Introduction: Why do things move?
Welcome to one of the most exciting parts of Physics! In the previous chapter on Vectors and Kinematics, we looked at how objects move (displacement, velocity, and acceleration). Now, we are going to look at why they move. This chapter focuses on Newton’s Laws of Motion and the concept of Momentum. These ideas allow us to predict everything from the path of a football to the landing of a spacecraft.
Don't worry if these laws feel a bit abstract at first. We will break them down into simple steps and use everyday examples to make them clear.
1. Understanding Momentum
In Physics, we describe "mass in motion" as momentum. Every moving object has it. The amount of momentum an object has depends on two things: how much stuff is moving (mass) and how fast it is moving (velocity).
The formula for momentum is:
\(p = m \times v\)
Where:
\(p\) = momentum (measured in \(kg \, m \, s^{-1}\))
\(m\) = mass (measured in \(kg\))
\(v\) = velocity (measured in \(m \, s^{-1}\))
Important Note: Momentum is a vector. This means the direction matters! If a ball moving to the right has a momentum of \(+10 \, kg \, m \, s^{-1}\), a ball moving to the left would have a momentum of \(-10 \, kg \, m \, s^{-1}\).
Quick Tip: Always check your units! If a mass is given in grams, convert it to kilograms (\(kg\)) before calculating.
2. Newton’s First Law: The Law of Inertia
Newton’s First Law tells us what happens when forces are balanced. It states that an object will remain at rest or continue to move at a constant velocity unless acted upon by a resultant force.
- If the resultant force is zero, the object's velocity won't change.
- If it’s standing still, it stays still.
- If it’s moving, it keeps moving at the same speed in a straight line.
Real-world example: Imagine a puck on an air-track (a practical you might see in class). Because the air-track reduces friction to almost zero, the puck keeps gliding at a steady speed. It doesn't need a force to keep it moving; it only needs a force to stop it or speed it up.
3. Newton’s Third Law: Interaction Pairs
You might have heard this as "every action has an equal and opposite reaction," but in Physics B, we need to be more precise. Newton’s Third Law describes how two objects interact.
When object A exerts a force on object B, object B exerts an equal and opposite force of the same type on object A.
How to spot a Newton’s Third Law pair:
1. The forces are the same size.
2. The forces act in opposite directions.
3. The forces are the same type (e.g., both are gravitational or both are contact forces).
4. The forces act on two different objects.
Common Mistake: A book resting on a table is NOT a Newton's Third Law pair. The weight of the book (pull of the Earth) and the contact force from the table are acting on the same object (the book). A real pair would be: The Earth pulls the book down (gravity), and the book pulls the Earth up (gravity)!
4. Conservation of Momentum
One of the most powerful rules in physics is that momentum is conserved. This is actually a direct consequence of Newton’s Third Law.
In any collision or interaction between objects, the total momentum before the event is equal to the total momentum after the event, provided no external forces (like friction) act on the system.
The Calculation Principle:
\(Total \, momentum \, before = Total \, momentum \, after\)
\((m_1 \times u_1) + (m_2 \times u_2) = (m_1 \times v_1) + (m_2 \times v_2)\)
Did you know? This principle is why a gun recoils backward when a bullet is fired forward. The forward momentum of the bullet must be balanced by the backward momentum of the gun so the total momentum stays zero (where it started).
5. Newton’s Second Law: Force and Change in Momentum
Newton’s Second Law explains what happens when there is a resultant force. It links force to the "rate of change of momentum."
The formula provided in your data sheet is:
\(F = \frac{\Delta(mv)}{\Delta t}\)
This means that Force is equal to the change in momentum divided by the time taken for that change.
The familiar \(F = ma\)
If the mass of the object stays the same (which is usually true for cars, balls, etc.), then the change in momentum is just \(m \times \Delta v\). Since acceleration (\(a\)) is the change in velocity divided by time (\(\frac{\Delta v}{\Delta t}\)), we get the most famous equation in physics:
\(F = m \times a\)
Key Takeaway: To get a large acceleration, you either need a very large force or a very small mass.
6. Practical Skills: Measuring Motion and Collisions
In your exams, you might be asked about how to measure these values in a lab. The syllabus highlights using trolleys or air-track gliders.
Common Equipment:
1. Light Gates and Data-loggers: These are the most accurate. As a trolley passes through the gate, it breaks a beam, allowing the computer to calculate velocity (\(v = \frac{length \, of \, card}{time \, beam \, is \, broken}\)).
2. Ticker Timers: An older method where a needle punches dots on paper tape 50 times a second. The distance between dots tells you the speed.
3. Video Analysis: Recording motion and using software to track displacement frame-by-frame.
Practical Tip: When studying collisions, always measure the mass of the trolleys using a balance first. To show conservation of momentum, calculate \(m \times v\) for both trolleys before they hit and compare it to the total \(m \times v\) after they hit.
7. Modelling Motion in Discrete Time Steps
Sometimes, motion is too complex to solve with one big equation. Instead, we can model it by looking at what happens in "small discrete time steps" (\(\Delta t\)).
If we know the resultant force acting on an object, we can predict its future position step-by-step:
1. Use \(F = ma\) to find the acceleration.
2. Use \(\Delta v = a \times \Delta t\) to find the change in velocity.
3. Add this to the old velocity to find the new velocity.
4. Use \(\Delta s = v \times \Delta t\) to find the change in displacement.
5. Add this to the old position to find the new position.
Note: At AS Level, you only need to model situations where the resultant force is zero (constant velocity) or constant (constant acceleration).
Chapter Summary Checklist
- Can you define momentum and state its units? \(p = mv\).
- Do you understand that Newton's First Law describes constant velocity when forces are balanced?
- Can you identify Newton's Third Law pairs (same type, different objects)?
- Can you apply the Conservation of Momentum to a one-dimensional collision?
- Do you know that Force is the rate of change of momentum (\(F = \frac{\Delta p}{\Delta t}\))?
- Can you describe a practical experiment using light gates to measure trolley momentum?
Next Chapter Cross-Reference: To see how forces do work and transfer energy, head over to the "Work, energy and power" notes!