Lesson 3: Newton's Laws of Motion

Weeks 3–4 — Understanding force and motion

🎯 Learning Objectives

🎯 Intuition First: What Makes Things Move?

Think about this: Why does a ball eventually stop rolling across the floor? Your intuition might say "because it runs out of force." But that's not quite right!

Newton realized that things don't stop because they run out of force — they stop because friction pushes back. Remove friction, and the ball would roll forever. This is the heart of Newton's First Law.

📋 Newton's Three Laws

First Law: The Law of Inertia

Newton's First Law: An object at rest stays at rest, and an object in motion stays in motion with constant velocity, unless acted on by a net external force.

Key term: Inertia — the tendency of objects to resist changes in motion. More mass = more inertia.

💡 Real-World Example:

When a car suddenly brakes, you lurch forward. Why? Your body wants to keep moving at the same speed (inertia). The seatbelt provides the force to change your motion.

Second Law: The Big One

Newton's Second Law: Fnet = ma

This is the single most important equation in mechanics. It tells us:

Third Law: Action-Reaction

Newton's Third Law: For every action force, there is an equal and opposite reaction force.

Key insight: The action and reaction forces act on different objects. When you push a wall, the wall pushes back on you.

💡 Think About It:

If the forces are equal and opposite, why don't they cancel out? They act on different objects! You push the wall (force on wall), wall pushes you (force on you). Each force affects its own object's motion.

📐 Free-Body Diagrams (FBD)

A free-body diagram isolates one object and shows all forces acting on it as arrows pointing away from it.

Common Forces:

ForceSymbolDirectionFormula
WeightW or FgDownward (toward Earth's center)Fg = mg
Normal ForceN or FnPerpendicular to surfaceDepends on situation
TensionT or FtAlong the rope/chainDepends on situation
Frictionfk or fsOpposite to motionfk = μkN, fs ≤ μsN
Air ResistanceFairOpposite to velocityDepends on speed

Rules for Drawing FBDs:

  1. Draw the object as a dot or simple box
  2. Draw only forces acting ON the object (not forces the object exerts)
  3. Draw arrows pointing away from the object in the direction the force acts
  4. Label each force clearly
  5. Choose a coordinate system (usually align one axis with acceleration)

🔧 Friction

Static friction (no slipping): fs ≤ μsN
Kinetic friction (sliding): fk = μkN

where N is the normal force and μ is the coefficient of friction (dimensionless, depends on the materials).

📝 Key Points:
  • Static friction is a range of forces (0 to μsN). It adjusts to match the applied force up to the maximum.
  • Kinetic friction is usually constant once the object is sliding.
  • Typically μs > μk (it's harder to start moving than to keep moving).

📝 Worked Example: Pushing a Box

A 10-kg box sits on a horizontal floor with μk = 0.3. You push horizontally with 50 N. What is the box's acceleration?

📝 Step-by-Step Solution:

Step 1 — Draw the FBD:

  • Weight downward: W = mg = 10 × 9.8 = 98 N
  • Normal force upward: N = 98 N (balances weight, no vertical acceleration)
  • Applied force forward: Fa = 50 N
  • Friction backward: fk = μkN = 0.3 × 98 = 29.4 N

Step 2 — Net force in x-direction:

Fnet = Fa − fk = 50 − 29.4 = 20.6 N

Step 3 — Apply Newton's Second Law:

a = Fnet/m = 20.6/10 = 2.06 m/s²

✅ The box accelerates at 2.06 m/s² forward.

📝 Worked Example: Box on a Ramp

A 5-kg block rests on a ramp inclined at 30°. The coefficient of static friction is μs = 0.4. Will the block slide?

Step 1 — Break weight into components:

Fg,parallel = mg sin(30°) = 5 × 9.8 × 0.5 = 24.5 N (down the ramp)
Fg,perpendicular = mg cos(30°) = 5 × 9.8 × 0.866 = 42.4 N

Step 2 — Normal force:

N = Fg,perpendicular = 42.4 N

Step 3 — Maximum static friction:

fs,max = μsN = 0.4 × 42.4 = 17.0 N

Step 4 — Compare:

Force down ramp (24.5 N) > fs,max (17.0 N) → 📉 The block WILL slide!

✏️ Practice Problems

Problem 1: A 1000-kg car accelerates at 2 m/s². What net force does it require?

Problem 2: A 2-kg book sits on a table. What is the normal force on it?

Problem 3: A 10-kg box is pulled across a floor with μk = 0.2 by a 40-N horizontal force. What is its acceleration?

✅ Check Your Understanding

Q1: You push a wall with 30 N. How hard does the wall push back?

Click to reveal answer

30 N. Newton's Third Law: the forces are equal and opposite. The wall pushes back with exactly the same force.

Q2: An elevator is moving upward at constant velocity. Is the tension in the cable greater than, less than, or equal to the weight of the elevator?

Click to reveal answer

Equal. Constant velocity means zero acceleration, so Fnet = 0. Therefore T = mg.

Q3 (mini-problem): A 15-kg box is pushed with 80 N on a surface with μk = 0.15. What is its acceleration?

Click to reveal answer

Normal force: N = mg = 15 × 9.8 = 147 N

Friction: fk = 0.15 × 147 = 22.05 N

Net force: Fnet = 80 − 22.05 = 57.95 N

Acceleration: a = 57.95/15 = 3.86 m/s²