION AND SUBTRACTION
• Statics – bodies at rest Only numbers in Scientific Notation that have identical exponent (n) may be added or subtracted
• Dynamics – bodies in motion EX: 7.9 x 102 - 6.4 x 10-1 = 7.8936 x 102
• Fluid Mechanics – motion of liquids and gases MULTIPLICATION
b. Thermodynamics – temperature and heat energy To get the M of the product, multiply the two M of both factors then add the exponent (n) of
c. Acoustics - sounds both factors.
d. Electrodynamics – electricity and magnetism EX: (5.1 x 105) (3.0 x 103) = 1.53 x 109
e. Optics – light DIVISION
• Physical optics – nature of light To get the M of the quotient, divide the M of both factors (M of the dividend by the M of the
• Geometrical Optics – behavior of light as it travels trough different divisor) then subtract the exponent (n) of both factors.
objects EX: (2.02 x 103) % (3.20 x 10-2) = 6.3125 x 104
• Modern Physics – basic structure of material world
Systems of Measurement
a. Quantum Physics – individual units of energy
English System – old system of measurement (e.g. inch, yard, mile, pint, ounce, pound, ton)
b. Atomic Physics - atoms
Metric System/SI units – units for scientific measurement (e.g. meter, liter, gram)
c. Molecular Physics - molecules
d. Nuclear Physics – atomic nucleus
SI Base Units
e. High energy Physics/Particle Physics – sub-atomic particles
PHYSICAL QUANTITY SI Base Unit SYMBOL
f. Solid State Physics/Condensed-matter Physics – solid materials
Length meter m
g. Plasma Physics – plasma Mass kilogram kg
Time second s
Scientific method - systematic approach to solve a problem Electric current ampere A
1. Observation 4. Prediction Temperature kelvin K
2. Organizing data 5. Experimentation Luminous intensity candela cd
3. Formulating hypothesis 6. Conclusion Amount of substance mole mol
OPRHEAC (Observation, Problem, Research, Hypothesis, Experiment, Analyze, Conclude)
Hypothesis –tentative explanation; no experimental proof Derived SI Units
Model – scientific assumptions; accurate under limited situations PHYSICAL QUANTITY SI Derived Unit SYMBOL
Theory – supported by several experimental evidences; flexible to be modified Area square meter m2
Law – theories that stand for a very long time and experimentally proven/ universal Volume cubic meter m3
Density kilogram per cubic meter Kg/m3
Scientific notation Speed meter per second m/s
Scientific notation - process of expressing very large or very small numbers in exponential form Force Kilogram meter per second Kg m/s2
square
A number expressed in scientific notation follows the format: a x 10 b
where: a = coefficient (a number between 1.0 to 9.99)
b = exponent (can be a positive or negative whole number) Exact numbers - e.g. 5 students, 3 teachers, 6 classrooms
Example: 2,358,000 = 2.358 x 106 Inexact numbers – e.g. 16.4 cm, 2.0 kg or rice
, Significant Figures
Significant figures refers to the number of digits in a quantity that is known to be certain. Express the following in scientific notation Express the following in standard form:
RULES FOR COUNTING SIGNIFICANT FIGURES form: 1. 2.437 X 103
1. Non-zero integers are always counted as significant figures. Ex: 4567 has 4 SF 1. 345,679,000 2. 2.245 X 102
2. Zeros are classified into three types: 2. 2000 3. 5 X 10-2
a. Leading zeros, those that precede all the non zero digits, are not significant figures. 3. 0.004 567 190 4. 4.5 X 10-1
Ex: 0.000035 has 2 SF only 4. 0.000 007 100 5. 6.34104 X 107
b. Captive zeros, those between non zero digits are always significant figures. Ex: 1005 has 4 SF 5. 234, 105 6. 5 X 102
c. Trailing zeros, those at the right end of the number are sometimes significant figures. They 6. 500 7. 3 X 101
are considered significant only if the number contains a decimal point. Ex: 1.567800 has 7 SF 7. 30 8. 3.424 X 10-3
300 can be expressed as: 3.00 x 10 2 (3 SF) 3.0 x 10 2 (2 SF) 3 X 10 2 (1 SF) 8. 0.000 034 590 9. 2.245 X 10-5
9. 0.451 10. 8.304 X 10-4
Multiplication/Division 10. 0.345 450
Always round off the final answer following the term with the LEAST number of SIGNIFICANT
FIGURES. Solve the given problems involving numbers Determine how many significant figures are
Ex: 1.62 x 5.6 = 9.072= 9.1 expressed in scientific notation. Show your in each of these numbers.
complete solution. 1. 6.2 in
Addition/Subtraction 1. (2.3 x 104) (4.2 x 103) 2. 5.083 ft
Always round off the final answer following the term with the largest rightmost significant 2. (1.03 x 106) + (6.3 x 104) 3. 315.0 m
digit. 3. (8.4 x 105) - (9.9 x 103) 4. 0.00400 mi
Ex: 419.35 + 2.7543 – 27. 0 = 395.1043 = 395.1 4. (8.03 x 109) ÷ (4.2 x 106) 5. 56.0 g
11,000 + 25 = 11,025 = 11,000 5. (7.3 x 109) (2.0 x 103) Express the following in accordance to the
6. (4.5 x 10-4) (7.2 x 10-2) indicated significant figures
Conversion of Units 7. (1.03 x 106) + (6.3 x 104) 1. 32.426 (4SF)
CONVERSION OF UNIT refers to the process of CHANGING the UNIT of a given MEASUREMENT 8. (6.24 x 106) - (6.9 x 103) 2. 77.015 (3SF)
to another unit (DESIRED unit) 9. (8.13 x 109) ÷ (2.4 x 10-6) 3. 0.08965 (3SF)
CONVERSION FACTOR refers to a ratio of two (2) measurements with different units. It can be 10. (8.3 x 109) (2.0 x 103) 4. 0.08975 (2SF)
written in fraction form. 5. 1.153 x 103 (3SF)
FACTOR-LABEL METHOD (Dimensional Analysis) refers to the process of converting units
wherein the given measurement is multiplied to a CONVERSION FACTOR to get the desired
measurement with a different unit Express the answers in correct number of Convert the following units of
LENGTH MASS VOLUME TIME significant figures measurement:
1km = 1000m 1kg = 1000g 1 L = 1000 mL 1 h = 60 min 1. 1.043 + 7.4 + 64.23 1. 25 km to cm
1m = 100cm 1g = 1000mg 1 L = 1.06 qt (quart) 1 min = 60 s 2. 73.45 – 4 + 16.8 2. 1500 m to km
1dm = 10cm 1oz = 28.35g 1 mL = 1 cm3 1 h = 3600 s 3. 621.6 + 140 + 315 3. 4km to dm
1in = 2.54cm 1lb = 454g 1 m3 = 1000 L 4. 37.3 x 3.54 4. 3850 g to kg
1ft = 0.30m 1kg = 2.21 lb 5. 0.18 ÷ 4.65 5. 450 lb to kg
1m = 3.28ft 6. 475.04 ÷ 2.0 6. A wrestler’s official weigh-in is
1mi = 1.61km 7. 6.0250 ÷ 3.22 220.5 kg. If the allowable range of
Example: 15 kg to oz
1ft = 12in 8. (23. 40) (1.9) weight for his fight is 400 – 500 lb,
15 kg x (1000g/1 kg) x (1 oz/28.35 g) = 529.10 oz (5SF)
1yd = 3ft 9. (780) (120) is he allowable to brawl/fight?
10. 125.350 ÷ 25.1 7. If a 78 years old man spent 13
Accuracy and Precision years of his life watching TV, how
Precision is the closeness of a set of repeatedly measured values. much hours did he consume in
Accuracy is linked to how close a single measurement is to the true value. front of the TV?
, Scalar and Vector Force - a push or a pull
Scalar Quantity - magnitude An object was pushed by exerting the listed forces below. What is the total force acting on
Symbol Name Example the object?
d distance 15 m F1 = 300 N due east F2 = 300 N due south F3 = 300 N 35° N of E
s speed 60 m/s F4 = 300 N 70° S of E F5 = 300 N due 120°
t time 60 s G- F1 = 300 N due east; F2 = 300 N due south S- F1x=300 F1y = 0
E energy 200 J F3 = 300 N 35° N of E ;F4 = 300 N 70° S of E F2x=0 F2y = -300
Vector Quantity – magnitude + direction F5 = 300 N due 120° F3x=300 cos 35 F3y = 300 sin 35
Symbol Name Example R- Ft = ? F4x=300 cos 70 F4y = -300 sin70
D displacement 15 m, N 30◦E E- x = r cos θ y = r sin θ F5x=300 cos120 F5y =3 00 sin120
v Velocity 60 m/s, East R =√ ∑x2 + ∑y2
F Force 45 N, 120◦ θ = tan -1 ∑y /∑x R =√ 498.352 + -150.032 = 520.44 N
θ = tan -1 150.03 /498.35 = 16.75°
a acceleration 5.0 m/s2, up
A vector is represented by an arrow
A- 520.44 N, south of east
Arrowhead – indicates the direction of the vector
Length of the arrow – represents the magnitude of the vector
Tail – represents the origin of the vector Vector Resolution - process of finding the component of a resultant vector
Vector component can be positive or negative
Resultant vector - the sum of 2 or more vectors Formula in getting the x and y components: x = r cos θ y = r sin θ
A heavy table is being pushed by a group of students towards 50° north of east with a force of
Addition of collinear vectors c. 30 m, east + 10 m, west =
a. 3 m, east + 4 m, east = d. 75 m, south + 100 m, north = 50 N. How much force is exerted horizontally and vertically to the table?
b. 6 m, north + 6 m, north = e. 30 m, north + 40 m, south = G- 50 N, 50° north of east – F S- x = 50 cos 50 y = 50 sin 50
R- Fx = ? Fy = ?
Addition of non-collinear vectors E- x = r cos θ y = r sin θ A- Fx = 32.1 N Fy = 38.30 N
• Analytical Method
1. Pythagorean Theorem (Addition of 2 vectors) Practice Exercises:
– Formula in getting the resultant magnitude: c2= +a2 b2 1. A plane flying with a velocity of 100 m/s due north is blown by a 500 m/s strong wind due
– Formula in getting the resultant direction: θ = tan-1 opposite side/adjacent east. What is the plane’s resultant velocity?
side 2. An object was pushed by exerting the listed forces below. What is the total force acting on
the object?
2. Component Method (Addition of 2 or more vectors) F1 = 12 N due north
– Formula in getting the x and y components: x = r cos θ y = r sin θ F2 = 10.2 N 30° S of E
– Formula in getting the resultant magnitude: R =√ ∑x2 + ∑y2 F3 = 8.5 N 70° N of E
– Formula in getting the resultant direction: θ = tan -1 ∑y /∑x F4 = 5.5 N due west
– Possible directions: N of E; S of E; N of W; S of W 3. A cabinet is being pulled 25° north of east through a ladder with a force of 20 N. How
much force is exerted horizontally and vertically to the cabinet?
• Graphical Method Seatwork
1. Parallelogram Method (Addition of 2 vectors) 1. A boat sailing with a velocity of 5 m/s due south is blown by a 25 m/s strong wind due
2. Polygon Method (Addition of 2 or more vectors) east. What is the boat’s resultant velocity?
2. A bag is being lifted and dragged 55° north of east through the floor with a force of 18
Distance – actual path taken by the object on its motion N. How much force is exerted to lift and drag the bag?
Displacement – distance of the object from the origin to the 3. An object was pushed by exerting the listed forces below. What is the total force
acting on the object?
The ship sails 20 km south, then 15 km east. What is the ship’s total distance & displacement?
F1 = 50 N due south
G- 20 km, south – d1 S- dt = 20 km + 15 km = 35 km
F2 = 30.25 N 50° N of E
15 km, east – d2 D = √202 + 152 = 25 km
F3 = 67 N 70° N of W
R- total distance = ? displacement = ? Θ = tan-1 15/20 = 36.9°
F4 = 25 N due southeast
E- dt = d1 + d2
4. Two groups of students are pulling a rope against each other. The first group pulls the
D2 = d12 + d22 A- dt = 35 km
rope eastward exerting 36 N of force. The second group pulls the rope westward with
tan θ = opposite side/adjacent side D = 25 km, 36.9° east of south
a force of 48 N. Who will win the pulling rope game?
Science – systematized body of knowledge (“Scientia” – knowledge) STEP 1. Locate the decimal point
STEP 2. Move the decimal point so as to follow the format M x10n
Branches of Science: STEP 3. Count the number of times you move the decimal point (AND THAT WILL BE THE
• Mathematics and Logic – analysis of numerical data and reasoning EXPONENT) RULEs: If you move the decimal point to the LEFT, the exponent will be POSITIVE.
• Natural Science – study of nature and universe If you move the decimal point to the RIGHT, the exponent will be NEGATIVE.
a. Physical Science – physical entities
b. Biological Science – study of living tings EXPRESSING NUMBERS FROM SCIENTIFIC NOTATION TO STANDARD FORMAT
• Social Science – concerned with society and human interactions STEP 1. Locate the decimal point
STEP 2. Move the decimal point depending on the given exponent.
Physics - study of matter and energy and their interaction to each other and in space and time (EXPONENT = the number of times you will move the decimal point)
RULEs: If the exponent is POSITIVE, move the decimal point to the RIGHT.
Branches of Physics If the exponent is NEGATIVE, move the decimal point to the LEFT.
• Classical Physics – study of motion and energy
a. Mechanics – motion and forces ADDITION AND SUBTRACTION
• Statics – bodies at rest Only numbers in Scientific Notation that have identical exponent (n) may be added or subtracted
• Dynamics – bodies in motion EX: 7.9 x 102 - 6.4 x 10-1 = 7.8936 x 102
• Fluid Mechanics – motion of liquids and gases MULTIPLICATION
b. Thermodynamics – temperature and heat energy To get the M of the product, multiply the two M of both factors then add the exponent (n) of
c. Acoustics - sounds both factors.
d. Electrodynamics – electricity and magnetism EX: (5.1 x 105) (3.0 x 103) = 1.53 x 109
e. Optics – light DIVISION
• Physical optics – nature of light To get the M of the quotient, divide the M of both factors (M of the dividend by the M of the
• Geometrical Optics – behavior of light as it travels trough different divisor) then subtract the exponent (n) of both factors.
objects EX: (2.02 x 103) % (3.20 x 10-2) = 6.3125 x 104
• Modern Physics – basic structure of material world
Systems of Measurement
a. Quantum Physics – individual units of energy
English System – old system of measurement (e.g. inch, yard, mile, pint, ounce, pound, ton)
b. Atomic Physics - atoms
Metric System/SI units – units for scientific measurement (e.g. meter, liter, gram)
c. Molecular Physics - molecules
d. Nuclear Physics – atomic nucleus
SI Base Units
e. High energy Physics/Particle Physics – sub-atomic particles
PHYSICAL QUANTITY SI Base Unit SYMBOL
f. Solid State Physics/Condensed-matter Physics – solid materials
Length meter m
g. Plasma Physics – plasma Mass kilogram kg
Time second s
Scientific method - systematic approach to solve a problem Electric current ampere A
1. Observation 4. Prediction Temperature kelvin K
2. Organizing data 5. Experimentation Luminous intensity candela cd
3. Formulating hypothesis 6. Conclusion Amount of substance mole mol
OPRHEAC (Observation, Problem, Research, Hypothesis, Experiment, Analyze, Conclude)
Hypothesis –tentative explanation; no experimental proof Derived SI Units
Model – scientific assumptions; accurate under limited situations PHYSICAL QUANTITY SI Derived Unit SYMBOL
Theory – supported by several experimental evidences; flexible to be modified Area square meter m2
Law – theories that stand for a very long time and experimentally proven/ universal Volume cubic meter m3
Density kilogram per cubic meter Kg/m3
Scientific notation Speed meter per second m/s
Scientific notation - process of expressing very large or very small numbers in exponential form Force Kilogram meter per second Kg m/s2
square
A number expressed in scientific notation follows the format: a x 10 b
where: a = coefficient (a number between 1.0 to 9.99)
b = exponent (can be a positive or negative whole number) Exact numbers - e.g. 5 students, 3 teachers, 6 classrooms
Example: 2,358,000 = 2.358 x 106 Inexact numbers – e.g. 16.4 cm, 2.0 kg or rice
, Significant Figures
Significant figures refers to the number of digits in a quantity that is known to be certain. Express the following in scientific notation Express the following in standard form:
RULES FOR COUNTING SIGNIFICANT FIGURES form: 1. 2.437 X 103
1. Non-zero integers are always counted as significant figures. Ex: 4567 has 4 SF 1. 345,679,000 2. 2.245 X 102
2. Zeros are classified into three types: 2. 2000 3. 5 X 10-2
a. Leading zeros, those that precede all the non zero digits, are not significant figures. 3. 0.004 567 190 4. 4.5 X 10-1
Ex: 0.000035 has 2 SF only 4. 0.000 007 100 5. 6.34104 X 107
b. Captive zeros, those between non zero digits are always significant figures. Ex: 1005 has 4 SF 5. 234, 105 6. 5 X 102
c. Trailing zeros, those at the right end of the number are sometimes significant figures. They 6. 500 7. 3 X 101
are considered significant only if the number contains a decimal point. Ex: 1.567800 has 7 SF 7. 30 8. 3.424 X 10-3
300 can be expressed as: 3.00 x 10 2 (3 SF) 3.0 x 10 2 (2 SF) 3 X 10 2 (1 SF) 8. 0.000 034 590 9. 2.245 X 10-5
9. 0.451 10. 8.304 X 10-4
Multiplication/Division 10. 0.345 450
Always round off the final answer following the term with the LEAST number of SIGNIFICANT
FIGURES. Solve the given problems involving numbers Determine how many significant figures are
Ex: 1.62 x 5.6 = 9.072= 9.1 expressed in scientific notation. Show your in each of these numbers.
complete solution. 1. 6.2 in
Addition/Subtraction 1. (2.3 x 104) (4.2 x 103) 2. 5.083 ft
Always round off the final answer following the term with the largest rightmost significant 2. (1.03 x 106) + (6.3 x 104) 3. 315.0 m
digit. 3. (8.4 x 105) - (9.9 x 103) 4. 0.00400 mi
Ex: 419.35 + 2.7543 – 27. 0 = 395.1043 = 395.1 4. (8.03 x 109) ÷ (4.2 x 106) 5. 56.0 g
11,000 + 25 = 11,025 = 11,000 5. (7.3 x 109) (2.0 x 103) Express the following in accordance to the
6. (4.5 x 10-4) (7.2 x 10-2) indicated significant figures
Conversion of Units 7. (1.03 x 106) + (6.3 x 104) 1. 32.426 (4SF)
CONVERSION OF UNIT refers to the process of CHANGING the UNIT of a given MEASUREMENT 8. (6.24 x 106) - (6.9 x 103) 2. 77.015 (3SF)
to another unit (DESIRED unit) 9. (8.13 x 109) ÷ (2.4 x 10-6) 3. 0.08965 (3SF)
CONVERSION FACTOR refers to a ratio of two (2) measurements with different units. It can be 10. (8.3 x 109) (2.0 x 103) 4. 0.08975 (2SF)
written in fraction form. 5. 1.153 x 103 (3SF)
FACTOR-LABEL METHOD (Dimensional Analysis) refers to the process of converting units
wherein the given measurement is multiplied to a CONVERSION FACTOR to get the desired
measurement with a different unit Express the answers in correct number of Convert the following units of
LENGTH MASS VOLUME TIME significant figures measurement:
1km = 1000m 1kg = 1000g 1 L = 1000 mL 1 h = 60 min 1. 1.043 + 7.4 + 64.23 1. 25 km to cm
1m = 100cm 1g = 1000mg 1 L = 1.06 qt (quart) 1 min = 60 s 2. 73.45 – 4 + 16.8 2. 1500 m to km
1dm = 10cm 1oz = 28.35g 1 mL = 1 cm3 1 h = 3600 s 3. 621.6 + 140 + 315 3. 4km to dm
1in = 2.54cm 1lb = 454g 1 m3 = 1000 L 4. 37.3 x 3.54 4. 3850 g to kg
1ft = 0.30m 1kg = 2.21 lb 5. 0.18 ÷ 4.65 5. 450 lb to kg
1m = 3.28ft 6. 475.04 ÷ 2.0 6. A wrestler’s official weigh-in is
1mi = 1.61km 7. 6.0250 ÷ 3.22 220.5 kg. If the allowable range of
Example: 15 kg to oz
1ft = 12in 8. (23. 40) (1.9) weight for his fight is 400 – 500 lb,
15 kg x (1000g/1 kg) x (1 oz/28.35 g) = 529.10 oz (5SF)
1yd = 3ft 9. (780) (120) is he allowable to brawl/fight?
10. 125.350 ÷ 25.1 7. If a 78 years old man spent 13
Accuracy and Precision years of his life watching TV, how
Precision is the closeness of a set of repeatedly measured values. much hours did he consume in
Accuracy is linked to how close a single measurement is to the true value. front of the TV?
, Scalar and Vector Force - a push or a pull
Scalar Quantity - magnitude An object was pushed by exerting the listed forces below. What is the total force acting on
Symbol Name Example the object?
d distance 15 m F1 = 300 N due east F2 = 300 N due south F3 = 300 N 35° N of E
s speed 60 m/s F4 = 300 N 70° S of E F5 = 300 N due 120°
t time 60 s G- F1 = 300 N due east; F2 = 300 N due south S- F1x=300 F1y = 0
E energy 200 J F3 = 300 N 35° N of E ;F4 = 300 N 70° S of E F2x=0 F2y = -300
Vector Quantity – magnitude + direction F5 = 300 N due 120° F3x=300 cos 35 F3y = 300 sin 35
Symbol Name Example R- Ft = ? F4x=300 cos 70 F4y = -300 sin70
D displacement 15 m, N 30◦E E- x = r cos θ y = r sin θ F5x=300 cos120 F5y =3 00 sin120
v Velocity 60 m/s, East R =√ ∑x2 + ∑y2
F Force 45 N, 120◦ θ = tan -1 ∑y /∑x R =√ 498.352 + -150.032 = 520.44 N
θ = tan -1 150.03 /498.35 = 16.75°
a acceleration 5.0 m/s2, up
A vector is represented by an arrow
A- 520.44 N, south of east
Arrowhead – indicates the direction of the vector
Length of the arrow – represents the magnitude of the vector
Tail – represents the origin of the vector Vector Resolution - process of finding the component of a resultant vector
Vector component can be positive or negative
Resultant vector - the sum of 2 or more vectors Formula in getting the x and y components: x = r cos θ y = r sin θ
A heavy table is being pushed by a group of students towards 50° north of east with a force of
Addition of collinear vectors c. 30 m, east + 10 m, west =
a. 3 m, east + 4 m, east = d. 75 m, south + 100 m, north = 50 N. How much force is exerted horizontally and vertically to the table?
b. 6 m, north + 6 m, north = e. 30 m, north + 40 m, south = G- 50 N, 50° north of east – F S- x = 50 cos 50 y = 50 sin 50
R- Fx = ? Fy = ?
Addition of non-collinear vectors E- x = r cos θ y = r sin θ A- Fx = 32.1 N Fy = 38.30 N
• Analytical Method
1. Pythagorean Theorem (Addition of 2 vectors) Practice Exercises:
– Formula in getting the resultant magnitude: c2= +a2 b2 1. A plane flying with a velocity of 100 m/s due north is blown by a 500 m/s strong wind due
– Formula in getting the resultant direction: θ = tan-1 opposite side/adjacent east. What is the plane’s resultant velocity?
side 2. An object was pushed by exerting the listed forces below. What is the total force acting on
the object?
2. Component Method (Addition of 2 or more vectors) F1 = 12 N due north
– Formula in getting the x and y components: x = r cos θ y = r sin θ F2 = 10.2 N 30° S of E
– Formula in getting the resultant magnitude: R =√ ∑x2 + ∑y2 F3 = 8.5 N 70° N of E
– Formula in getting the resultant direction: θ = tan -1 ∑y /∑x F4 = 5.5 N due west
– Possible directions: N of E; S of E; N of W; S of W 3. A cabinet is being pulled 25° north of east through a ladder with a force of 20 N. How
much force is exerted horizontally and vertically to the cabinet?
• Graphical Method Seatwork
1. Parallelogram Method (Addition of 2 vectors) 1. A boat sailing with a velocity of 5 m/s due south is blown by a 25 m/s strong wind due
2. Polygon Method (Addition of 2 or more vectors) east. What is the boat’s resultant velocity?
2. A bag is being lifted and dragged 55° north of east through the floor with a force of 18
Distance – actual path taken by the object on its motion N. How much force is exerted to lift and drag the bag?
Displacement – distance of the object from the origin to the 3. An object was pushed by exerting the listed forces below. What is the total force
acting on the object?
The ship sails 20 km south, then 15 km east. What is the ship’s total distance & displacement?
F1 = 50 N due south
G- 20 km, south – d1 S- dt = 20 km + 15 km = 35 km
F2 = 30.25 N 50° N of E
15 km, east – d2 D = √202 + 152 = 25 km
F3 = 67 N 70° N of W
R- total distance = ? displacement = ? Θ = tan-1 15/20 = 36.9°
F4 = 25 N due southeast
E- dt = d1 + d2
4. Two groups of students are pulling a rope against each other. The first group pulls the
D2 = d12 + d22 A- dt = 35 km
rope eastward exerting 36 N of force. The second group pulls the rope westward with
tan θ = opposite side/adjacent side D = 25 km, 36.9° east of south
a force of 48 N. Who will win the pulling rope game?
