Mechanics: Force and Newton’s Laws

Key Concepts to Revise from Grade 11:

Vectors:

• Definition: A vector has both magnitude (size) and direction. Represented as R or $\vec{R}$
  
• Graphical Representation: Add vectors using:
  • Head-to-tail method: Place the tail of one vector at the head of the other.
  • Resultant Vector: The vector from the start of the first to the end of the last vector.
• Vector Resolution:
• Break vectors into horizontal ($R_x$) and vertical ($R_y$) components:
• $R_x=R\cos \theta$
• $R_y=R\sin \theta$

Trigonometry Refresher:

• Pythagoras’ Theorem: $R=\sqrt{(R_x^2+R_y^2)}$
• Angle $\theta$: $\tan \theta =\frac{R_y}{R_x}$

Definitions to Memorize:

1. Force: A push or pull resulting from the interaction between two objects.
2. Gravitational Force ($F_g$): The attraction between objects due to mass.
3. Normal Force ($F_N$): Perpendicular force exerted by a surface on an object in contact with it.
4. Resultant Force ($F_R$): The vector sum of all forces acting on an object.

Newton’s Laws of Motion:

First Law (Law of Inertia):
An object remains at rest or in uniform motion unless acted upon by a net external force.
Key Point: Objects resist changes in motion.

Second Law:

FR=m⋅a
a is proportional to the net force (FR) and inversely proportional to the object’s mass (mm).

Third Law:

For every action, there is an equal and opposite reaction.
Example: When you push against a wall, the wall pushes back with equal force.

Law of Universal Gravitation

$F=G\cdot \frac{m_1{m}_2}{r^2}$, where:$G$: Gravitational constant.
$m_1,m_2$: Masses of the objects.
$r$: Distance between the centers of the objects.

Types of Forces:

Contact Forces:

• Frictional Force ($F_f$)
• Tension (T)
• Applied Force
• Normal Force ($F_N$)

Non-Contact Forces:

• Gravitational Force ($F_g$)
• Electrostatic Force
• Magnetic Force

Force Diagrams:

Free Body Diagram (FBD):

Represents forces acting on a single object.

Arrows indicate force magnitude and direction.

Tips for Drawing:
Always label forces clearly (e.g., $F_g$, $F_N$).

Include angles and components for vectors if necessary.

Exam Tips:

Understand Concepts:
Focus on definitions and laws. Ensure you understand rather than memorize.

Practice Force Diagrams:
Draw clear, labeled diagrams for each problem.

Work Through Examples:
Practice resolving vectors and calculating resultant forces.

Memorize Key Formulas:

Keep $F = m \cdot a$, $w = m \cdot g$, and $R_x = R \cos \theta$ handy.

Use Mnemonics: 

First Law: "Inertia keeps things still or moving."
Second Law: "Force, mass, acceleration – FMA!"
Third Law: "Action and reaction."

Memory Aids:

• Vector Directions: "Tail-to-head for adding, head-to-head for subtracting."
• Force Types: "Gravitational pulls, normal pushes, friction slows, tension stretches."
• Newton’s Laws Order: "Rest, Resultant, Reaction – 1st, 2nd, 3rd!"

Common Mistakes to Avoid:

• Forgetting that weight ($w$) is $m \cdot g$, not mass ($m$).
• Confusing normal force with gravitational force.
• Not breaking vectors into components when solving problems.
• Overcomplicating free-body diagrams – keep them simple and clear.

Let's Practice!

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