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Forces and Newton's Laws

Subject: Physics
Topic: 2
Cambridge Code: 0625

Force Concepts​

Force - Push or pull that changes motion (vector)

Unit: Newton (N) = kg·m/s²

Types of Forces​

Contact forces:

  • Friction
  • Normal force
  • Tension
  • Air resistance

Non-contact forces:

  • Gravity
  • Electromagnetic
  • Magnetic

Mass and Weight​

Mass - Amount of material (scalar, property of object)

  • Unit: kg
  • Constant everywhere

Weight - Force due to gravity (vector) W=mgW = mg

  • Unit: Newtons (N)
  • Varies with location (g changes)
  • On Earth: g ≈ 10 m/s² or 9.8 m/s²

Newton's First Law​

If no net force, velocity remains constant

No net force→a⃗=0\text{No net force} → \vec{a} = 0

Consequences:

  • Objects continue moving in straight line at constant velocity
  • Objects at rest stay at rest
  • No net force needed to maintain constant velocity

Inertia - Resistance to acceleration

  • Greater mass = greater inertia
  • Seatbelts protect (prevent inertial motion)

Newton's Second Law​

Net force equals mass times acceleration

Fnet=maF_{\text{net}} = ma

Key insights:

  • Force and acceleration same direction
  • Doubling force doubles acceleration
  • Doubling mass halves acceleration

Applying F = ma​

Single force: a=Fma = \frac{F}{m}

Multiple forces: Find net force first Fnet=Fx2+Fy2F_{\text{net}} = \sqrt{F_x^2 + F_y^2} (vector sum)

Or in components: Fx=maxF_x = ma_x Fy=mayF_y = ma_y

Newton's Third Law​

If A exerts force on B, B exerts equal and opposite force on A

F⃗AB=−F⃗BA\vec{F}_{AB} = -\vec{F}_{BA}

Action-reaction pairs:

  • Always same type of force
  • Always on different objects
  • Can never cancel (on different objects)

Examples:

  • Book on table pushes down, table pushes book up
  • Person walks: foot pushes ground back, ground pushes person forward
  • Rocket expels gas down, gas expels rocket up

Equilibrium​

Equilibrium - No net force (a = 0)

∑F=0\sum F = 0

Conditions for Equilibrium​

Translational equilibrium: ∑Fx=0 and ∑Fy=0\sum F_x = 0 \text{ and } \sum F_y = 0

Rotational equilibrium: ∑moments=0\sum \text{moments} = 0

Equilibrium Scenarios​

Static equilibrium:

  • Object at rest
  • Velocity = 0
  • Acceleration = 0

Dynamic equilibrium:

  • Object moving at constant velocity
  • Velocity ≠ 0 but constant
  • Acceleration = 0

Friction​

Friction - Force opposing motion

Static Friction​

Exists when object is stationary fs≤μsNf_s ≤ μ_s N

Where:

  • μsμ_s = coefficient of static friction
  • N = normal force
  • Increases with applied force up to maximum

Kinetic Friction​

Exists when object sliding fk=μkNf_k = μ_k N

Where:

  • μkμ_k = coefficient of kinetic friction
  • Usually μk<μsμ_k < μ_s (easier to keep sliding than start sliding)

Properties​

Friction always:

  • Opposes motion (or potential motion)
  • Depends on normal force
  • Independent of contact area
  • Independent of sliding speed (approximately)

Connected Objects​

Pulley Systems​

Tension - Force transmitted through rope/cable

Key assumptions:

  • Light rope (negligible mass)
  • Inextensible (doesn't stretch)
  • Pulley frictionless

For connected objects:

  • Tension same throughout rope
  • Accelerations related by constraint

Atwood Machine​

Two masses connected by light string over pulley: a=(m1−m2)gm1+m2a = \frac{(m_1 - m_2)g}{m_1 + m_2}

Tension: T=2m1m2gm1+m2T = \frac{2m_1m_2g}{m_1 + m_2}

Inclined Planes​

Weight Components​

Weight mg acts vertically downward:

  • Parallel to plane: mgsin⁡θmg\sin θ (causes sliding)
  • Perpendicular to plane: mgcos⁡θmg\cos θ (normal force)

Motion on Incline (No Friction)​

a=gsin⁡θa = g\sin θ

Motion with Friction​

Normal force: N=mgcos⁡θN = mg\cos θ Friction: f=μN=μmgcos⁡θf = μN = μmg\cos θ

Net acceleration: a=g(sin⁡θ−μcos⁡θ)a = g(\sin θ - μ\cos θ)

(assuming sliding down)

Moments (Torque)​

Moment - Turning effect of force about pivot

M=FdM = Fd

Where:

  • F = force
  • d = perpendicular distance from pivot line
  • Unit: N·m

Principle of Moments​

For equilibrium (no rotation): ∑Mclockwise=∑Mcounterclockwise\sum M_{\text{clockwise}} = \sum M_{\text{counterclockwise}}

Center of Mass​

Point where all mass effectively concentrated

  • For uniform objects: geometric center
  • For irregular objects: balance point
  • Weight acts here

Key Points​

  1. Force = mass × acceleration (F = ma)
  2. Weight = mass × g
  3. Newton's 1st law: No force → no acceleration
  4. Newton's 2nd law: F = ma
  5. Newton's 3rd law: Equal and opposite forces
  6. Friction opposes motion
  7. Kinetic friction = μ_k × N
  8. Static friction ≤ μ_s × N
  9. Equilibrium: Net force = 0
  10. Moment = force × perpendicular distance

Practice Questions​

  1. Calculate forces and accelerations
  2. Draw free-body diagrams
  3. Apply Newton's laws
  4. Analyze equilibrium situations
  5. Calculate friction forces
  6. Solve connected object problems
  7. Analyze inclined planes
  8. Calculate moments
  9. Apply principle of moments
  10. Solve complex force scenarios

Revision Tips​

  • Draw clear free-body diagrams
  • Resolve forces into components
  • Remember action-reaction pairs
  • Apply F = ma correctly
  • Check signs carefully
  • Understand equilibrium conditions
  • Know friction relationships
  • Practice moment equilibrium
  • Visualize force directions