Comprehensive Study Notes: Force and Motion (Gaya dan Gerak)

LEARNING OBJECTIVES FOR FORCE AND MOTION

• 1. Explain the definition of force and its influence on objects through simple demonstrations.

• 2. Apply various types of forces in daily life.

• 3. Measure forces that are collinear and in the same direction, as well as collinear and in opposite directions.

• 4. Calculate the resultant of collinear forces and apply it to daily life with critical thinking.

• 5. Compare the weight and mass of objects and their measurement methods.

• 6. Explain the definition/concept of motion in daily life events.

• 7. Compare types of motion according to their kind, nature, and path.

• 8. Differentiate between speed ($v$) and velocity ($v$) in motion and their application in daily life.

• 9. Explain Newton's Laws and the application of motion in daily life.

10. Create an experimental report on force, motion, and Newton's laws in groups.

DEFINITION AND INFLUENCE OF FORCE (GAYA)

• Definition: A force is a push or a pull that can cause changes to an object.

• Effects of Force on Objects:

• Motion from Rest: Causes a stationary object to move or change location.

• Rest from Motion: Causes a moving object to stop.

• Directional Change: Changes the direction of a moving object.

• Shape Change: Changes the physical form of an object (e.g., clay/tanah liat being molded).

• Speed Adjustment: Accelerates or decelerates the movement of an object.

TYPES OF FORCES

Forces are categorized based on their source and application in daily life:

• Gaya Pegas (Spring Force): Generated by elastic materials like springs.

• Gaya Listrik (Electric Force): Generated by electrical charges.

• Gaya Gravitasi (Gravitational Force): The pull towards the center of a celestial body (e.g., Earth pulling objects).

• Gaya Magnetik (Magnetic Force): The attraction or repulsion caused by magnets.

• Gaya Gesek (Frictional Force): Occurs when two surfaces rub against each other.

• Gaya Otot (Muscle Force): Generated by human or animal muscle activity.

VECTOR REPRESENTATION AND RESULTANT OF FORCES

• Vector Characteristics: Force is a vector quantity, meaning it has both magnitude and direction. In a tug-of-war (tarik tambang), the direction of the rope follows the greatest sum of forces.

• Drawing a Vector Diagram:

• $O$: Point of origin (titik tangkap).

• $A$: Tip of the vector (ujung vektor).

• Direction: Indicated from $O$ to $A$.

• Length of $OA$: Represents the magnitude of the force ($F$).

• Scale Rules: The length must be proportional to the magnitude. For example, if $1\,cm = 5\,N$, then a $10\,N$ force is represented by a $2\,cm$ line.

• Negative Vectors: $-F_1$ is a vector with the same magnitude as $F_1$ but in the exactly opposite direction.

• Sign Convention: Typically, forces directed to the right or upwards are positive ($+$), while forces to the left or downwards are negative ($-$).

CALCULATING RESULTANT FORCES ($R$)

• Collinear and Same Direction: The resultant is the sum of all forces.

• Formula: $R = F_1 + F_2$

• Collinear and Opposite Direction: The resultant is the difference between the forces.

• Formula: $R = F_1 - F_2$

• Example Comparison:

• If $F_1 = 400\,N$ (Right) and $F_2 = 300\,N$ (Left), then $R = 400 - 300 = 100\,N$ to the right.

• If $F_1 = 2\,N$ (Right) and $F_2 = 3\,N$ (Right), then $R = 5\,N$ to the right.

MASS, WEIGHT, AND GRAVITY

• Mass ($m$):

• Definition: The amount of matter contained in an object.

• Property: Constant everywhere.

• Measurement: Measured using an Ohaus balance (neraca Ohaus).

• Unit: Kilograms ($kg$).

• Weight ($w$):

• Definition: The force of gravity acting on an object towards the core of Earth.

• Property: Varies depending on gravitational strength (decreases as distance from Earth's core increases).

• Measurement: Measured using a spring balance (neraca pegas/dinamometer).

• Unit: Newtons ($N$).

• Mathematical Relationship:

• Formula: $w = m \times g$

• Where:

• $w$ = Weight ($N$)

• $m$ = Mass ($kg$)

• $g$ = Acceleration due to gravity ($m/s^2$ or $N/kg$).

• Standard Values (at $g = 10\,N/kg$):

• $100\,g = 0.1\,kg \rightarrow 1\,N$

• $500\,g = 0.5\,kg \rightarrow 5\,N$

• Example Problem: A mass of $50\,kg$.

• On Earth ($g = 9.8\,m/s^2$): $w = 50 \times 9.8 = 490\,N$.

• On the Moon ($g = 1.6\,N/kg$): $w = 50 \times 1.6 = 80\,N$.

UNDERSTANDING MOTION (GERAK)

• Definition: An object is said to move if there is a change in position or state relative to a reference point (titik acuan).

• Key Elements of Motion:

• Reference Point: The starting location used to judge movement.

• Path (Lintasan): The points an object passes through during movement.

• Distance (Jarak): The total length of the path traveled. (Scalar).

• Displacement (Perpindahan): The straight-line length from the initial point to the final position. (Vector).

• Velocity (Kecepatan): Displacement per unit of time.

• Speed (Kelajuan): Distance per unit of time.

• Acceleration (Percepatan): Change in velocity per unit of time.

TYPES OF MOTION

• By Path:

• Linear Motion (Gerak Lurus): Path is a straight line.

• Parabolic Motion (Gerak Parabola): Path is a parabola.

• Circular Motion (Gerak Melingkar): Path is a circle.

• By State:

• Real Motion (Gerak Nyata): Movement relative to a reference point due to actual displacement.

• Pseudo Motion (Gerak Semu): An object appears to move while actually stationary (e.g., trees appearing to move past a car window).

SPEED AND VELOCITY CALCULATIONS

• Formula for Speed/Velocity:

• $v = \frac{s}{t}$

• Where:

• $v$ = Speed or Magnitude of Velocity ($m/s$)

• $s$ = Distance or Displacement ($m$)

• $t$ = Time ($s$)

• Displacement Formula ($\Delta x$):

• $\Delta x = X_t - X_0$

• 2D Displacement (Pythagorean Theorem):

• If movement involves vertical and horizontal components (e.g., South then East):

• $AC = \sqrt{AB^2 + BC^2}$

LINEAR MOTION (GERAK LURUS)

• Uniform Linear Motion (GLB):

• Path is a straight line.

• Speed is constant ($v$ is fixed).

• The graph of distance ($s$) vs. time ($t$) is a rising linear line.

• The graph of velocity ($v$) vs. time ($t$) is a flat horizontal line.

• Uniformly Accelerated Linear Motion (GLBB):

• Path is a straight line with constant acceleration ($a$).

• Velocity changes at a fixed rate.

• GLBB Formulas:

• 1. Final Velocity: $v_t = v_0 + (a \times t)$

• 2. Distance: $s = (v_0 \times t) + (\frac{1}{2} \times a \times t^2)$

• 3. Velocity-Distance (No Time): $v_t^2 = v_0^2 + (2 \times a \times s)$

• 4. Acceleration: $a = \frac{v_t - v_0}{t}$

• Types of GLBB:

• Accelerated (Dipercepat): Speed increases (e.g., coconut falling from a tree).

• Decelerated (Diperlambat): Speed decreases (e.g., ball thrown vertically upwards).

NEWTON'S LAWS OF MOTION

• Newton's First Law (Law of Inertia/Kelembaman):

• "If the resultant force on an object is zero, an object at rest stays at rest, and an object in motion stays in motion at a constant velocity."

• Mathematical form: $\sum F = 0$

• Examples: Passengers jerking forward when a car stops suddenly; a glass staying on a table when the paper underneath is pulled quickly.

• Newton's Second Law:

• "The acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass."

• Mathematical form: $F = m \times a$

• Examples: A loaded truck accelerates more slowly than an empty truck using the same engine force; pushing a full cart requires more force than an empty one.

• Newton's Third Law (Action-Reaction):

• "For every action force, there is an equal and opposite reaction force."

• Mathematical form: $F_{aksi} = -F_{reaksi}$

• Examples: A rocket pushing gas downwards moves upwards; a ball bouncing off a wall; friction between a foot and the ground while walking.

QUESTIONS & DISCUSSION (PRACTICE EXERCISES)

• Practice 1: Vector Drawing: Draw a vector for $F_1 = 4\,N$ ($2\,cm$ length). Then draw $F = 10\,N$, $-10\,N$, $-12\,N$, and $-15\,N$.

• Practice 2: Gravity: If a ball weights $245\,N$ on Earth ($g = 9.8\,m/s^2$), find its weight on Jupiter ($g = 24\,m/s^2$).

• Practice 3: Motion: Ahmad walks $400\,m$ West, then turns and walks $300\,m$ East. Jarak (Distance) = $700\,m$; Perpindahan (Displacement) = $100\,m$ West.

• Practice 4: GLBB Analysis: Identify GLBB types.

• (1) Ball rolling on a field (Decelerated).

• (2) Ball thrown vertically up (Decelerated).

• (3) Coconut falling (Accelerated).

• (4) Vehicle overtaking (Accelerated).

• Practice 5: Calculations:

• A car accelerates from $54\,km/jam$ to $90\,km/jam$ in $10\,s$. Find acceleration ($a$).

• Converting $54\,km/jam = 15\,m/s$ and $90\,km/jam = 25\,m/s$.

• $a = \frac{25 - 15}{10} = 1\,m/s^2$.

• A marble starts from rest, reaching $7.5\,m/s$ in $5\,s$. Find $a = \frac{7.5 - 0}{5} = 1.5\,m/s^2$.