Welcome to Forces and Newton’s Laws!
In our previous chapters, we looked at how things move (Kinematics). Now, we are going to explore why they move. Whether it’s a car accelerating on a motorway or a book sitting still on a desk, it’s all down to Forces. Don’t worry if this seems a bit abstract at first—we’ll break it down into simple "pushes and pulls" that you see every day!
1. What is a Force?
At its simplest, a force is a push or a pull acting on an object. It is a vector quantity, which means it has two vital parts:
1. Magnitude: How strong the push or pull is (measured in Newtons, N).
2. Direction: Which way the force is pointing.
Because forces are vectors, we represent them using arrows in force diagrams. The longer the arrow, the bigger the force!
Key Terms to Remember:
Mass: The amount of "stuff" in an object, measured in kilograms (kg). It doesn't change wherever you are in the universe.
Weight: The force of gravity pulling on that mass. It is measured in Newtons (N).
Resultant Force: The single overall force that has the same effect as all the individual forces acting on an object combined.
Quick Review: If you push a box with 10N to the right and a friend pushes it with 10N to the left, the resultant force is 0N. The forces are balanced.
Key Takeaway: Forces cause objects to change their velocity (speed up, slow down, or change direction). No resultant force means no change in velocity.
2. Newton’s First Law: The Law of "Lazy" Objects
Newton’s First Law states that an object will stay at rest or keep moving at a constant velocity unless a resultant external force acts on it.
Think of it as objects being "lazy"—they want to keep doing exactly what they are already doing. This property is called inertia.
Equilibrium
When the resultant force on an object is zero, we say the object is in equilibrium. This happens in two cases:
1. The object is perfectly still.
2. The object is moving at a steady speed in a straight line.
Example: A book on a table. Gravity pulls it down, and the table pushes it up with an equal force. Because the forces are collinear (in a line) and opposite, they cancel out.
Key Takeaway: If you see the words "constant velocity" or "stationary" in a physics problem, immediately think: Resultant Force = 0!
3. Weight and Gravity
Everything with mass is pulled toward the Earth by gravity. We model this as a force called Weight (W) acting vertically downwards.
The formula is: \(W = mg\)
In your exams, we usually use \(g = 9.8 \, \text{m s}^{-2}\) (the acceleration due to gravity).
Common Mistake to Avoid: Never confuse mass and weight! Mass is in kg; Weight is a force in Newtons. If a person has a mass of 70 kg, their weight is \(70 \times 9.8 = 686 \, \text{N}\).
Did you know? Your mass would be the same on the Moon, but your weight would be much less because the Moon's gravity (\(g\)) is weaker!
4. Newton’s Second Law: \(F = ma\)
If there is a resultant force, the object must accelerate. Newton’s Second Law gives us the most famous equation in mechanics:
\(F = ma\)
Where:
\(F\) = Resultant Force (N)
\(m\) = Mass (kg)
\(a\) = Acceleration (\(\text{m s}^{-2}\))
Working with Vectors
Sometimes, forces are given as 2D vectors using i, j notation or column vectors. Don't let the brackets scare you! The law works exactly the same way.
Example: A body of mass 2 kg has an acceleration of \(\mathbf{a} = (4\mathbf{i} - 3\mathbf{j}) \, \text{m s}^{-2}\).
To find the force in vector form:
\(\mathbf{F} = m\mathbf{a}\)
\(\mathbf{F} = 2 \times (4\mathbf{i} - 3\mathbf{j}) = (8\mathbf{i} - 6\mathbf{j}) \, \text{N}\)
In column vector notation, this would look like:
\(\mathbf{F} = 2 \times \begin{pmatrix} 4 \\ -3 \end{pmatrix} = \begin{pmatrix} 8 \\ -6 \end{pmatrix}\)
Key Takeaway: The direction of the acceleration is always the same as the direction of the resultant force.
5. Newton’s Third Law: Action and Reaction
Newton’s Third Law says: "Every action has an equal and opposite reaction."
This means if Object A pushes Object B, Object B pushes Object A back with the exact same amount of force in the opposite direction.
The Normal Reaction Force (R)
When an object rests on a surface, the surface pushes back. This is called the Normal Reaction Force (often labeled R or N). "Normal" here is a mathematical term meaning "perpendicular" (at 90 degrees).
Example: If you are standing on the floor, your weight acts down. The floor pushes up on your feet with a force \(R\). If you aren't falling through the floor or flying into the air, then \(R = W\).
Important Tip: If contact is lost (e.g., a ball leaves the ground), the reaction force \(R\) becomes zero.
6. Connected Particles and Pulleys
Sometimes objects are joined together, like a car pulling a trailer or two weights on a pulley string. To solve these, we follow these steps:
Step 1: Treat them as one. If the objects move together, you can often treat them as a single mass to find the acceleration.
Step 2: Use Tension (T). Tension is the force in the string or tow-bar. It pulls inwards from both ends.
Step 3: Draw separate diagrams. Look at each object individually and apply \(F = ma\).
Smooth Pulleys: In the OCR syllabus, pulleys are often "smooth." This is a fancy way of saying there is no friction and the tension \(T\) is the same on both sides of the string.
Key Takeaway: For connected particles, the acceleration \(a\) is usually the same for both objects!
7. Frictional Forces
Friction is a force that opposes motion. It acts along the surface where two objects touch and always tries to slow things down.
If a surface is described as "smooth," we assume friction is zero. If it is "rough," friction is present.
Analogy: Sliding on ice (smooth/low friction) vs. sliding on carpet (rough/high friction).
Quick Summary Review:
- First Law: No force = Constant velocity (Equilibrium).
- Second Law: Resultant Force = Mass \(\times\) Acceleration (\(F = ma\)).
- Third Law: Forces come in equal and opposite pairs.
- Weight: Always acts down (\(W = mg\)).
- Reaction: Always acts perpendicular to the surface (\(R\)).