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Newton's laws and the resultant force
Three laws, one running theme: forces change motion rather than sustain it, and only the resultant counts. Add the free-body diagram habit and the third law's real meaning, and most of the marks in this topic follow.
Builds on Scalars and vectors.
IN THIS TOPIC
- State and apply all three laws of motion in appropriate situations.
- Use ΣF = ma for constant mass, starting from a labelled free-body diagram.
- Identify genuine third-law pairs, and explain why weight and the normal contact force are not one.
WHAT YOU PROBABLY THINK
Weight and the normal force are a third-law pair.
All three laws, properly
First law. An object stays at rest, or keeps moving at constant velocity, unless a resultant force acts on it. This is not a special case of the second law; it defines what a force does. Forces change motion. They do not sustain it, and nothing needs a force to keep moving.
Second law. The resultant force on an object equals the rate of change of its momentum, which for the constant-mass situations AQA sets becomes
with F meaning the resultant force, ΣF, and the acceleration always parallel to it.
Third law. If body A exerts a force on body B, then B exerts a force on A that is equal in magnitude, opposite in direction, of the same type, and, critically, acting on a different body.
The free-body diagram
Every force problem starts the same way: isolate one object and draw every force acting on it, each from the object, each labelled by type. Miss one force and the resultant swings to a different size and direction entirely, which is why the diagram comes first and why the diagram alone can score marks.
With the diagram drawn, resolve along and perpendicular to the motion, sum each direction, and feed the resultant into ΣF = ma. A resultant of zero returns the first law: constant velocity, which includes standing still.
The third-law trap
The most common error in the topic: pairing the weight of a book with the normal contact force from the table beneath it. They are not a third-law pair. They act on the same object, the book, and they are different types of force, gravitational and contact. They happen to be equal here only because the book is not accelerating; put the book in an accelerating lift and they stop matching, while genuine third-law pairs never stop matching.
The real pairs are these: the Earth pulls the book down, so the book pulls the Earth up; the table pushes the book up, so the book pushes the table down. Same type, equal size, opposite direction, two different bodies, every time.
THE EXAM BIT
- Write ΣF, not F. Examiners' reports return to “resultant” every series: quoting F = ma without identifying the resultant loses the method mark even beside a right answer.
- For third-law questions, name both bodies in both sentences: “the Earth pulls the book down; the book pulls the Earth up”. A pair described on one object is automatically wrong.
- Draw the free-body diagram before any algebra and label forces by type, weight, normal contact, friction, tension. Diagram marks are free and routinely dropped.
- Resolve along and perpendicular to the direction of motion; on a slope that means along the slope. The perpendicular direction usually hands you the normal force for free.
- “Constant velocity” anywhere in the question translates to resultant force zero. Use it before hunting for accelerations that do not exist.
CHECK YOURSELF
A book rests on a table. A student claims the book's weight and the table's normal contact force on it are a Newton's third law pair. Give two reasons the claim is wrong, and state the two genuine pairs.
Show a hint
Check the third law's small print: same type of force, different bodies.
Show the answer
Both forces act on the same body, the book, and they are different types, gravitational and contact. A third-law pair fails on either count alone; this fails on both.
The genuine pairs: the Earth pulls the book down and the book pulls the Earth up (gravitational); the table pushes the book up and the book pushes the table down (contact).
The equality of weight and normal force here is equilibrium, not the third law, and it breaks the moment the book accelerates vertically.
Forces change motion, never sustain it.
Third-law pairs live on different bodies.
No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.