Newton's Laws

Lesson goal: build accurate physics fluency for newton's laws and use that fluency to support clear HSC-style scientific writing.

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• How do forces change the motion of objects?

From The Feynman Lectures on Physics, Vol I, Chapter 10:

Newton's laws are not explanations of why motion occurs. They are rules that connect force, mass, and acceleration so that motion can be calculated.

• State Newton's three laws in words and symbols.
• Apply $F_{net} = ma$ to solve motion problems.
• Identify action-reaction force pairs.
• Use free-body diagrams to justify equations.

Newton's First Law (Law of Inertia)

If the net force on an object is zero, it remains at rest or moves at constant velocity.

This law describes inertia-the tendency of objects to resist changes in their motion.

Key implications:

• An object at rest stays at rest unless a net force acts
• An object in motion continues at constant velocity unless a net force acts
• "Constant velocity" means constant speed AND direction

When a car brakes suddenly, passengers continue forward-they have inertia. Seatbelts provide the force needed to decelerate you with the car.

Interactive: First Law Demonstration

A puck on a frictionless surface maintains constant velocity:

Observation: Equal spacing between positions means constant velocity. Zero net force → zero acceleration.

Newton's Second Law

The acceleration of an object is proportional to the net force and inversely proportional to its mass.

$$\vec{F}_{net} = m\vec{a}$$

Or equivalently: $a = \frac{F_{net}}{m}$

This is the most-used equation in mechanics. It connects:

• Force (N) - the cause
• Mass (kg) - the resistance to acceleration
• Acceleration (m/s^2) - the effect

Interactive: Force, Mass, and Acceleration

See how doubling force or doubling mass affects acceleration:

Observation: Increasing spacing between positions indicates acceleration. The velocity arrows grow because $v = v_0 + at$.

Interactive: Free-Body Diagram with Net Force

A 12 kg crate with 30 N applied force:

With $F_{net} = 30$ N and $m = 12$ kg: $$a = \frac{F_{net}}{m} = \frac{30}{12} = 2.5 \text{ m/s}^2$$

Newton's Third Law

For every action force, there is an equal and opposite reaction force acting on a different object.

Key features of action-reaction pairs:

• Equal magnitude and opposite direction
• Act on different objects
• Same type of force (both gravitational, both contact, etc.)
• Exist simultaneously

Action-reaction pairs never cancel because they act on different objects. Forces only cancel when they act on the same object.

Interactive: Action-Reaction Pairs

When you push on a wall, the wall pushes back on you:

Important: These forces act on different objects-one on the wall, one on you.

Connecting the Laws

Law	Statement	Key Equation
First	No net force → no acceleration	$\vec{F}_{net} = 0 \Rightarrow \vec{a} = 0$
Second	Net force causes acceleration	$\vec{F}_{net} = m\vec{a}$
Third	Forces come in pairs	$\vec{F}{AB} = -\vec{F}{BA}$

Example 1: Acceleration from net force

A 12 kg crate is pushed with a net force of 30 N.

Solution:

1. Use Newton's Second Law: $F_{net} = ma$

2. Rearrange for acceleration: $a = \frac{F_{net}}{m} = \frac{30}{12} = 2.5$ m/s^2

3. Acceleration is in the direction of the net force

Example 2: Net force from acceleration

A 0.80 kg cart accelerates at 4.0 m/s^2.

Solution:

1. Use $F_{net} = ma$

2. $F_{net} = 0.80 \times 4.0 = 3.2$ N

3. Force acts in the direction of the acceleration

Example 3: Action-reaction pair (Skaters)

Two skaters push apart with equal force. Skater A has mass 50 kg, skater B has mass 70 kg. The push force is 140 N.

Solution:

1. Both experience 140 N force (Third Law)

2. Acceleration of A: $a_A = \frac{F}{m_A} = \frac{140}{50} = 2.8$ m/s^2

3. Acceleration of B: $a_B = \frac{F}{m_B} = \frac{140}{70} = 2.0$ m/s^2

Key insight: Same force, different masses → different accelerations. The lighter skater accelerates more.

Example 4: Connected carts

Two carts (6 kg and 4 kg) connected by a rope are pulled with 30 N on a frictionless surface.

Solution:

1. Total mass: $m_{total} = 6 + 4 = 10$ kg

2. System acceleration: $a = \frac{F}{m_{total}} = \frac{30}{10} = 3.0$ m/s^2

3. Tension in rope (analyse the 4 kg cart):

   • Only force on 4 kg cart is tension T
   • $T = m_2 \times a = 4 \times 3.0 = 12$ N

• Misconception: Action-reaction pairs cancel. Correction: They act on different objects and cannot cancel. Only forces on the same object can cancel.

• Misconception: A larger force always means a larger acceleration. Correction: Acceleration depends on both force AND mass: $a = F/m$

• Misconception: An object in motion must have a net force. Correction: An object can move at constant velocity with zero net force (First Law).

• Misconception: Heavier objects fall faster. Correction: In a vacuum, all objects have the same gravitational acceleration $g$. Mass cancels in $a = \frac{mg}{m} = g$.

• Misconception: The reaction to your weight is the normal force from the floor. Correction: The reaction to Earth pulling you down is you pulling Earth up. The normal force is a separate interaction.

Easy (2 marks)

A 5.0 kg object experiences a net force of 15 N. Calculate its acceleration.

• Use $a = F/m$ (1)
• Correct acceleration: $a = 15/5.0 = 3.0$ m/s^2 with units (1)

Answer: 3.0 m/s^2

Medium (4 marks)

A 20 kg box is pulled along a floor with 50 N while friction is 18 N. Find the acceleration.

• Net force calculation: $F_{net} = 50 - 18 = 32$ N (2)
• Acceleration calculation: $a = 32/20 = 1.6$ m/s^2 (2)

Answer: 1.6 m/s^2 in the direction of the pull

Hard (5 marks)

Two carts are connected by a light rope. The system of 6 kg and 4 kg carts is pulled with 30 N on a frictionless surface. Find the acceleration and the tension in the rope.

• Total mass and system approach: $m = 10$ kg (1)
• Acceleration: $a = 30/10 = 3.0$ m/s^2 (1)
• Isolate one cart for tension analysis (1)
• Tension calculation: $T = 4 \times 3.0 = 12$ N (1)
• Correct units throughout (1)

Solution:

Step 1: Treat system as one object

• Total mass = 6 + 4 = 10 kg
• $a = F/m = 30/10 = 3.0$ m/s^2

Step 2: Analyse the rear cart (4 kg)

• Only horizontal force is tension T
• $T = ma = 4 \times 3.0 = 12$ N

Answer: Acceleration = 3.0 m/s^2, Tension = 12 N

Test your understanding with these interactive questions:

• First Law: Zero net force means zero acceleration (inertia)
• Second Law: $\vec{F}_{net} = m\vec{a}$ connects force, mass, and acceleration
• Third Law: Forces come in equal and opposite pairs on different objects
• Connected systems can be analysed as a whole or as separate free bodies
• Action-reaction pairs never cancel (they act on different objects)

Check your understanding:

After studying this section, you should be able to:

• State all three laws in your own words
• Apply $F_{net} = ma$ to find force, mass, or acceleration
• Identify action-reaction pairs correctly
• Explain why action-reaction pairs don't cancel
• Analyse connected systems using Newton's Second Law

When answering questions from this lesson, separate:

• the physical quantity being discussed,
• the model or law being applied,
• the mathematical relationship, including units,
• the conclusion in words.

For explanation questions, write in the pattern: claim -> physics reason -> consequence. For calculation questions, state the formula, substitute with units, calculate, then interpret the answer.