Physics › Mechanics › Newton's laws and the resultant force
Newton's laws and the resultant force
One theme runs through all three laws. Forces change motion, they never sustain it, and only the resultant counts. Add the free-body diagram habit and the third law's real meaning, and the rest of the topic follows.
Pick your board and the few notes written for the other boards quietly fold away, here and in the practice players. Nothing is deleted: every folded piece reopens on a tap.
Builds on Scalars and vectors.
The maths behind it: Forces and Newton's laws on InkMaths.
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.
COMMON MISCONCEPTION
Weight and the normal force are an action-reaction 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. Treating that as a special case of the second law misses its job, which is to define what a force does. Forces change motion. They do not sustain it, and nothing whatever 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 set at this level 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 opens with the same move. Isolate one object and draw every force acting on it, each arrow starting from the object, each labelled by type. Miss a single force and the resultant swings to a different size and a different direction. Hence the diagram first, before any algebra, and hence the marks that sit on the diagram alone.
With the diagram drawn, resolve along and perpendicular to the motion, sum each direction, then feed the resultant into ΣF = ma. A resultant of zero returns you straight to the first law, meaning constant velocity, and standing still counts as constant velocity.
WORKED EXAMPLE
A person in an accelerating lift
A 70 kg person stands in a lift accelerating upward at 2.0 m s−2. Find the force the floor exerts on them.
Free-body diagram first. Two forces act on the person, weight mg down and the normal contact force N up. Nothing else.
Newton's second law, taking up as positive, gives N − mg = ma, so N = m(g + a) = 70 × (9.81 + 2.0) = 830 N.
Check the limiting cases. At a = 0 the floor pushes with exactly the weight, 687 N. Accelerating upward it has to push harder, and that extra is the heaviness you feel as a lift sets off.
GUIDED PRACTICE
The force between the blocks
A 30 N force pushes a 4.0 kg block, which in turn pushes a 2.0 kg block ahead of it on a frictionless surface. Find the acceleration, then the force between the blocks. Sketch the free-body diagrams first.
Show the working
Treat both blocks as one body first, giving a = 30/(4.0 + 2.0) = 5.0 m s−2.
Now isolate the front block on its own. The contact force is the only horizontal force acting on it, so F = 2.0 × 5.0 = 10 N. Where you draw the free-body boundary determines which forces appear in your equation, and that choice is the key skill.
INDEPENDENT PRACTICE
Car and trailer
A 1200 kg car tows a 400 kg trailer with a driving force of 3200 N; ignore resistance. Find the acceleration and the tension in the tow bar.
Show the working
Whole system first, so a = 3200/1600 = 2.0 m s−2.
Then the trailer alone, where the tow bar supplies the only horizontal force, so T = 400 × 2.0 = 800 N.
As a check, the car alone obeys 3200 − 800 = 1200 × 2.0. The same tension appears in both bodies' diagrams, pointing opposite ways: an action-reaction pair acting through the bar.
The third-law trap
Here is the error this topic is famous for. A student pairs the weight of a book with the normal contact force from the table beneath it. Those two are not an action-reaction pair. They act on the same object, the book, and they are different types of force, one gravitational and one contact. Their equality here is an accident of the book not accelerating. Put the book in an accelerating lift and the two stop matching, whereas a genuine third-law pair never does.
The real pairs run like this. 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 single time.
ASSESSMENT FOCUS
- 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 gives 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 are gravitational and contact respectively. The Earth pulls the book down and the book pulls the Earth up. The table pushes the book up and the book pushes the table down.
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.
WORKBOOK
Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.
Or read them with their mark schemes on the newton's laws and the resultant force questions page.
WHERE TO GO NEXT
- Trigonometry and resolving vectors is the maths this lesson leans on, worked through from GCSE.
CHECK YOUR PROGRESS
Rate how confident you feel with each objective for this lesson. Ratings are saved in this browser, on this device, unless you sign in.
- 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.
Open the full revision checklist to track your progress across the whole unit.